Optimal control problem for mathematical modeling of Zika virus transmission using fractional order derivatives

Résumé

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.

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