In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than a critical value. Moreover, sufficient conditions are obtained to guarantee the local and global stability of the equilibrium points of the model. The numerical analysis reveals that multiple endemic equilibria may exist even when the basic reproduction number is less than one, and some interesting dynamics can be observed when the treatment parameter and immunity waning rate are varied.
Oluyori, David A.; Adebayo, Helen O.; and Pérez, Ángel G.C.
(R1468) Global Analysis of an SEIRS Model for COVID-19 Capturing Saturated Incidence with Treatment Response,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
2, Article 9.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss2/9