Time-dependent non-homogeneous stochastic epidemic model of SIR type
To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a possible quarantine of the infectious individuals. We provide a...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/415412 |
| Acceso en línea: | https://hdl.handle.net/2117/415412 https://dx.doi.org/10.3934/math.20231181 |
| Access Level: | acceso abierto |
| Palabra clave: | Stochastic analysis SIR model Basic reproduction number Epidemic model Stochastic differential equations Markov chain Anàlisi estocàstica Classificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a possible quarantine of the infectious individuals. We provide an analytic description of this Markovian model and investigate its dynamics. Both a diffusion approximation and the basic reproduction number are derived. Through several simulations, we show how the evolution of a disease is affected by the distribution of the number of daily encounters and its dependence on time. Finally, we show how the appropriate choice of this parameter allows a suitable application of our model to two real diseases. |
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