Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative

In this research, we propose a deterministic model to study the transmission dynamics of HIV infection in the Caputo fractional operator context and analyze the impact of horizontal and vertical transmissions of the infection. The model consisting of mutually exclusive compartments representing the human dynamics, has a locally-asymptotically stable disease free equilibrium (DFE) whenever a certain epidemiological threshold quantity known as the basic reproduction number R0 is less-than unity. Significant model characteristics such as the existence and uniqueness of the solution and sensitivity analysis are investigated. Finally, In order to evaluate the approximate solution and dynamical behavior of the model under consideration, the well-known and efficient numerical scheme called the fractional Euler method is employed and the results show that, the infections from the compartments of each state variables decreases with time which causes an increase in the compartments of new born child with no HIV infection and susceptible adults. It should be noted that, unlike many studies recently carried out, dimensional consistency is taken into account during the classical model fractionalization process.