Global stability in an age-structured SIRS malaria transmission model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915866819428352 |
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| author | Djaoue, Seraphin Richard, Quentin Perasso, Antoine Damakoa, Irépran |
| author_facet | Djaoue, Seraphin Richard, Quentin Perasso, Antoine Damakoa, Irépran |
| contents | This paper proposes and analyzes a malaria transmission model structured by the chronological age of the human host population. The model couples an age-structured SIRS system for humans, incorporating waning immunity, with an SI system for mosquitoes under mass-action transmissions. Using integrated semigroup theory and spectral analysis, we establish the well-posedness of the model, derive the basic reproduction number, and prove the global asymptotic stability of the parasite-free equilibrium by using a Lyapunov functional, when $R_0\leq 1$, thereby excluding the possibility of backward bifurcation. Numerical simulations further suggest the global stability of the endemic equilibrium when $R_0>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global stability in an age-structured SIRS malaria transmission model Djaoue, Seraphin Richard, Quentin Perasso, Antoine Damakoa, Irépran Analysis of PDEs This paper proposes and analyzes a malaria transmission model structured by the chronological age of the human host population. The model couples an age-structured SIRS system for humans, incorporating waning immunity, with an SI system for mosquitoes under mass-action transmissions. Using integrated semigroup theory and spectral analysis, we establish the well-posedness of the model, derive the basic reproduction number, and prove the global asymptotic stability of the parasite-free equilibrium by using a Lyapunov functional, when $R_0\leq 1$, thereby excluding the possibility of backward bifurcation. Numerical simulations further suggest the global stability of the endemic equilibrium when $R_0>1$. |
| title | Global stability in an age-structured SIRS malaria transmission model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.15201 |