Stochastic Model of Dengue: Analysing the Probability of Extinction and LLN — Oak Academic Publishing
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Stochastic Model of Dengue: Analysing the Probability of Extinction and LLN
Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso
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Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso
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Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso
1 Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso
2 Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso
3 Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso
In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.
KeywordsDengue FeverContinuous-Time Markov ChainMultitype Branching ProcessProbability of Disease ExtinctionLaw of Large Numbers
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