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A Stochastic SVIR Model for Measles
Department of Mathematics and Informatics, Abdou Moumouni University, Niamey, Niger
Department of Mathematics and Informatics, Abdou Moumouni University, Niamey, Niger
- 1 Department of Mathematics and Informatics, Abdou Moumouni University, Niamey, Niger
- 2 Department of Mathematics and Informatics, Abdou Moumouni University, Niamey, Niger
Applied Mathematics·Volume 12 (2021)·Pages 209–223·Published 11 March 2021·DOI10.4236/am.2021.123013
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Abstract
In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.
KeywordsMeaslesCompartmental ModelSVIRBasic Reproductive NumberMarkov ChainsLyapunov FunctionStochastic StabilityStochastic SimulationNiger
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