Modeling of the COVID-19 pandemic in the limit of no acquired immunity

We propose the SEIRS compartmental epidemiology model aimed at modeling the COVID-19 pandemy dynamics.  The limit case of no acquired immunity (neither natural nor via vaccination) is considered mimicking the situation (i) when no effective vaccine being developed or available yet, and (ii) the virus strongly mutates causing massive reinfections.  Therefore, the only means of suppressing the virus spread are via quarantine measures and effective identification and isolation of infected individuals.  We found both the disease-free and the endemic fixed points and examined their stability.  The basic reproduction ratio is obtained and its dependence on the parameters of the model is discussed.  We found the presence of the contact rate threshold beyond which the disease-free fixed point cannot be reached.  Using the numeric solution, the approximate analytic solution of the model, characterized by rescaled contact rate, is obtained.  Several possible "quarantine on"/"quarantine off" scenarios are considered and the one combined with flexible adjustment of the identification and isolation rates is found to be the most effective in bringing the second and consequent waves down.  The study can be interpreted as a reference point for the case when the natural or acquired immunity, as well as vaccination, are taken into account.  It will be a topic of a separate study.

epidemiology
compartmental models
ordinary differential equations
COVID-19
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