Stochastic Modeling Effect on HIV Infection with Special Distribution

https://doi.org/10.46610/JOSME.2023.v09i02.001

Abstract

One of the key elements in the analysis of HIV infection is the estimation of the period until seroconversion. The seroconversion time is a crucial element of the seroconversion distribution in the analysis of the HIV epidemic. Elements that speed up the process of seroconversion include homo or hetero sexual interactions, the use of non-sterile needles, etc. Given that the timing of HIV conversion is unpredictable, one would anticipate that the distribution of seroconversion would have a significant influence on how the HIV pandemic develops. The intervals between sexual encounters were pointed out as a probable factor. To investigate the non-linear damage process affecting the immune system, we suggest a stochastic model. Alpha Poisson distribution has been derived keeping the Mittag-Leffler distribution as the inter-arrival time of the infection. A three-parameter Weibull distribution for the seroconversion time distribution is also introduced. HIV's seroconversion time's mean and variation are calculated. To demonstrate the seroconversion rates of HIV transmission, a numerical example is provided. The means and variance of seroconversion time decreases as the HIV intensity of the infected partner rises. The practical implication of the finding is that HIV spreads more quickly as immune system intensity decreases.