Mathematical model of evasion of immune system by virus

Virus needs to infect cells to spread the disease in the host and to achieve this, they have developed specific tactics to evade the immune system, which is in charge of trying to prevent any infection. In this way, we develop a mathematical model to represent the evasion of immune system by virus using a non-monotonic functional response describing an antipredator behavior, where the virus is the prey and the immune cells are the predator. We found four equilibrium points, the disease free equilibrium, immune evasion equilibrium and two immune activation equilibrium points. The disease free equilibrium is globally asymptotically stable if R0 ≤ 1, the immune evasion equilibrium and two immune activation equilibria are locally asymptotically stable if R0 >1. We conclude that in our model the evasion of immune system is always possible when there is a inoculation of virus in the host, but there is also a chance to control the infection or to activate the immune system when there are a cross-reactive antibodies.