Mathematical modelling of within-host Chikungunya virus dynamics with adaptive immune response

Abstract

It is well known that mathematical biology and dynamical systems provide useful information for the study of viral infection models such as HIV, HBV, HCV, Dengue and Chikungunya virus. Chikungunya, a mosquito-borne viral disease is now a global public health problem. It is in this context that this paper studies the global asymptotic stability of two within-host Chikungunya virus (CHIKV) dynamics models with cytotoxic T-lymphocytes (CTL) cells and antibodies representing the adaptive immune response. The first model is governed by a five-dimensional system of differential equations with adaptive immune response, while the second model is six-dimensional in the presence of latency. In particular, the second model considers two types of infected cells, namely latently infected cells which do not generate CHIKV, and actively infected cells which produce the CHIKV particles. A biological threshold number ${\mathcal {R}}_{0}$ which determines the clearance or persistence of CHIKV in the body is derived for each of the models. We establish the existence of CHIKV-free and CHIKV-present steady states. Using the method of Lyapunov function, we prove that, when ${\mathcal {R}}_{0}\le 1$, then the CHIKV-free steady state is globally asymptotically stable and when ${\mathcal {R}}_{0}>1$, the endemic steady state is globally asymptotically stable. Numerical simulations are performed to confirm our obtained theoretical results. Both the theoretical and numerical results may help to improve the understanding of CHIKV dynamics