Abstract
The present paper deals with a fractional-order mathematical epidemic model of malaria transmission accompanied by temporary immunity and relapse. The model is revised by using Caputo fractional operator for the index of memory. We also recommend the utilization of temporary immunity and the possibility of relapse. The theory of locally bounded and Lipschitz is employed to inspect the existence and uniqueness of the solution of the malaria model. It is shown that temporary immunity has a great effect on the dynamical transmission of host and vector populations. The stability analysis of these equilibrium points for fractional-order derivative α and basic reproduction number mathcal{R}_{0} is discussed. The model will exhibit a Hopf-type bifurcation. The two control variables are introduced in this model to decrease the number of populations. Mandatory conditions for the control problem are produced. Two types of numerical method via Laplace Adomian decomposition and Runge–Kutta of fourth order for simulating the proposed model with fractional-order derivative are presented. To validate the mathematical results, numerical simulations, sensitivity analysis, convergence analysis, and other important studies are given. The paper is finished with some conclusions and discussion.
Highlights
Malaria is a vector-borne disease that affects the developing countries of the world
Since bifurcation is a key rule in computational models of viral diseases and is studied by a lot of researchers prepared a structure model to show the effects of relapse rate in malaria disease [2,3,4, 15, 19, 26, 39, 40]
We address the locally asymptotically stable of the positive equilibrium point of the system (3.3)
Summary
Malaria is a vector-borne disease that affects the developing countries of the world. As per World Health Organization (WHO) reports that malaria is deadly to host life and remains a dangerous infectious epidemic disease [46]. This endemic disease is an economic load on the countries. Several researchers from epidemiological backgrounds have mathematically researched the propagation mechanisms of the disease to understand and capture the complex relationship between a susceptible host and populations of infected vectors. A periodic mathematical epidemic model has been considered by Ross-MacDonald [16]. They focus on the effects of spatial and temporal heterogeneity on illness’s dynamical transmission. The given mathematical epidemic model incorporated periodic variation in vector seasonal and ecology host shifting to catch changes of malaria disease spread among different areas
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