Munguwampaga Chihungu Innocent is a mathematician and emerging researcher from the Democratic Republic of the Congo with expertise in dynamical systems, differential equations, machine learning theory, and infectious disease modeling. He earned his Bachelor’s degree in Mathematics and Physics from the Institut Supérieur Pédagogique de Bukavu and completed a Master of Science in Mathematical Sciences at the African Institute for Mathematical Sciences (AIMS) Senegal. As an Erasmus+ Exchange Scholar at the University of Crete, Greece, he conducted research on the dynamics of gradient descent in linear neural networks. His research interests include mathematical epidemiology, artificial intelligence, dynamical systems, and the application of mathematical modeling to public health challenges in Africa. He is a member of the Ecology Meets Infectious Diseases (EMID) Research Community of the American Institute of Mathematics, where he contributes to studies on disease dynamics, climate change, and ecological systems. In addition to his research activities, he serves as a Teaching Assistant at the Institut Supérieur Pédagogique de Kaziba and Université Libre des Grands-Lacs, teaching courses in probability, statistics, operations research, and differential equations. A recipient of the Mastercard Foundation Scholarship, AIMS Senegal Scholarship, and Erasmus+ Scholarship, Innocent is also actively engaged in leadership and community service initiatives focused on education, climate action, and youth development across Africa.

A stochastic approach to HIV/AIDS transmission dynamics in the Democratic Republic of Congo: Analysis and simulations
Mathematical modeling of HIV/AIDS constitutes an essential tool for understanding transmission dynamics and evaluating the impact of control strategies (Anderson & May, 1991;
Hethcote, 2000). This work develops a comprehensive analysis of a four-state compartmental
model (Susceptible, HIV-Infected, AIDS Patients, ARV-Treated) adapted to the epidemiological context of the Democratic Republic of Congo. We rigorously establish the properties of the
deterministic model: positivity, boundedness, calculation of the basic reproduction number R0,
existence and stability of equilibria (Diekmann et al., 1990; Van den Driessche & Watmough,
2002). The major methodological contribution builds on the work of Emvudu et al. (2016) and
Bongor (2021) concerning the construction of the associated stochastic model by approximating
the underlying Poisson processes, leading to an Itô stochastic differential equation whose diffusion matrix is made explicit and the work of Mozart Umba Nsuami and Peter Joseph Witbooi
(2018) on a stochastic epidemic model for HIV with treatment. Analysis of the stochastic model
demonstrates the almost sure positivity of solutions and exponential stability in mean square
of the disease-free equilibrium (Afanasiev, 1996; Mao, 2007). Numerical simulations, calibrated
on UNAIDS (2022) data for the DRC (R0 ≈ 1.47), illustrate the dynamics over 50 years and
quantify stochastic fluctuations in accordance with the work of Liptser and Shiryaev (1980).
Our results confirm the persistence of the epidemic in a stable endemic regime, the crucial role
of treatment in controlling transmission, and the reliability of the deterministic approximation
for large populations (Brauer et al., 2008; Castillo-Chavez et al., 2002). This work provides a
rigorous theoretical framework for evaluating public health policies in contexts of uncertainty.

Keywords: HIV/AIDS, Stochastic modeling, Stochastic differential equations, Basic reproduction number, Stability, Democratic Republic of Congo, Numerical simulation, Poisson
process, Markov chain, Antiretroviral treatment.