Epidemic Models with Several Levels of Immunity

Flavius Guiaş ()
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Flavius Guiaş: Dortmund University of Applied Sciences and Arts, Department of Mechanical Engineering

Chapter Chapter 13 in Quantitative Demography and Health Estimates, 2023, pp 163-174 from Springer

Abstract: Abstract We introduce a model for epidemics with stochastic dynamics based on two main states: susceptible and infected. To each susceptible individual is assigned an additional parameter which describes its level of immunity, which may vary in time. The underlying dynamics considers the natural decay of this level or its sudden increase by a jump at a maximal value corresponding to full immunity (due to vaccination or recovery from infection). Moreover, the susceptible individuals may become infected by contact with infectious ones, while the infection and vaccination rates depend on the immunity level. We analyze the properties of this stochastic model based on Markov jump processes, show its convergence towards a deterministic limit and perform numerical simulations in order to illustrate its behaviour.

Keywords: Epidemic model; Markov jump processes; Ordinary differential equations (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:ssdmcp:978-3-031-28697-1_13

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DOI: 10.1007/978-3-031-28697-1_13

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