Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus



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Human adaptive immune response consists of three major types of cells, namely, CD4 T cells, CTL (Cytotoxic T Lymphocytes), and antibodies. CTL attack and kill cells that are infected by viruses. Antibodies are capable of identifying and neutralizing viruses. In the presence of virus infection, CD4 T Cells stimulate the proliferation of CTL. Also the proliferation of antibodies becomes stimulated by viruses. These ideas are used to introduce a new ordinary differential equation model for exploring the dynamics of infection. Production of viruses by infectious CD4 T cells are not instantaneous and they require time to occur. Thus, explaining the dynamics of infections more accurately in the model, it is important to consider a time gap, which is known as delay. The new delay differential equation model, which considers a delay in the production of viruses, is also analyzed in this thesis. Both models are useful to be applied for HIV and hepatitis C infections, because in these models target cells are CD4 T cells, infectious agents are viruses, and the biological implications of the mathematical results are similar to the stages of the infections.



Mathematical immunology, Virus dynamics, Reproduction number, Asymptotic stability, Global stability