Mathematical Modeling and Optimal Control Strategy \ for a Discrete-Time H5N5 Virus Transmission Model

Résumé

This paper presents a discrete-time mathematical model to study the transmission dynamics of the H5N5 avian influenza virus. The population under investigation is divided into six compartments: susceptible individuals ($S_k$), exposed individuals ($E_k$), infectious individuals ($I_k$), hospitalized individuals ($H_k$), recovered individuals ($R_k$), and deceased individuals ($D_k$). Our objective is to find the optimal strategy to reduce the number of infectious and hospitalized individuals while minimizing intervention costs. We propose four control strategies: preventive vaccination ($u_{1,k}$), quarantine measures ($u_{2,k}$), antiviral treatment ($u_{3,k}$), and public awareness campaigns ($u_{4,k}$). The discrete version of Pontryagin's Maximum Principle \cite{pontryagin1962} is used to characterize the optimal controls. Numerical simulations performed using MATLAB demonstrate the effectiveness of the proposed control strategies in reducing disease transmission and burden. The results show that implementing all four controls simultaneously can reduce peak infections by up to 70\% and hospitalizations by 65\%, providing valuable insights for public health policy makers.