Modeling How the Different Parts of the Immune System Fight Viruses

Viruses cause a large number of diseases. After penetrating into a host, the virus starts infecting healthy cells. Then it uses the RNA or DNA of the cell to replicate and afterward it explodes the infected cell, letting out many copies of the virus that can infect new cells. The innate and adaptive parts of the immune system defend the body by eliminating both the free viruses and the infected cells. Neutrophils, macrophages, natural killer cells, helper T cells (CD4+) and cytotoxic T lymphocytes (CD8+) are among the participating immune cells. The interactions are complex and not fully understood. In this paper, we present and study three mathematical models based on ordinary differential equations of virus and immune system interactions with different complexities, and also introduce possible treatments. We discuss the advantages and disadvantages of each model. We do global sensitivity analysis and numerical simulations. Finally, we present conclusions including comments about the complexity of mathematical models.