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

Abstract

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.