Mathematical modeling and optimal control strategies to limit the spread of fowl pox in poultry

Abstract

This paper presents a mathematical model aimed at elucidating the dynamics of fowl pox transmission within poultry populations. The model focuses on implementing control strategies to manage the spread of the disease, considering two primary modes of transmission: direct contact and transmission via mosquitoes. Our objective is to enhance understanding of disease propagation and to propose a control strategy aimed at minimizing the number of infected birds $I_b\left(t\right)$ and increasing the number of recovered birds $R_b\left(t\right)$ during the time interval $\left(t_0,t_f\right)$, while also minimizing the costs associated with implementing the control strategy. The proposed mathematical framework facilitates the integration of various control strategies to effectively manage fowl pox transmission dynamics. By employing Pontryagin’s maximum principle, efficient control measures are identified to mitigate the spread of the disease. Finally, numerical simulations are performed to verify the theoretical analysis using MATLAB.