Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment

Abstract

The mathematical model for analyzing the transmission dynamics of HIV/AIDS epidemic with treatment is studied by considering the three latent compartments for slow, medium and fast progresses of developing the AIDS. By constructing the system of differential equations for the different population groups namely susceptible, three types of latent individuals, symptomatic stage group and full blown AIDS individuals, the mathematical analysis is carried out in order to understand the dynamics of disease spread. By determining the basic reproduction number (R 0 ), the model examines the two equilibrium points (i) the disease free equilibrium and (ii) the endemic equilibrium. It is established that if < 1, the disease free equilibrium is locally and globally asymptotically stable. The stability of endemic equilibrium has also been discussed.

Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis

“…Mathematical methods also inform clinical guidelines for HIV/AIDS diagnosis, monitoring, and treatment [8]. Furthermore, research has focused on modeling and controlling HIV/AIDS transmission in China using real data from 2004 to 2016 [9], analyzing the stability of infection-age structured HIV-1 models that connect within-host and between-host dynamics [10], developing peptide inhibitors for HIV transmission [11], creating mathematical models of HIV transmission and infection dynamics [12], understanding the dynamics of HIV/AIDS transmission concerning protection awareness and fluctuations [13], conducting numerical investigations of stochastic HIV/AIDS infection models [14], exploring global dynamics of age-infection HIV models with a nonlinear infection rate [15], and modeling epidemic dynamics of HIV/AIDS transmission with different latent stages based on treatment [16]. Additionally, [17] developed an epidemic model for HBV infection, incorporating vaccination and medication administered through hospitalization.…”

Dynamics of HIV-TB Co-Infection Model

“…Another HIV-TB co-infection model was formulated by Roeger et al [12], assuming TB-infected individuals in the active stage of disease to be sexually inactive. Singh et al [13] studied the transmission dynamics of the HIV/AIDS epidemic model considering three different latent stages based on treatment. Torres et al [14], in his model, incorporates both TB and AIDS treatment for individuals suffering with either or both disease.…”