Mathematical Model of the Behaviour of T Cytotoxic, T Helper, B and Natural Killer Cells in the Presence of Viruses

Abstract

The behaviour of lymphoid cells in the absence of viruses has already been published in the year 2013. This study is a continuation of recent attempts to understand, via mathematical modeling, the behavior of lymphoid cells in the absence and in the presence of viruses. In this study, which is the behaviour of lymphoid cells in the presence of viruses will be treated in three respects. Firstly, the innate immune response stage, secondly, the overlap of innate and adaptive immune responses stage and finally, the adaptive immune response stage of viral infections. The adaptive immune response stage considers the viremia and cell-mediated immune responses stage. The steady states and the stability for these differential models are deduced. Each of the models permit the existence of two types of stationary states. There is the state of no infection, with no virus cells while the other is the state of co-existence where a virus cell persists against the background of immune response. The state of no infection is asymptotically stable and a state of infection is unstable. It is found from the study that the state of no infection represents the preparedness of the immune state prior to the infection. Numerical simulation analysis suggests that the cells (NK, T c , T h and B) grow exponentially as a result of proliferation and saturation because of the contacts between them and reach therefore reach plateau as time (t) increases. These immune cells are able to reduce viral load to the barest minimum if not reducing it to zero.