HIV Dynamics

This paper provides a mathematical model of HIV dynamics that involves the interactions between HIV and the human immune system with a certain combination of proteins and fatty acids, especially omega-3. In order to explain CD4 T cell HIV infection, the model is formulated as a system of nonlinear differential equations. Using the next-generation matrix method, we calculate the basic reproduction number ($R_0$) and analyze the stability of the infection-free equilibrium. The given results indicate that the equilibrium is both locally and globally asymptotically stable when $R_0<1$ but becomes unstable for $R_0>1$. An important feature in this paper is the use of Artificial Neural Networks (ANNs) to determine the numerical solutions of the system, which increases the accuracy and computation speed of the model solutions. A sensitivity analysis of $R_0$ is conducted to identify critical parameters that determine the spread of HIV. Numerical simulations are performed using a fourth-order Runge–Kutta (RK4) method to understand the effects of nutritional interventions. The results prove that a specific combination of proteins, omega-3, and omega-6 fatty acids may be a potential way to control the immune response and change the progression of HIV and find a new approach to managing the disease.