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Modeling and Analysis of the Dynamics of Rabies using Nonstandard Finite Difference Approach with Optimal Control |
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PP: 1013-1026 |
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doi:10.18576/amis/190504
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Author(s) |
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Dominic Otoo,
Elvis Kobinah Donkoh,
Razak Gbummie Chuaya,
Kennedy Mensah,
Charles Sebil,
Baaba Abassawah Danquah,
Hawa Adusei,
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Abstract |
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| Rabies is a viral disease caused by the neurotropic virus belonging to the Lyssavirus genus. It is a fatal disease affecting primarily the central nervous system of both humans and animals, resulting in inflammation of the brain and eventual death. In this paper, we formulated a deterministic model for rabies to better understand the dynamics of transmission and control strategies in the Ashanti Region of Ghana. Employing the nonstandard finite difference scheme, we establish key stability properties of the disease-free equilibrium (E0) with epidemiological interpretations: Local asymptotic stability implies that if a small number of cases arise, the disease will eventually fade out when the basic reproduction number is kept below 1. Global asymptotic stability demonstrates that rabies can be eliminated even if it starts at high prevalence levels. The asymptotic nature of stability confirms that disease elimination requires continuous intervention implementation over extended periods. The rabies model was expanded to incorporate an optimal control strategy using treatment of exposed dogs, policy and education on good petting, and effective education and campaigns on rabies. By optimizing our objective function, our optimal control analysis demonstrates that integrating effective public education and awareness campaigns, with the treatment of exposed dogs offers a highly effective strategy with strong long-term potential to reduce rabies transmission in the Ashanti Region of Ghana.
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