Mathematical Model for Hiv and Cd4+ Cells Dynamics in Vivo

Abstract

A particle begins in the first quadrant at coordinates (h, k). On each independent step, it moves either up, down, left, or right one unit at a time with probabilities p u , p d , p l , and p r , respectively. We derive the probability that the particle hits the x-axis before reaching the y-axis. We then derive the expected value of the number of steps needed to hit the x-axis, and the conditional average for those paths that hit before ever having reached the y-axis. Finally, we give the average number of steps needed to hit an axis and the average number of steps needed to hit both axes.

A Stochastic Model for Malaria Transmission Dynamics

“…In our model there are two possible events (production and death/removal) for each population. The corresponding rates in the deterministic model are replaced in the stochastic version by the probabilities that any of these events occur in a small time interval of length Δ [25,26].…”

Stochastic Modeling for HIV and AIDS Epidemics With Viral Load Detectability

“…There are numerous ways of deriving a stochastic model from the deterministic model: parametric perturbation stochastic model which introduces diffusion coefficient of the specific parameter(s) of interest to be perturbed, while on other hands non-parametric perturbation stochastic model involves adding Brownian processes to each differentia equation and assume that each compartment has uncertainty (Nsengiyumva et al, 2013;N'zi and Kanga, 2016;Miao et al, 2017). Several authors have undertaken various stochastic models for HIV and AIDS including authors such as (Mbogo et al, 2013;Zhang and Zhou, 2019;Fan et al, 2017). However, none of these models have considered stochastic models for HIV and AIDS particular by incorporating viral load detectability in the model, and the stochastic model is derived from deterministic counterpart as considered by Tengaa et al (2020).…”