Modeling, analysis and numerical solution to malaria fractional model with temporary immunity and relapse

Autor: Attiq ul Rehman, Ram Singh, Thabet Abdeljawad, Eric Okyere, Liliana Guran
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-27 (2021)
Druh dokumentu: article
ISSN: 1687-1847
99571544
DOI: 10.1186/s13662-021-03532-4
Popis: 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 R 0 $\mathcal{R}_{0}$ 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.
Databáze: Directory of Open Access Journals
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