Dynamics of an HIV Infection Model with Two Infection Routes and Evolutionary Competition between Two Viral Strains

The existing combination therapy of HIV antiretroviral drugs can lead to the emergence of drug-resistant viruses, and cannot effectively block direct cell-to-cell infections, these factors results in incomplete virus suppression and increased risk of disease progression. In this paper, we formulate an HIV model with two strains representing a drug-sensitive virus and a drug-resistant virus to study the joint mechanism of drug resistance. We first reduce the infection-age model to a system of integro-differential equations with infinite delays. Then the stability of the equilibria and the dynamics of competition between two viruses are studied to illuminate the joint effects of infection-age and two infection routes on the evolution of both drug-sensitive and drug-resistant strains before and during drug treatment. Applying a persistence theorem for infinite dimensional systems, we obtain that the disease is always present when the basic reproduction number is larger than unity. Numerical simulations confirm that the basic reproduction numbers and mutation coefficient are the key threshold parameters for determining the competition results of the two viral strains and indicate the cell-to-cell transmission increases the likelihood that HIV breaks out within the host. Finally, sensitivity analyses suggest that the available combination therapy should be taken once symptoms of resistance appear during drug treatment, and demonstrate that the presence of cell-to-cell transmission attenuates the efficacy of the existing antiretroviral drug treatments.