International Journal of Mathematical Analysis and Modelling

Numerical approach to optimal control problems governed by delay differential equations

2026-01-03T11:23:40+00:00

This research presents a comprehensive framework for solving optimal control problems (OCPs) governed by delay differential equations (DDEs) with mixed constraints. For this more complex case of DDE-constrained problems, where analytical solutions are generally unavailable, a numerical methodology is developed. The approach involves discretizing the cost functional and the
DDE constraints using Simpson’s rule and the Crank-Nicolson method, respectively. The resulting finite-dimensional, constrained optimization problem is then transformed into an unconstrained form using the Augmented Lagrangian Method (ALM). This formulation gives rise to an associated operator that facilitates the application of the Extended Conjugate Gradient Method (ECGM) to efficiently solve the problem. Numerical experiments demonstrate that the solutions obtained from the proposed ALM-ECGM scheme are in strong agreement with analytical solutions for ODE cases and outperform existing methods for DDE cases. A rigorous convergence analysis confirms the scheme’s effectiveness, accuracy, and linear convergence rate, establishing it as a robust computational tool for this challenging class of OCPs.

A mathematical model of human Metapneumovirus (HMPV) dynamics

2026-03-18T19:22:55+00:00

Human metapneumovirus is a viral infectious disease of health concern. In this paper, we developed a mathematical model on HMPV spread and showed that the modeled equation was mathematically well posed and epidemiologically meaningful. We adopted the dynamical system analysis technique in the model, particularly obtaining the threshold quantity R0, the basic reproduction number via the next generation matrix approach and also proved the existence of fixed points (steady states). The study on sensitivity analysis informed that the exposure rates of human population are the most significant in influencing new infections in the system. Lastly, we examined the short and long term dynamics of the disease within the basin of attractions using appropriate tools, and found out that there is possibility of wiping out HMPV from the populace with time
provided attention is paid to awareness, exposure, and improved dietary to boost immunity level.

Mathematical model for dynamics of Tuberculosis epidemiology with optimal control strategies

2026-01-03T09:57:33+00:00

Tuberculosis (TB) is caused by bacteria (Mycobacterium tuberculosis) and it most often affects the lungs. TB is spread through the air when people with lung TB cough, sneeze or spit. A person needs to inhale only a few germs to become infected. To curtail the disease a mathematical model strictly on the Susceptible - Vaccinated - Latent - Active - Chronic - Treatment-Recovery (SVLACTR) compartments for tuberculosis is formulated. We assume the recruitment factor to be Vertical. Already existing tuberculosis data was used in verifying the model to comprehend the transmission of TB dynamics as it will help in warding off, regulating, eliminating the disease, and enhance the well being of lives. We show that the Global Dynamics are completely figured out
by basic infection rate RT B0 , that if RT B0 < 1 the disease free equilibrium is locally and globally stable. But if RT B0 > 1, and endemic equilibrium exist and is uncertain. Sensitivity analysis was performed on the model parameters in RT B0 to determine the effect of each of the parameter value on the TB propagation. Four control strategies, vaccination, reduce contact rate, treatment and sensitization are introduced. By combining these strategies, we can effectively control the spread of TB, improve lives, and ultimately work towards eradicating the disease from the population. This study contributes to the existing literature by highlighting the importance of a multi-faceted approach to TB control and eradication. The model system was solved using the classical Runge-Kutta of order four, forward in 60 years and the algorithm were implemented using MATLAB and MAPLE.

Approximate solution to nonlinear system of equation: Pourreza transform variational iteration method

2026-01-03T15:07:00+00:00

Novel mathematical methods were established to investigate the numerical results of a coupled Burger’s equation (CBE) and a shallow water- coupled system of fractional order with Caputo, Caputo Fabrizio (CF), and Atangana Baleanu Caputo (ABC) derivatives under initial conditions. The method was obtained by coupling the Pourreza transform with the variational iteration method. The stability analysis of PVIMABC was conducted to show the effectiveness of the scheme, and the comparison of the numerical results of PVIMC , PVIMCF , and PVIMABC with existing methods was presented to show the validity and accuracy of this proposed numerical technique. The 3D graphical results were used to compare the exact and the approximate solution at the classical order of the illustrated examples, and 2D graphical results are obtained to show the numerical results of the illustrated examples at different fractional orders. Also, the tables obtained show the reliability and the convergence of the proposed method. For calculations, the Maple software package was utilized.

On a version of strong convergence theorems for the Jungck Picard-Multistep hybrid iterative scheme for a general class of functions

2026-01-03T11:07:09+00:00

This paper establishes a version of strong convergence results for the Jungck Picard-Multistep hybrid iterative scheme. The results improve, generalize and extend some of the known ones in literature especially those of Olatinwo and Imoru (2008), Berinde (2001), and Akewe and Olaluwa (2017).

A new epidemiological model for the transmission dynamics of Tuberculosis incorporating vaccination and impact of environmental intervention

2026-03-18T18:58:40+00:00

Tuberculosis (TB) remains one of the most lethal infectious diseases globally, with a disproportionate impact on low- and middle-income countries. Its continued transmission is fueled by airborne spread, delayed diagnosis, and inadequate access to treatment. In response, this study develops a comprehensive mathematical model to assess the combined effects of vaccination and environmental interventions on TB transmission dynamics. The model incorporates key control strategies including vaccination, treatment, isolation, improved ventilation, environmental disinfection, and public awareness campaigns. Using the next-generation operator method, the basic reproduction number (R0) is derived to determine the threshold conditions for disease eradication or persistence. A thorough analytical investigation is carried out to examine the stability of both the
disease-free and endemic equilibrium. Numerical simulations conducted in MATLAB confirm the theoretical findings, illustrating that TB can be eliminated when R0 < 1, but persists when R0 > 1. Sensitivity analysis identifies the most impactful parameters, showing that early diagnosis, timely treatment, and environmental improvements significantly reduce disease transmission. This study presents a new integrated modeling approach that incorporates both biomedical interventions and
environmental control strategies, offering a more holistic a more holistic and realistic framework for TB control. The proposed model incorporates several critical features including vaccination, treatment, environmental interventions, and re-infection dynamics that are often absent or under- represented in many existing models. By capturing the complex interactions between these factors, the model provides deeper insights into the mechanisms driving TB transmission and control. Furthermore, the study emphasizes the importance of incorporating localized epidemiological data and realtime surveillance systems to enhance model accuracy and relevance through data fitting. It is recommended that future research should focus on using region-specific parameters and realtime monitoring to guide the development of targeted, evidence-based public health policies aimed at
reducing TB burden more effectively.

Mathematical modeling and simulation of liquid chromatography for bi-Langmuir isothermal process

2026-01-03T08:58:20+00:00

A general rate model of liquid chromatography is used to simulate isothermal operating conditions considering the bi-Langmuir isotherm in a cylindrical column. Radial dispersion inside the column are ignored, hence making it a one-dimensional flow problem. The governing equation is composed of a system of partial differential equations together with the nonlinear expression
of isotherm and completed with the Danckwerts boundary conditions. A high resolution finite volume scheme of Koren is used to obtain approximate solutions of the governing equation. The scheme is second to third order accurate and easily implemented. Several case studies of single and multi-components are carried out to study the behaviors of key model parameters. The results
show that the suggested finite volume scheme avoids numerical oscillations and provides optimum predictions for the obtained solutions.

Spectral-block hybrid method for high-order numerical solution of Volterra integro-differential equations

2026-01-03T14:32:04+00:00

This paper focuses on the numerical solution of first-order Volterra integro-differential equations (VIDEs), which frequently arise in science and engineering to describe systems with memory and hereditary effects. Conventional numerical approaches often exhibit limited accuracy or increased computational cost when dealing with such problems. To address these challenges, a
Spectral-Block Hybrid Method (SHBM) is proposed for the high-order approximation of VIDEs. The method employs shifted Legendre polynomials as basis functions for the spectral representation of the approximate solution, while Simpson’s 3/8 quadrature rule is utilized to evaluate the integral term within each block efficiently. The proposed SHBM combines the global accuracy of spectral methods with the parallel efficiency of block formulations, enabling multiple solution points to be computed simultaneously. This integration enhances accuracy, stability, and computational efficiency. Numerical experiments show that the SHBM yields significantly smaller absolute errors and reduced CPU times compared with existing methods in literature. The results confirm that SHBM maintains strong convergence and numerical stability as the step-size decreases. Given its precision and efficiency, the SHBM is a promising tool for solving practical integro-differential problems encountered in fields such as population dynamics, viscoelastic material modeling, heat transfer, and biological systems with memory.

A mathematical approach on the dynamics of kidnapping with apprehended kidnappers

2026-01-03T10:50:47+00:00

Kidnapping has emerged as a critical security challenge in Nigeria and other parts of the world. This study formulates a compartmental mathematical model that divides the population into vulnerable individuals V (t), kidnappers Q(t), hostages H(t), and apprehended kidnappers A(t). We introduce a Crime Propagation Number (CPN ) to assess the risk of kidnapping. Analysis of the model shows that if CPN < 1 and λ > μ, the kidnapping-free equilibrium is locally and globally asymptotically stable. Numerical simulations indicate that increasing the apprehension and rescue rates reduces the incidence of kidnapping.

Mathematical modelling of norovirus transmission incorporating human and environmental factors with evaluation of screening and supportive treatment

2026-03-11T13:02:10+00:00

Norovirus is a highly contagious viral pathogen that causes acute gastroenteritis, resulting in vomiting and diarrhoea. It accounts for approximately 200,000 deaths each year, including 50,000 child fatalities globally, highlighting its substantial impact on public health. This study investigated the transmission dynamics of norovirus using a mathematical modelling approach. The basic re-
production number is computed and used to establish the stability of the disease-free equilibrium (DFE) and the endemic equilibrium (EE), such that the DFE is locally and globally asymptotically stable when R0 < 1, while the EE is locally and globally asymptotically stable whenever R0 > 1. With the aid of Partial Rank Correlation Coefficients (PRCCs) and Latin Hypercube Sampling
(LHS), a global sensitivity analysis identifies pathogen decay due to disinfection and proper sanitation (μa), recovery rate resulting from screening and supportive treatment (γ), shedding rate (π), and effective environment-to-human transmission rate (βEH ) as the most significant parameters influencing disease spread. Findings from numerical simulations show that, to control this disease in society, intensive screening, supportive treatment, hygiene practices, disinfection, and proper sanitation should be implemented.

Sensitivity analysis of Dengue transmission: Impact of integrated pathways and control interventions

2026-01-03T08:37:49+00:00

Dengue fever remains a significant global health challenge, driven by complex interactions between human and mosquito populations. This study develops and analyzes a compartmental mathematical model to investigate the transmission dynamics of dengue virus, incorporating human and mosquito populations. The model captures key disease progression stages, including susceptible, exposed, infectious, and recovered compartments for humans, and susceptible, exposed, and infectious compartments for mosquitoes. Numerical simulations reveal critical trends in the human and mosquito populations, highlighting peak infection periods and the interplay between host and vector dynamics. Sensitivity analysis using Partial Rank Correlation Coefficients (PRCC) identifies key parameters influencing the basic reproduction number, such as transmission probabilities, mosquito biting rates, and progression rates. The results emphasize the importance of integrated vector management, personal protective measures, and healthcare interventions to mitigate dengue outbreaks. These findings provide actionable insights for designing targeted public health strategies and inform future research to improve dengue control and prevention.

Human infertility due to undetected asymptomatic chlamydia infections: A mathematical modelling approach

2026-01-03T11:50:57+00:00

Chlamydia remains one of the commonest sexually transmitted infections (STIs) around the world, which has caused infertility and public health concern to many families and communities in both underdeveloped and developed countries. Chlamydia trachomatis has been observed to have negative health consequences in humans hence much research work is needed to avert the ugly trend of the disease in the population. In this work, a mathematical model for chlamydia, which splits the asymptomatic population into detected and undetected asymptomatic population is developed and analyzed. The reproduction number (Rc) was obtained using the next generation method. The model upon qualitative analysis exhibits the phenomenon of forward bifurcation near Rc = 1. The existence of forward bifurcation in the model shows that having the reproduction number less than one is enough pointer to guarantee the elimination of chlamydia in a community no matter the initial sizes of the infected subpopulation. Intuitively, this implies that the disease-free equilibrium of the model whenever Rc < 1 is globally asymptotically stable. Analytical and numerical results shows that the reproduction number (Rc) is a decreasing function of the treatment rate (τ1). Results from sensitivity analysis reveal that the chlamydia transmission rates and treatment rate are the prominent parameters that significantly drive the dynamics of chlamydia in the population. A close attention should be paid on these parameters in order to check the spread of the disease in the population. Numerical simulation results suggest that a low detection rate (10%) of the asymptomatic individuals (i.e., from undetected to detected state) is a potential threat to human
fertility, no matter the level of treatment given to the identified persons and thus not sufficient for Chlamydia elimination in about 40 years time. Further, it is also observed that a high detection rate (70%) of individuals infected with asymptomatic infection (from undetected to detected state) leads to the elimination of undetected asymptomatic individuals with the disease in the population in about 12 years time with the administration of sufficient treatment rate. Hence, identifying
more cases of undetected asymptomatic individuals immediately for treatment will help in reducing human infertility due to chlamydia infections in families and communities. In that light, preventive measures and optimized treatment was introduced into the basic model to formulate the optimal control model. The Pontrayagin′s maximum principle is utilized and the study shows that condom use and optimized treatment could be the best options for curbing the menace of chlamydia in the
family and community cycles.

Medicolegal model for time of death of a homicide victim using computational approach

2026-01-03T10:30:09+00:00

The study explores the medicolegal model for time of death of a homicide victim using computational approach. Matlab software using Runge-kutta ODE45 numerical scheme was used to simulate the results output which was analyzed as well. Three statements of problem were studied computationally and various time of death were predicted using step size h = 1, h = 0.1 and
h = 0.01. The decaying rate parameter which was used in the construction of the predictive model equations for the four three statements of problem were computed as well with the values of beta1, beta2, beta3 and beta4 being stated as 0.0028, 0.6931, 0.1335, and 0.2877 respectively. The study achieved the following results: construction of predictive model equation for various statements of homicide victims’ cases using secondary data, computation of the various decaying rate parameters, predictions of the time of dead using computational method.

Stochastic modeling of soil biogeochemical processes in drought-prone ecosystems

2026-01-03T15:41:16+00:00

This review shows how stochastic modeling of soil biogeochemical processes in drought-prone ecosystems could provide an essential framework for understanding how random fluctuations in environmental conditions, particularly precipitation and temperature shape microbial functioning, nutrient cycling, and overall ecosystem resilience. In water-limited regions, these stochastic variations influence microbial metabolic rates, suppress carbon use efficiency (CUE), alter enzyme-driven decomposition, and weaken nutrient turnover. Integrating stochastic differential equations (SDEs) with microbial biomass dynamics, the article offers deeper insight into how moisture variability produces nonlinear feedbacks, including reduced mineralization during prolonged drought. Analytical tools such as Monte Carlo simulations and Fokker-Planck equations help quantify the probability of soil organic matter persistence and reveal early warning indicators of ecosystem instability, such as
increased variance in CO2 fluxes preceding potential tipping points. These approaches demonstrate that stochastic forcing may either buffer or intensify nutrient losses depending on drought frequency and intensity, and underscore the critical role of microbial adaptation in sustaining ecosystem function under climatic stress, hence the call for more research in this field considering the recent climate extremes globally.

Improved Convergence Theorems for Monotone α-Nonexpansive Mappings in Uniformly Convex Banach Spaces

2025-10-26T16:56:25+00:00

This paper investigates convergence properties of monotone α-nonexpansive
mappings in uniformly convex Banach spaces and introduces new inertial and hybrid schemes that extend and unify classical Mann and Halpern iterations. We
first establish weak and strong convergence theorems for the Mann and Halpern
processes under natural control conditions on {βn} and {αn}. The strong convergence results are then extended beyond Opial’s condition to Banach spaces that
are uniformly smooth or possess Gateaux/Fr´echet differentiable norms, using the
continuity of the normalized duality mapping.
An accelerated inertial Halpern–Hybrid algorithm is proposed, incorporating
an explicit inertial term {µn} to enhance convergence speed. Strong convergence
and asymptotic regularity of the new scheme are rigorously proven. Furthermore,
several analytical counterexamples are constructed to demonstrate that the boundedness of {βn}, the non-summability of {αn}, and the decay of {µn} are essential
for stability. These results collectively provide a comprehensive framework for understanding and improving iterative fixed-point algorithms in smooth, convex, and
non-Hilbert settings.

On Bohr and Bohr-Rogosinski phenomena for subclasses of univalent functions

2026-01-03T11:32:22+00:00

In this paper, we establish sharp Bohr and Bohr–Rogosinski-type inequalities for several sub-classes of univalent functions in the unit disk, including starlike, convex, odd, and even functions, as well as Mocanu’s class of analytic functions. Using refined coefficient estimates and growth bounds, we determine exact Bohr and Rogosinski radii for each class, with sharpness verified through extremal examples such as the Koebe function and its variants. We also derive the Bohr radii for the convolution analogues of univalent and convex functions. Our results refine and extend existing inequalities, provide new radii for symmetric subclasses, and contribute to a deeper understanding of the Bohr phenomenon in geometric function theory.

Approximation of four step iteration scheme with errors on closed convex subsets of normed linear spaces

2026-03-18T20:05:09+00:00

This paper investigates the convergence of four-step iteration schemes with error terms defined on closed convex subsets of normed linear spaces. Sufficient conditions are established for convergence to a fixed point of certain classes of norm linear operators. The results extend and unify several known theorems in fixed point approximation theory such as Berinde [9], Agarwal [11], Bosede [3] and Wasfi [6].

On impact of experimental time of mangrove forest relative abundance in the absence of Artisinal hydrocarbon effect

2026-01-03T10:09:09+00:00

An impact study of experimental time of mangrove forest relative abundance in the absence of artisanal hydrocarbon effect has been investigated. The analytical solutions of tree growth mod- els were derived and used to predict the impact of experimental time of mangrove forest relative abundance through computational method using MATLAB ODE45. Three different mangrove
sites in the Niger delta and considered as natural mangrove forest vegetation sites in the absence of artisanal hydrocarbon. It is observed that on the based day of our experimental time called the initial condition, the relative abundance of the three sites was recorded as 0.01 units, same values each. Furthermore, from the tenth month up to the one hundred and twentieth month, the data base result shows a monotonic increasing pattern in the relative abundance of the three coordinates as 0.0246 units on the tenth month to a saturating value of 0.2427 units on the one hundred and twentieth months. These observations show a strong increase in the numerical strength of the relative abundance of the second coordinate followed by the first coordinate with a slow increase in numerical strength and a strong increase pattern in the third coordinate which converges earlier to its saturated value.

Application of Markov models in income tax revenue forecasting in Nigeria

2026-01-03T15:23:14+00:00

Accurate tax revenue forecasting is vital for effective fiscal policy and economic planning, especially in contexts marked by data scarcity and economic volatility. Traditional statistical and machine learning models often underperform when confronted with non-linear patterns and limited historical data. This research proposes a novel hybrid Grey-Markov model that synergizes the
trend-extraction strength of Grey System Theory (GM(1,1)) with the stochastic correction capability of Markov Chain Analysis. The Grey model forecasts long-term revenue trends using a minimal data requirement, while the Markov component dynamically adjusts predictions by modeling the probabilistic behavior of forecast errors. Through empirical validation using historical tax revenue data, the hybrid model will be benchmarked against conventional methods such as ARIMA, exponential smoothing, and neural networks. The anticipated outcome is a robust forecasting tool with improved accuracy and reliability, offering policymakers a more resilient framework for fiscal decision-making under uncertainty. This approach holds particular relevance for developing economies where data irregularities and economic shocks are prevalent.

Age-structured deterministic model for the dynamics of Hepatitis B Virus in Nigeria incorporating vertical and horizontal transmission

2026-01-03T11:15:45+00:00

This study introduces an age-structured deterministic model for the transmission dynamics of the Hepatitis B Virus (HBV) in Nigeria, accounting for both vertical (mother-to-child) and horizontal (person-to-person) transmission pathways. The population is categorized into children and adults to reflect differences in transmission and intervention effects. Analytical outcomes demon-
strate the non-negativity of solutions and the existence of an invariant region, confirming the model’s biological validity. The disease-free equilibrium (DFE) and the basic reproduction number (R0) were determined using the next generation matrix approach. The local and global stability of the DFE were assessed using the Jacobian and Castillo–Chavez and Song methods, respectively, while the global stability of the endemic equilibrium was verified through a Lyapunov function. An optimal control problem was developed to examine three intervention strategies: childhood vaccination (u1), adult catch-up vaccination (u2), and birth-dose vaccination (u3). Numerical simulations indicated that increasing childhood vaccination coverage results in an immediate reduction of acute infections among children and a delayed yet significant decline among adults through herd effects. Adult catch-up vaccination leads to a rapid decrease in acute infections and a gradual reduction in chronic cases, although some persistence occurs due to slow clearance and progression rates. Improved birth-dose vaccination demonstrated the most significant impact, preventing vertical transmission and moving the system toward near-elimination levels. Long-term simulations
suggested that HBV reaches an endemic equilibrium under current conditions but could move towards elimination with sustained vaccination efforts. The analysis indicates that age-specific interventions, particularly universal birth-dose and intensified childhood vaccination, represent effective and sustainable strategies for controlling and eventually eliminating HBV in high-endemic regions such as Nigeria

Mathematical analysis of Hepatitis B virus infection with logistic growth for proliferation of Hepatocytes cells

2026-03-18T19:09:36+00:00

A logistic growth model was developed which investigates the proliferation of hepatocytes cells for hepatitis B virus infection. The results from the model analysis show that the disease-free equilibrium (DFE) is globally asymptotically stable (GAS) when the basic reproduction number (R0) is equal to or below a unity value, and unstable when it is above the unity value. It also reveals that when R0 is above the unity value with some conditions an endemic equilibrium of the model is GAS, indicating a real proliferation of the hepatocytes cells within the boundary of the liver. Numerical simulations are also carried out using maple software to illustrate the effects of fulminant, acute and chronic infections on the number of HBV, healthy and infected (unhealthy) hepatocytes.

Numerical solution of fractional order COVID-19 model via the generalized fractional Adams-Bashforth-Moulton approach

2026-01-03T09:45:50+00:00

The objective of the paper is to conduct an inquiry of a few of the epidemiological characteristics of COVID-19 infection by invoking a fractional-order mathematical framework in measuring the impact of vaccination and treatment to the dynamics of the spread of COVID-19. It qualifies the conditions of existence and uniqueness of the solution of the model in the fractional repetition
and stabilities the endemic equilibrium by the use of the method of the Lyapunov function. The sequence of numerical simulations that used the fractional Adams-Bashforth Moulton approach elaborates on the role played by the chosen model parameters, and the fractional-orders values improving the control and dynamics of COVID-19. Additional mathematical simulations that utilize surface and contour plots indicate that the prevalence of COVID-19 would be higher in case of higher contact rates and lower efficiency of treatment. The study further establishes that an optimal strategy on vaccination and treatment would end up countering the high rate of COVID-19 among the population.

Computational analysis of flow of an incompressible magnetohydrodynamic third grade fluid in an inclined cylindrical pipe with temperature-dependent viscosity

2026-01-03T14:54:00+00:00

This present paper considers the MHD flow of third grade fluid in an inclined isothermal cylindrical pipe with temperature-dependent viscosity. The resulting governing momentum and energy equations of motion are highly nonlinear and are solved using perturbation technique. Vogel model viscosity is introduced to represent temperature-dependent viscosity. Results from the analysis show that increase in the third grade and the gravitational parameters increases the flow velocity while increase in the magnetic field reduces the flow velocity. It is observed that increase in third grade parameter increases the temperature at the wall of the cylindrical pipe. It is further observed that within the Vogel model viscosity, increase in the indices decreases the flow velocity. Results further show that increase in Vogel index increases the temperature at the walls of the cylinder.

Mathematical modeling of trauma dynamics: Exploring the impact of therapeutic interventions

2026-01-03T11:01:04+00:00

Trauma resulting from sustained external violence, such as that seen in protracted conflicts, poses a severe public health challenge. While mathematical models have been used to study social contagions, few have explicitly addressed scenarios where a community is persistently traumatized by a distinct, external group of perpetrators. This paper introduces a novel deterministic compartmental model that conceptualizes this dynamic as a predator-prey interaction. The model incorporates a multi-stage healing process augmented by a therapeutic intervention parameter (η). Qualitative analysis of the model demonstrates that a trauma-free equilibrium is impossible under conditions of constant external influx of perpetrators (Π). Instead, the system always converges to a unique, globally stable endemic equilibrium where trauma persists. Numerical simulations illustrate the model’s dynamics, showing that while therapeutic interventions (η > 0) dramatically reduce the endemic level of trauma. The results underscore that the most effective public health strategy is a dual approach: simultaneously implementing measures to reduce the external threat (e.g., targeting perpetrator influx and activity) and, of course, intensifying therapeutic interventions - Cognitive
Behavioral Therapy (CBT) and Eye Movement Desensitization and Reprocessing (EMDR) at a parameter value η = 0.25 and above.

Ulam-Hyers stability Analysis of Caputo fractional order derivative

2026-03-18T18:36:31+00:00

This study investigates the Ulam-Hyers stability of fractional derivatives for a given fractional-order system. As a theoretical foundation, fundamental definitions of various fractional derivatives are introduced. By applying the Gronwall inequality, sufficient conditions ensuring stability in the sense of Ulam-Hyers are rigorously established. The derived results constitute notable extensions
and refinements of existing findings in the literature.

Sensitivity analysis of Human Africa Trypanosomiasis with human host

2026-01-03T08:48:57+00:00

Human African Trypanosomiasis (sleeping sickness) remains a significant public health challenge in sub-Saharan Africa, transmitted through the bite of infected tsetse flies. To better understand its transmission dynamics, we develop a compartmental SEIR model that accounts for both human and tsetse fly populations, incorporating varying transmission rates between exposed and infectious individuals — a key feature often overlooked in prior studies. Using the next-generation matrix method, we derive the basic reproduction number (R0), a critical threshold for disease persistence. We establish the positivity, boundedness, and existence and uniqueness of solutions, ensuring the mathematical well-posedness of the model. A normalized forward sensitivity analysis identifies the most influential epidemiological parameters, providing insights for targeted intervention strategies. In particular, parameters related to tsetse fly - human transmission rates (β1, β2) and human treatment rate (βh) showed the highest sensitivity indices, indicating their strong influence on R0 and overall disease spread. We also analyze the disease-free and endemic equilibria, demonstrating that R0 governs the long-term behavior of the system. Numerical simulations validate our
analytical findings and illustrate how variations in transmission rates, vector control, and treatment efficacy shape disease dynamics. Our results underscore the importance of adaptive intervention strategies in mitigating Trypanosomiasis outbreaks and inform public health policies for sustainable disease control.

Heat and mass distribution by mixed convection in an unsteady power law fluid over an accelerated riga plate under the influence of heat generation/absorption and thermal radiation

2026-01-03T14:07:14+00:00

The significance of heat generation/absorption, thermal radiation, inclination angle and chemical reaction on the convective heat and mass transfer in a power law fluid over an accelerated Riga plate is examined. This study investigates the non-Newtonian power law index for the cases when (pseudo-plastic fluid), and (dilatant fluid). The Grinberg term incorporated into the momentum equation is utilized to express the Riga plate. By employing suitable transformation technique, related non-linear partial differential equations formulated are converted to ordinary differential equations. The resulting similarity equations are solved numerically by employing shooting method embedded in Matlab computational software. Graphs are utilized to illustrate the impact of fluid variables entering the velocity, temperature, and concentration profiles. Further, numerical outcomes of the combined effects of thermal radiation, chemical reaction and heat generation on the skin friction coefficients, heat transfer rate and mass transfer rate are tabulated and analysed. The results disclose contribution of sundry parameters on the fluid flow, mass and heat transfers.

Mathematical modelling of the endemic phase of Covid-19 infection considering vaccination breakthrough, revaccination and reinfection

2026-01-03T10:42:27+00:00

The transition of COVID-19 from a pandemic to an endemic phase requires a better understanding of its long-term dynamics, especially regarding vaccination breakthroughs, reinfection, and revaccination. This study develops and analyzes a deterministic mathematical model to quantify the endemic dynamics of COVID-19, using New York, USA, as a case study. The model takes into account vaccination, vaccine breakthrough infections, revaccination of previously immunized individuals, and reinfection. The well-posedness of the model is established by demonstrating the non-negativity of solutions and identifying an invariant region. The disease-free equilibrium (DFE) is derived, and its basic reproduction number (R0) is computed using the next-generation matrix. Local stability of the DFE is confirmed through the Jacobian matrix, while global stability of both the DFE and the endemic equilibrium is proven using suitably constructed Lyapunov functions. A sensitivity analysis of (R0) indicates that the contact rate among non-vaccinated individuals (βc) and the asymptomatic transmission modification factor (ηA) are the most significant parameters, with positive sensitivity indices of 0.987 and 0.518, respectively. In contrast, the recovery rate for symptomatic individuals (γ2) and the vaccination rate (θ) showed substantial negative effects. Numerical simulations, conducted in Python, quantified the endemic equilibrium, revealing stable patterns across population compartments and a notably lower force of infection among vaccinated individuals. Scenarios that examined varying contact rates (βc) demonstrated a direct, linear relationship with the force of infection. Additionally, a three-dimensional analysis of vaccine coverage and efficacy revealed a compensatory relationship, illustrating the herd immunity threshold. Importantly, the revaccination rate emerged as a critical control parameter, with increases from 0.1 to 0.3 day−1 correlating with a 40-60% reduction in peak infections and a 50-70% decrease in hospitalizations. The findings indicate that the endemic persistence of COVID-19 is highly sensitive to contact rates within the unvaccinated population and the infectiousness of asymptomatic cases. The results support the need for targeted interventions, such as ongoing vaccination and revaccination campaigns, rather than broad, uniform measures, to keep the epidemic below critical thresholds and effectively manage the burden on healthcare systems. This study provides a quantitative framework for public health policy in the endemic phase of COVID-19.

Modelling TikTok video category transitions using Markov chains

2026-03-11T12:13:24+00:00

In this paper, we develop a discrete-time Markov chain framework to model transitions between video content categories on TikTok based on observed sequential viewing behavior. Using a dataset of 65 consecutively viewed videos classified into six categories;motivational, dance, comedy, lifestyle, educational, and food, we estimate empirical transition probabilities and construct the associated transition matrix. We analyze the structural properties of the resulting Markov chain, establishing irreducibility, aperiodicity, and ergodicity, which guarantee the existence and uniqueness of a stationary distribution. The stationary distribution is computed explicitly and interpreted as the long-run exposure pattern across content categories under stable viewing dynamics. While the dataset is limited in size, the study is positioned as a methodological proof-of-concept demon-
strating how classical Markov chain theory can be applied to analyze category-level navigation on short-form video platforms. The proposed framework is transparent, reproducible, and readily extensible to larger datasets and more complex sequential models.

The Singly Implicit Runge-Kutta Methods for nonlinear singular initial value problems

2026-01-03T08:22:31+00:00

The use of collocation process for constructing numerical methods for solving ordinary differential equations has been attractive for nonlinear singular initial value problems. In this paper, a class of singly implicit Runge-Kutta methods has been developed which can efficiently solve non-linear singular initial value problems in ordinary differential equations. The methods are derived
based on collocation at the polynomial nodes which produce dense output within the integration interval. Preliminary numerical calculations using the new methods clearly show improved performance, efficiency and effectiveness compared to some methods with strong algebraic stability properties. In order to capture the system behavior for long period, graphic surface curves of phase
plots were generated, which show very strange and new behaviors. The obtained surface phase plots are portions of the phase space of the systems, often depicting real world observed facts.

A modified Dai-Liao-type conjugate gradient method for unconstrained optimization

2026-01-03T11:39:17+00:00

Conjugate gradient (CG) methods have proved over the years to be efficient for solving large-scale unconstrained optimization problems. In this paper, a Dai-Liao (DL)-type CG method is proposed using proper combination of the update parameters of LS-CG and AyO-CG methods. Under some certain assumptions, descent and convergence properties were established. Preliminary results illustrate that the new schemes can compete favorably well with some existing ones, when subjected to numerical test under Dolan and More performance profile tools.

Coronavirus disease: A mathematical approach to analyzing its transmission dynamics

2026-03-18T20:18:55+00:00

The novel Coronavirus Disease (also known as COVID-19) remains a persistent global health threat requiring continuous monitoring and protection of vulnerable populations. Current global surveillance highlights the persistence reoccurring of the disease in some parts of the world, hence the need for understanding its transmission dynamics. In this research, a mathematical model was developed to analyse the transmission dynamics of the disease amongst human population. The model shows the dynamical flow of the virus from person to person using a schematic diagram which was then translated into a system of ordinary differential equations comprising equations for susceptible individuals, exposed individuals, infectious individuals, individuals undergoing treatment and recovered individuals. The models validity and epidemiological significance was confirmed. Key metrics, including the epidemic indicator R0 are calculated using the next generation matrix approach and the equilibrium states were identified while the local and global stabilities of the disease free equilibrium were investigated using Jacobean matrix approach and Lyapunov function respectively. The global asymptotic stability of the endemic equilibrium was also investigated using Lyapunov function. With normalized forward sensitivity indices, sensitivity analysis was carried out to know the critical parameters influencing Covid-19 transmission. The discovery offers promising strategies in mitigating Covid-19 prevalence.

Numerical solutions of first order delay differential equations using second derivative block Adams Moulton Methods

2026-01-03T10:22:28+00:00

In this paper, we formulated and applied Second Derivative Block Adams Moulton Methods in solving first order delay differential equations without the introduction of interpolation formula in evaluating the delay argument. The delay argument was evaluated by applying an acceptable idea of sequences. The continuous forms of these of block methods were worked-out through the use
of linear multistep collocation procedure using matrix inversion approach. The resulting discrete schemes obtained from the various continuous expressions of the block methods were observed to be self-starting, consistent, zero-stable, convergent and satisfying region of P −and Q−stabilities. From the results obtained, the scheme for step number k = 4 performed better than the schemes for step numbers k = 3 and 2 in terms of accuracy when compared with their exact results.

Mathematical model on impact of velocities for stratified deep water under modified gravity and coriolis effect with simulation

2026-01-03T15:31:15+00:00

This study presents a mathematical model for simulating the dynamics of stratified deep water under the influence of modified gravity and the Coriolis effect. The model is developed to capture the complex interactions between density stratification, gravitational forces, and rotational effects in large-scale oceanic and geophysical fluid systems. The governing equations are derived from the principles of fluid dynamics, incorporating the effects of buoyancy, pressure gradients, and the Coriolis force, which arises due to the Earth’s rotation. A modified gravity term is introduced to account for variations in gravitational acceleration, which is essential for modeling phenomena such as oceanic circulation, geostrophic flows, and internal wave propagation in stratified fluids. The mathematical formulation includes the Navier-Stokes equations, the continuity equation, and
the equation of state for a stratified fluid. The Coriolis effect is incorporated through the Coriolis parameter, which depends on latitude and the Earth’s angular velocity. The modified gravity term is introduced as a perturbation to the standard gravitational acceleration, allowing for the simulation of non-uniform gravitational fields in different regions of the ocean. To analyze the behavior of the system, numerical simulations were performed. The simulations are validated against known solutions and experimental data to ensure the accuracy and reliability of the model. The results demonstrate the influence of modified gravity and the Coriolis effect on the velocity structure, density distribution, and overall flow patterns in stratified deep water. The model provides a valuable tool for understanding and predicting the behavior of geophysical fluids in various environmental
and climatic contexts.