SEIRS epidemiology model for the COVID-19 pandemy in the extreme case of no acquired immunity

TL;DR

This paper models the COVID-19 pandemic using the SEIRS framework in a scenario with no acquired immunity, analyzing stability, reproduction ratio, and effects of quarantine strategies.

Contribution

It provides a detailed stability analysis and introduces a threshold contact ratio for disease-free states, including numeric and approximate solutions for pandemic evolution.

Findings

Stable disease-free fixed point depends on contact ratio

Flexible quarantine measures can prevent multiple waves

Analytic solutions describe early spread and decay phases

Abstract

We consider the SEIRS compartment epidemiology model suitable for predicting the evolution of the COVID-19 pandemy in the extreme limiting case of no acquired immunity. The disease-free and endemic fixed points are found and their stability is analysed. The expression for the basic reproduction ratio is obtained and discussed, emphasizing on its dependence on the model parameters. The threshold contact ratio is found which determines the possibility for a stable disease-free fixed point existence. Numeric solution for the pandemy evolution is also undertaken together with the approximate analytic solutions for the early stage of the disease spread as well as as for its decay after the rapid measures are undertaken. We analysed several possible scenarios for introducing and relaxing the quarantine measures. The cyclic "quarantine on" and "quarantine off" strategy at fixed identification and isolation ratios fail to reduce the lowering of the second and the consecutive waves, whereas this goal is possible to achieve if the flexible increase of the identification and isolation ratios is also involved.