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Allen, L.J.S. and van den Driessche, P. (2013) Relations between Deterministic and Stochastic Thresholds for Disease Extinction in Continuous and Discrete-Time Infectious Disease Models. Mathematical Biosciences, 243, 99-108.
https://doi.org/10.1016/j.mbs.2013.02.006

has been cited by the following article:

• TITLE: Stochastic Model of Dengue: Analysing the Probability of Extinction and LLN

  AUTHORS: Ragnimwendé Sawadogo, Fourtoua Victorien Konané, Wahabo Baguian

  KEYWORDS: Dengue Fever, Continuous-Time Markov Chain, Multitype Branching Process, Probability of Disease Extinction, Law of Large Numbers

  JOURNAL NAME: Applied Mathematics, Vol.15 No.9, September 11, 2024

  ABSTRACT: 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.