In this paper, optimal control theory is applied to a system of ordinary differential equations representing a hantavirus infection in rodent and alien populations. The effect of the optimal control in eliminating the rodent population that caused the hantavirus infection is investigated. In addition, Pontryagin’s maximum principle is used to obtain the necessary condition for the controls to be optimal. The Runge–Kutta method is then used to solve the proposed optimal control system. The findings from the optimal control problem suggest that the infection may be eradicated by implementing some controls for a certain period of time. This research concludes that the optimal control mathematical model is an effective method in reducing the number of infectious in a community and environment...

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In this paper, a type of Zika virus model with immigration is considered. Additionally based on the risk of infected immigrants, we propose a control measure of screening for immigrants and a three-measure control model of combined mosquito prevention and killing. The existence and stability of the equilibrium in the Zika virus model are analyzed. The necessary conditions for the existence of the optimal solution are given using Pontryagins maximum principle. We focused on testing screening of the immigrating population to ensure a reduction in the transmission of the virus. Models have demonstrated that in combination with routine mosquito control measures and the appropriate use of mosquitoicides, the transmission of Zika virus in the population can be effectively reduced. 2023 the Author(s), licensee AIMS Press...

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