On the generalized Chikungunya virus dynamics model with distributed time delays
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On the generalized Chikungunya virus dynamics model with distributed time delays Taofeek O. Alade1 Received: 15 September 2020 / Revised: 19 October 2020 / Accepted: 27 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, a stability analysis of a general nonlinear Chikungunya virus dynamics model is presented. Two kinds of infected cells, namely latently infected and actively infected are incorporated into the model. It is assumed that, the incidence rate of infection as well as the production, removal and proliferation rates of all compartments are modeled by general nonlinear functions that satisfy sufficient conditions. The model contains two distributed time delays. The nonnegativity and boundedness of the solutions of the model are investigated. Constructions of suitable Lyapunov functionals are established to prove the global stability of the steady states of the model. Numerical simulations are performed to confirm the validity of the established theoretical results. Keywords Chikungunya virus · Distributed delays · General nonlinear function · Global stability · Lyapunov function
1 Introduction In recent years, several mathematical models of different viral infections have been proposed and developed such as Human immunodeficiency virus, Hepatitis B virus, Hepatitis C virus, Dengue virus and CHIKV, etc (see Refs. [1–29]). These mathematical models are more important in order to understand the dynamical behavior of the viral infections, to estimate the strength of the immune responses and to provide estimate for drug efficacy that can lead to virus clearance. In particular, Chikungunya virus (CHIKV), which is an emerging and re-emerging mosquito-borne viral infection, that has become a serious public health issue in different regions worldwide [30]. It is an arbovirus that belongs to the Alphavirus genus of the Togaviridae family [31,32]. The virus is endemic in subtropical and tropical countries in Africa and Asia. It was confirmed recently that people living in over 60 countries are now at the risk of CHIKV infection [31]. CHIKV is mainly transmitted to humans through the bites of infected female mosquitoes (Aedes aegypti and Aedes albopictus). The infected female mosquito acquires
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Taofeek O. Alade [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
the virus while feeding on the blood meal of an infectious human host. After 7–12 days of virus incubation, the infected mosquito is capable of passing the virus to healthy individuals via bite [33]. The virus attacks the host cells and causes Chikungunya fever [34]. The intrinsic incubation period in humans usually takes 1–12 days after the infective bite and infected patients may appear viremia until 10 days [33]. CHIKV shows symptoms like muscle pain, fever, rash, nausea, fatigue and headache. In the literature, most of the mathematical models of CHIKV presented describe the transmission dynamics of the virus in human
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