A generalized model of chikungunya virus with both modes of transmission and humoral immunity

Abstract

In this paper, we develop a mathematical model to describe the interactions between Chikungunya virus (CHIKV), host cells and antibodies. The proposed model considers two types of infected cells and incorporates two modes of transmission, the classical virus-to-cell infection and the direct cell-to-cell transmission. These both modes are modeled by two general incidence functions that include many special cases existing in the literature. We first prove the well-posedness of the model, including the positivity and boundedness of solutions. The stability and instability of equilibria are established by means of direct and indirect Lyapunov methods. Furthermore, numerical simulations are presented in order to support our analytical results.