Abstract
We present an epidemic model capable of describing key features of the Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic reproduction number, the number of deaths due to the virus and various other statistics. Numerical integrations are used to illustrate the adherence of the evolutions described by the model to specific well known real features of the present pandemic. In particular, this model is consistent with the well known relevance of quarantine, shows the dramatic role of care houses and accounts for the increase in the death toll when spatial movements are not constrained.
Highlights
Our aim here is to present a model that contains key features of the Covid-19 outbreak
We describe below the effects of different quarantine policies, from the pandemic evolution point of view
We show some effects of care houses, that is of places where the virus spreads faster, in accelerating the infection, in the case where only one age class is present in the care house
Summary
Our aim here is to present a model that contains key features of the Covid-19 outbreak. At a given time, age and space dependent rate, infective individuals are hospitalized or constrained to quarantine, entering the H population. Though not strictly necessary form the analytic point of view, we assume the individuals’ velocities to be assigned are time, age and space dependent functions, so that boundary data are essential whenever the velocities point inward X , while they are neglected when velocities point outward. 2.1 Simplified versions While the model (1) looks quite general, in its use on a time scale of, say, a year or less, the terms ∂aS, ∂aI, ∂aH and ∂aR, typically describing the aging of the population, can be neglected. With lower values of κ, the disease spreads more rapidly, so that the number of infectives is far higher, see Fig. 4, and less individuals recover, see Fig. 5. This effect is better accounted for when introducing movements in space
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