Optimal treatment of an SIR epidemic model with time delay |
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Authors: | Gul Zaman Yong Han Kang Il Hyo Jung |
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Affiliation: | aCentre for Advanced Mathematics and Physics, National University of Sciences and Technology, Rawalpindi 46000, Pakistan;bDepartment of Mathematics, Pusan National University, Busan 609-735, South Korea |
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Abstract: | In this paper the optimal control strategies of an SIR (susceptible–infected–recovered) epidemic model with time delay are introduced. In order to do this, we consider an optimally controlled SIR epidemic model with time delay where a control means treatment for infectious hosts. We use optimal control approach to minimize the probability that the infected individuals spread and to maximize the total number of susceptible and recovered individuals. We first derive the basic reproduction number and investigate the dynamical behavior of the controlled SIR epidemic model. We also show the existence of an optimal control for the control system and present numerical simulations on real data regarding the course of Ebola virus in Congo. Our results indicate that a small contact rate(probability of infection) is suitable for eradication of the disease (Ebola virus) and this is one way of optimal treatment strategies for infectious hosts. |
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Keywords: | Epidemic model Time-delay Optimality Existence Numerical simulation Ebola outbreak |
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