Abstract
We revisit here a landmark five-parameter SIR-type model, which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also generalize it by adding essential vaccination and vaccination-induced death parameters, with the aim of revealing the role of vaccination and its possible failure. The main result is Theorem 1, which describes the stability behavior of our model in all possible cases.
Highlights
IntroductionThe discrepancy with what is expected from the corresponding stochastic model suggests that the deterministic model is inappropriate in this range.)
This paper has the dual purpose of providing a short guide to students of deterministic mathematical epidemiology, among which we count ourselves, and to simultaneously illustrate the technical work one is faced with in an elementary, but not simple “exercise”
Note that at its beginning, mathematical epidemiology was a collection of similar examples dealing with current epidemics
Summary
The discrepancy with what is expected from the corresponding stochastic model suggests that the deterministic model is inappropriate in this range.) This last stream of literature is quite important, since a constant birth rate per capita is a natural assumption. [33,34,35,36,37,38,39] (which preferred all direct stability analyses to the next-generation matrix approach)—the literature on models with varying total populations, unlike the two preceding streams, has not yet reached a general result To understand this failure, it seemed to us a good idea to revisit an important SIR model with disease-induced deaths and loss of immunity [32,35]. Turns out to ensure the local stability of the disease-free equilibrium (disease-free Equilibrium)–see
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