International Journal of Mathematical Analysis and Modelling

An eﬀective new one-step block integrator for the numerical solution of system of ﬁrst order diﬀerential equation arising from epidemiology models

2024-11-24T06:28:42+00:00

This paper proposes an eﬀective new one-step block integrator for the solution of system of ﬁrst order ordinary diﬀerential equation that arises from models in epidemiology in life science. Showing the performance of this method, SIR, SEIR and more compartmental models are solved numerically and thus comparing with the classical Runge-Kutta to reveal its accuracy. The numerical results obtained clearly shows that the proposed method is more eﬃcient and robust for obtaining the numerical solution of mathematical models in epidemiology.

Numerical solution approximation of nonlinear functional integral by Homotopy perturbation method

2024-09-24T10:01:45+00:00

A numerical method for solving nonlinear functional integral is presented. Numerical examples are presented to show the validity of the numerical algorithm developed using Homotopy Perturbation Method (HPM). This method is simple to implement and gives good approximation at first iteration.

Fractional order model of dynamical behavior and qualitative analysis of Anthrax with infected vector and saturation

2024-11-13T10:31:37+00:00

We present a fractional order model to capture the transmission dynamics of anthrax infection with a nonlinear force of infection and its long-term impacts. An analysis with the standard Caputo–Fabrizio approach established that the model is well posed, and for the investigation on the stability of the model, an anthrax-free equilibrium as connected to the basic reproduction number R0 < 1 and other important conditions that consolidate epidemiological feasibility of the model were established. Using a normalized forward sensitivity index, we conducted the sensitivity analysis of important variables, the contact rates, and the recruitment rate of the vectors to examine the effects of their variation on the dynamics of anthrax. These allow us to identify the most sensitive parameters that healthcare professionals need to pay attention to. The results from simulations also demonstrated that the presence of saturation instantly causes the system to approach an anthrax-free equilibrium (DFE), and our findings from the qualitative analysis compel us to recommend maximum hygiene practices for humans and domestic animals, early intervention, and the treatment of anthrax with a vaccine (as well as all other medical interventions) on the infected and periodic evaluation of these practices in households and the community at large to achieve a disease-free community.

The influence of aquatic mosquitoes on Lymphatic Filariasis transmission dynamics: mathematical model approach

2024-09-23T18:01:52+00:00

The disease burden of lymphatic filariasis (LF) is a concern worldwide as it is one of the leading
causes of permanent disability. In this study, a mathematical model of lymphatic filariasis is formulated with interest in the aquatic mosquito population (egg, larva and pupa) on the metamorphosis
of the mosquito life cycle. The existence of the disease-free and the endemic equilibrium states and
the basic reproduction number are established. In addition, the sensitivity indices indicate that the
biting rate of mosquitoes, the recruitment rate of the aquatic mosquito population, the probability
of transmitting infection during contact between humans and mosquitoes and the mortality rate
of mosquitoes are the sensitive parameters in the disease dynamics. Through numerical simulations, it is observed that the sensitive parameters have an effect in reducing the burden of lymphatic
filariasis in the population. Thus, public health education and the usage of larvicides should be
encouraged as these would cause a drastic reduction in the maturation rate of mosquitoes, especially
in communities where stagnant waters are endemic.

Detection and correction of heteroscedasticity and its effect on modelling of Nigerian economic data

2024-09-25T11:34:42+00:00

The study centred on detection and correction of heteroscedasticity and its effect on modelling of economic data. Data were collected from CBN Statistical bulletin on five economic variables namely; Gross Domestic Product (GDP), Inflation Rate, Exchange Rate (Exch_rate), Balance of Payment and Government Debt from 1987 - 2017. The data was analysed using the Ordinary Least Square method and variance stability techniques was used to correct heteroscedasticity using log transformation of the dependent variable while Breusch-Pagan, White and HarveyGodfrey tests were used to detect the presence of heteroscedasticity in the variables at 5% level of significance with the aid of E-views 9. The regression model fitted to the data set was GDP = 37242.63 - 256.7745 Inflr – 40.196 Exchr + 252.364 BoP + 3.147 GovD and it showed that only inflation rate and Government debt were discovered to be significant predictors (p < 0.05) while and heteroscedasticity was detected. Result showed that after log transforming the variables, heteroscedasticity was eliminated as shown by Breusch-Pagan, White and HarveyGodfrey test respectively. It is concluded therefore that transforming economic data helps correct and eliminate detected heteroscedasticity in modelled economic variables.

Effect of thermal radiation and chemical reaction on unsteady MHD plane – Poiseuille flow of fourth-grade fluid in horizontal parallel plates

2024-11-24T07:16:28+00:00

A fourth-grade fluid is an important subclass of differential type that is capable of describing shear thinning and shear thickening effects (examples are ketchup, blood, paint, cream, nail polish, etc.). This sort of model is used to explain the flow behaviour of non-Newtonian fluids which are considered vital and applicable in many industrial production processes such as in the drilling of oil and gas wells, polymer extrusion from dye, glass fibre, paper production and draining of plastics films, etc. There is a dearth of knowledge in this area, therefore, this study investigated the thermal radiation and chemical reaction effects on unsteady magnetohydrodynamics plane – poiseuille flow of fourth-grade fluid in horizontal parallel plates channel. The equations that governed the flow were the momentum equation; which is a coupled nonlinear differential equation, the energy equation and concentration equation. The partial differential equations were solved using He – Laplace method which is a combination of Homotopy perturbation method and Laplace transformation method. The findings of the study revealed that: (i) Velocity and temperature fields rise due to the increment of thermal radiation parameter. (ii) For upsurging data of chemical reaction, velocity and concentration fields diminish. (iii) Velocity profile goes up when third and fourth-grade parameters get to raise; Velocity and skin friction fields decline due to the increment of magnetic parameter. (iv) Increasing Prandtl number tend to diminish the velocity and temperature profiles. (v) Strong values of Schmidt number decrease the boundary layer of the Sherwood number field. The results of this work are applicable to industrial processes such polymer extrusion of dye, draining of plastic films etc.

Mathematical model for transmission dynamics of Malaria disease: impact of invasive alien plants

2024-09-25T11:01:29+00:00

A mathematical model to study the impact of invasive alien plants on the dynamics of malaria transmission and its analyses is studied in this work. The resulted model equations are divided into homogeneous and non-homogeneous equations. The homogeneous equations are solved to determine its disease free equilibrium (DFE) and their stabilities. A basic reproduction number was determined from the DFE. It was found that when R0 < 1, the disease will die out, when R0 = 1, the model undergoes a backward bifurcation, R0 = 0, the model undergoes forward bifurcation and whenever R0 > 1, the disease will persist in the population. At R0 > 1, the global analysis of the model was carried out and it was found to be globally and asymptotically
stable (GAS). A sensitivity analysis of the model parameters was also investigated to determine the parameters that are sensitive for malaria transmission. A travelling wave equations and solutions were also provided for possible understanding of the behaviour of mosquito’s mobility in human environment.

Mathematical model showing preventive measure as a key to reducing Coronavirus disease (COVID-19) spread

2024-11-24T06:49:07+00:00

A set of non-linear Mathematical equations of COVID-19 model, presented in a ﬂow diagram was proposed to study and ascertain the impact of preventive measures (self isolation and social distancing) to curtailing the spread of the disease. To this eﬀect, we computed the threshold quantity Reff (Eﬀective Reproduction Number), carried out the stability analysis on the equilibrium points obtained using Jacobian technique (Eigenvalue approach), Castilo-Chavez method and a suitable Lyapunov function. We discovered that the Disease Free equilibrium point failed the long term test whereas the Endemic Equilibrium was globally asymptotically stable, thus implying that the COVID-19 spread could be curtailed or curbed in the presence of preventive measures (self isolation and social distancing) as advocated.

A theoretical investigation of the impact of a 2-dose vaccination strategy on Monkeypox transmission dynamics at population level

2024-09-24T10:07:35+00:00

In order to qualitatively evaluate the influence of a two-dose monkeypox (MPV) vaccination strategy when decreased human-to-human infection is accounted for, a new deterministic model for
MPV is created and implemented. The backward bifurcation phenomena is demonstrated to occur in the model as a result of the parameter that describes how quickly susceptible individuals receive their first dose of the MPV vaccination. Additionally, a distinct cutoff point for the rate at which vulnerable individuals receive the first dose of the MPV vaccination was discovered An example
of the model demonstrated that, in the absence of the rate at which susceptible individuals receive the first dose of the MPV vaccine, the disease-free equilibrium was globally asymptotically stable. The endemic equilibrium point of the distinguished case was also shown to globally asymptotically stable.

An infection-age-structured modelling for Monkey-Pox disease dynamics incorporating control measures

2024-11-13T11:17:51+00:00

Monkey-pox is known as pathogens affecting livestock animals and humans and belongs to the orthopox virus. The pathogen causes lymph nodes to swell and increasing transmission risk associated with factors involving introduction of virus to the oral mucosa. In this paper, we developed an Age-Structured model for Monkey-pox disease in a population with vital dynamics, incorporating standard incidence rate and vaccination. We showed the existence and uniqueness of the solution of the model. We obtained the Disease-Free Equilibrium state and shown the effective reproduction number of the model. We proved the conditions for Local and Global Stability of the Disease-Free Equilibrium (DFE) State and we found that the disease free equilibrium state is locally asymptotically stable if 1 )0( G (RE < 1) and Globally Asymptotically Stable (GAS) in Ω if RE ≤ 1 while unstable if RE ≥ 1.

Approximate common solution of variational inequality and fixed point problems for family of nonexpansive semigroup

2024-09-24T09:52:59+00:00

In this paper, we prove a path convergence theorem and introduce a new iterative scheme for approximation of common element of fixed point sets of family of nonexpansive semigroup and the set of solutions of variational inequality problem for an α-inverse strongly accretive mapping in strictly convex q-uniformly smooth real Banach space. As an application, solution is given to the problem of finding a common element of fixed point sets of family of nonexpansive semigroup and the set of zeros of an α-inverse strongly accretive operator. The result obtained augment and generalize several existing results.

Options pricing using combination of Brownian motion with a random time component

2024-09-25T11:45:32+00:00

This paper provides an efficient option pricing technique for European call options. The technique is a process that combines Geometric Brownian motion with random time component. The additional parameter to the Geometric Brownian motion is the volatility of the time change. This additional parameter provides control over the skewness and kurtosis of the return distribution. Partial integro-differential equation (PIDE) for pricing options under the proposed process was derived. Its values were priced numerically and the pricing performance of the new model is compared on option data sourced from Bloomberg on 28th April, 2023 with the Geometric Brownian motion. The result revealed that the additional parameter was able to address the pricing biases of the Geometric Brownian motion. Recommendation was made that more work should be done in the advancement of quick and effective procedures for calculating PIDE’s having in view to calibrating stochastic processes to a surface of option prices.

Utility maximization and portfolio management with administrative fee and dividend

2024-09-23T17:47:58+00:00

The study of utility maximization cannot be over emphasized in the study of portfolio management
as it plays crucial role in the determination of investor’s strategy over any investment. In this
research work, we investigate some utility functions and their applications to portfolio optimization
and risk management. Also, a portfolio consisting of one risk free asset and a risky asset which
follows the geometric Brownian motion was considered. We took into consideration transaction
cost, dividend and tax on invested funds. By applying Ito’s lemma and maximum principle, we
obtained an optimization problem which comprise of a nonlinear PDE (Hamilton Jacobi Bellman
equation) and a control problem (optimal investment strategy). These problems are functions of the value function which is dependent on the utility of the investor at the expiration of such investment. Furthermore, the exponential and logarithm utility were used in solving for the optimal investment strategies and some numerical results also presented. It was observed for both cases that the optimal investment strategies (OIS) were directly proportional to appreciation rate, dividend and inversely proportional to the administrative charges, instantaneous volatility, tax and risk averse coefficient. Also, the OIS under logarithmic utility does not depend on the risk averse coefficient and tax while the optimal investment strategy under exponential utility does not depend on wealth.

On the nilpotents of the semigroup of partial contractions of a finite chain

2024-09-25T11:17:02+00:00

Let [n] = {1, 2, . . . , n} denote a finite chain. Consider the semigroups Pn and OIn, consisting of all partial, and all injective and order-preserving transformations on [n], respectively. Furthermore, let CPn = {α ∈ Pn : |xα − yα| ≤ |x − y| ∀ x, y ∈ Dom α} and OCIn = {α ∈ OIn : |xα − yα| ≤ |x − y| ∀ x, y ∈ Dom α}. It follows that CPn and OCIn are subsemigroups of Pn and OIn, respectively. In this paper, we characterize the nilpotent elements in CPn, compute the number of nilpotents of height (n − 1) in CPn, and determine the number of nilpotents in OCIn of a specific type

On the vector Lyapunov functions and eventual stability of nonlinear impulsive differential equations

2024-11-24T07:02:30+00:00

In this paper, the eventual stability of nonlinear impulsive differential equations with fixed moments of impulse is examined using the vector Lyapunov functions which is generalized by a class of piecewise continuous functions. The novelty in the use of the vector form of the Lypunov function lies in the fact that the "restrictions" encountered via the use of scalar Lyapunov function is safely handled especially for large scale dynamical systems, since it involves splitting the Lyapunov functions into components so that each of the components can easily describe the behaviour of the solution state Together with comparison results, sufficient conditions for eventual stability are presented. Results obtained are extensions and improvements on existing results.

Complex Ebola Virus Disease fractional order model in the Caputo sense with Laplace Adomian Decomposition Method model solution

2024-09-24T10:27:59+00:00

Ebola Virus Disease is a life-threatening disease that is transmitted between humans and animals. The aim of this study is to develop a fractional order Ebola Virus Disease model for the dynamics of Ebola considering the control measures;quarantine,isolation,treatment, vaccine and protection (condom use) with a view to study the effects of these control measures on the spread of Ebola in a given population of humans and animals in the Caputo Sense. The fractional order Ebola Virus Disease model in the Caputo sense to control the spread of the disease with eighteen compartments is considered in this paper.This model considered vaccination, condom use, quarantine, use of treatment drugs and isolation as control measures combined together. We analyzed the model where the validity of the model was proven by establishing a region of invariance and the positivity of solutions. We also established the model disease-free equilibrium (DFE)and endemic equilibrium (EE). The reproduction number (a threshold value) (B) was obtained using the next generation matrix. The result of the study produced an expression for B, where if the reproduction number B, is less than 1 then the model DFE point is stable, so the Ebola virus disease dies out. If the reproduction number B is greater than 1, then the model DFE point is unstable, so the Ebola Virus disease persists in the populations.We also analysed the local stability of the DFE point and found out it will be stable when the reproduction number B < 1. The novel application of the Laplace–Adomian decomposition method to the model obtained a result of the complex fractional model in an infinite series form which converges further to its exact value. Comparing the solutions of the fractional Ebola virus disease model with that of the classical case using simulation plots we found out that the case of fractional order has more degree of freedom in such a way that can be varied as the fraction (α) could be varied to get different results. We proved convergence of the Laplace Adomian Decomposition method using the Cauchy-Kovalevskaya theorem for differential
equations with analytic vector fields and then obtained a new result on the convergence rate of the Laplace Adomian Decomposition Method.