Abstract
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases.
Highlights
There exists a wide class of mathematical models that analyse the spread of epidemic diseases, either deterministic or stochastic, and may involve many factors such as infectious agents, mode of transmission, incubation periods, infectious periods, quarantine periods, etcetera (Allen 2003; Anderson and May 1991; Bailey 1975; Daley and Gani 1999; Diekmann et al 2013)
A basic model of infectious disease population dynamics, consisting of susceptible (S), infective (I) and recovered (R) individuals were first considered in a deterministic model by Kermack and McKendric (1927)
These models, despite their simplicity, are very unrealistic to catch the characteristic of the COVID-19 disease and for this reason in this paper we introduce a more complex system, that we call SEIAHCRD, that better describes this new disease
Summary
There exists a wide class of mathematical models that analyse the spread of epidemic diseases, either deterministic or stochastic, and may involve many factors such as infectious agents, mode of transmission, incubation periods, infectious periods, quarantine periods, etcetera (Allen 2003; Anderson and May 1991; Bailey 1975; Daley and Gani 1999; Diekmann et al 2013). A basic model of infectious disease population dynamics, consisting of susceptible (S), infective (I) and recovered (R) individuals were first considered in a deterministic model by Kermack and McKendric (1927). In this paper we will adapt a simple SIR-type model proposed by Ferrante et al (2016) and we will divide the population into several classes to better describe the evolution of the COVID epidemic. To model the evolution of the epidemic, we will describe the evolution of every single individual in the population, modelling the probability on every day to be infected. The construction of the theoretical model is carried out, where we are able to compute the probability of contagion and an estimate of the basic reproduction number R0. The use of the simulation is justified by the complexity of the model, that prevent to carry out any further exact computation. As expected, the group immunity plays a very important role to prevent the development of the disease
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