A Mathematical and Optimal Control Model for Rabies Transmission Dynamics Among Humans and Dogs with Environmental Effects
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911138083504128 |
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| author | Charles, Mfano Mfinanga, Sayoki G. Lyakurwa, G. A. Torres, Delfim F. M. Masanja, Verdiana G. |
| author_facet | Charles, Mfano Mfinanga, Sayoki G. Lyakurwa, G. A. Torres, Delfim F. M. Masanja, Verdiana G. |
| contents | This study presents a deterministic model to investigate rabies transmission dynamics, incorporating environmental effects and control strategies using optimal control theory. Qualitative and quantitative analyses reveal that the disease-free equilibrium is stable when the effective reproduction number $\mathcal{R}_e < 1$, and unstable when $\mathcal{R}_e > 1$. Mesh and contour plots illustrate an inverse relationship between $\mathcal{R}_e$ and control strategies, including dog vaccination, health promotion, and post-exposure treatment. Increased intervention reduces transmission, while higher contact rates among dogs raise $\mathcal{R}_e$. Numerical simulations with optimal control confirm the effectiveness of integrated strategies. Vaccination and treatment are identified as key interventions for achieving rabies elimination within five years. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Mathematical and Optimal Control Model for Rabies Transmission Dynamics Among Humans and Dogs with Environmental Effects Charles, Mfano Mfinanga, Sayoki G. Lyakurwa, G. A. Torres, Delfim F. M. Masanja, Verdiana G. Optimization and Control Populations and Evolution This study presents a deterministic model to investigate rabies transmission dynamics, incorporating environmental effects and control strategies using optimal control theory. Qualitative and quantitative analyses reveal that the disease-free equilibrium is stable when the effective reproduction number $\mathcal{R}_e < 1$, and unstable when $\mathcal{R}_e > 1$. Mesh and contour plots illustrate an inverse relationship between $\mathcal{R}_e$ and control strategies, including dog vaccination, health promotion, and post-exposure treatment. Increased intervention reduces transmission, while higher contact rates among dogs raise $\mathcal{R}_e$. Numerical simulations with optimal control confirm the effectiveness of integrated strategies. Vaccination and treatment are identified as key interventions for achieving rabies elimination within five years. |
| title | A Mathematical and Optimal Control Model for Rabies Transmission Dynamics Among Humans and Dogs with Environmental Effects |
| topic | Optimization and Control Populations and Evolution |
| url | https://arxiv.org/abs/2507.08895 |