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This paper presents a study of regional optimal control strategies of a spatiotemporal SIR epidemic model which is formulated from existing SIR epidemic models by including a diffusion term. Our main objective is to characterize the two optimal controls that minimize the number of infected individuals, the corresponding vaccination and treatment costs. For that matter, we prove the existence of a pair of control and provide a characterization of optimal controls in terms of state and adjoint functions. Finally, we present numerical simulations on data concerning the evolution of the zoonotic Ebola virus in Africa. Results show that control is effective if regional treatment and vaccine strategies are used simultaneously. [ABSTRACT FROM AUTHOR]

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. The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation. Pontryagin's maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy. [ABSTRACT FROM AUTHOR]