Mathematical model for managing vector-borne pathogen outbreaks in chickens using impulsive vaccination and drug treatment.

In this paper, we propose an epidemic mathematical model with an impulsive vaccination strategy to predict outbreaks in chickens caused by vectors. The analysis of the model is divided into two parts: one considering impulsive vaccination and the other without it. We determine the basic reproduction number of disease transmission and analyze the stability conditions of the proposed model for both disease-free and endemic equilibria, addressing both local and global stability. The results reveal that the disease will die out when the basic reproduction number is less than one. Numerical simulations demonstrate that impulsive vaccination significantly reduces the number of exposed and infected chickens, leading to disease eradication in approximately 270 days, compared to over 360 days without impulsive vaccination. The existence and non-negativity of the model solutions are also investigated. The susceptible population is considered to be vaccinated. We find that the periodic solution of the disease-free equilibrium is locally asymptotically stable under specific conditions outlined in the proposed theorem. This highlights the effectiveness of impulsive vaccination strategies in controlling disease transmission.