Model for prognostic of symptomatic, asymptomatic and hospitalized COVID-19 cases with correct demography evolution

Antonio Rafael Selva Castañeda; Erick Eduardo Ramirez-Torres; Luis Eugenio Valdés-García; Hilda María Morandeira-Padrón; Diana Sedal Yanez; Juan I. Montijano; Luis Enrique Bergues Cabrales

arXiv · 2206.03806

Model for prognostic of symptomatic, asymptomatic and hospitalized COVID-19 cases with correct demography evolution

Antonio Rafael Selva Castañeda·Erick Eduardo Ramirez-Torres·Luis Eugenio Valdés-García·Hilda María Morandeira-Padrón·Diana Sedal Yanez·Juan I. Montijano·Luis Enrique Bergues Cabrales

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Abstract

The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the behaviour of symptomatic, asymptomatic and hospitalized patients of COVID-19 epidemic, including the effect of demographic variation of population. It is shown that considering a population growth proportional to the total population leads to solutions with a qualitative behaviour different from the behaviour obtained in many studies, where constant growth ratio is assumed. An exhaustive theoretical study is carried out and the basic reproduction number $R_0$ is computed from the model equations. It is proved that if $R_0<1$ then the disease-free manifold is globally asymptotically stable, that is, the epidemics remits. Global and local stability of the equilibrium points is also studied. Numerical simulations are used to show the agreement between numerical results and theoretical properties. The model is fitted to experimental data corresponding to the pandemic evolution in the República de Cuba, showing a proper behaviour of infected cases which let us think that can provide a correct estimation of asymptomatic cases. In conclusion, the model seems to be an adequate tool for the study and control of infectious diseases in particular the COVID-19 disease transmission.

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Antonio Rafael Selva Castañeda, Erick Eduardo Ramirez-Torres, Luis Eugenio Valdés-García, Hilda María Morandeira-Padrón, Diana Sedal Yanez, Juan I. Montijano, Luis Enrique Bergues Cabrales. 2022-06-08. Model for prognostic of symptomatic, asymptomatic and hospitalized COVID-19 cases with correct demography evolution. https://arxiv.org/abs/2206.03806

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