Analysis of combined langerhans and CD4⁺ T cells HIV infection

We develop a mathematical model that captures the combined infection of Langerhans cells and CD4⁺ T cells and their contribution to early HIV infection within the host. Mathematical analysis of the mathematical model revealed a threshold parameter denoted by alternative reproduction ratio with three different cycles of generations of secondary HIV infections, namely (i) cycle from infected CD4⁺ T cells to free virus and back to infected CD4⁺ T cells, (ii) cycle from infected CD4⁺ T cells to infected Langerhans cells and back to infected CD4⁺ T cells, and (iii) cycle from infected CD4⁺ T cells to free virus to infected Langerhans cells and back to infected CD4⁺ T cells. The relationship between the alternative reproduction ratio and the basic reproduction ratio showed that the predictions of results using the alternative reproduction ratio could be easily inferred from those of the basic reproduction ratio. Each of the cycles of infection raised the viral load whenever they were a dominant mechanism of viral production. The viral degradation mechanism, an antagonistic mechanism to viral lysis, was shown to slow down the growth of the virus.