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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 Ib(t) and increasing the number of recovered birds Rb(t) during the time interval t0,tf, 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.

To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid.

This study delves into the dynamics of Zika virus transmission by employing a mathematical model to explain virus spread with fractional order derivatives. The population is divided into two groups: the human group and the ticks group to accurately explain the transmission routes of the virus. The objective of this research is to protect susceptible individuals from infection and curb the spread of this endemic disease. To achieve this, we have included two control measures: the first is a sensibilization program, and the second is treatment. We investigate the use of optimal control strategies and fractional derivative techniques under the Caputo method to reduce the number of exposed and infected individuals. By employing the Pontryagin maximum principle to analyze and characterize the optimal controls, the proposed method is further validated through numerical simulations. The outcome of this study highlights the importance of containing the rate of dynamic dissemination in preventing the Zika epidemic. [ABSTRACT FROM AUTHOR]