Dynamics of an Arbitrary Order Model of Toxoplasmosis Ailment in Human and Cat Inhabitants

Abstract

In this article, a non-integer nonlinear mathematical model for toxoplasmosis disease in human and cat population is proposed and studied. The basic concepts of the model's dynamic are given. The study of qualitative dynamics is done by the basic threshold parameter (Formula presented.). Local and global stabilities are done and the system's disease free equilibrium point is an attractor when (Formula presented.). Besides of it, endemic equilibrium point is an attractor when (Formula presented.). The sensitivity analysis of (Formula presented.) shows which parameter has positive/negative impact on the model. Numerical simulation of the model for the parameters occurred in threshold parameter is also discussed. The techniques of Adams Bashforth Moulton will be considered to justify all the derived theoretical results which will help in understanding to study the effect of various parameters to both the transient and steady-state dynamics of the disease infection. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.