On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

Abstract

In this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.

Modeling the COVID-19 pandemic: a primer and overview of mathematical epidemiology

“…However, the vaccine-induced immune response may not be as strong or long-lasting [ 83 ]. Apart from these problems, the initial and limited vaccine supply has raised some discussion on how to distribute COVID-19 vaccines [ 19 , 39 , 47 , 64 , 87 , 91 ]. Beyond prioritizing healthcare workers and the elderly, the optimal strategy for the general public remains complex.…”

“…In response to the COVID-19 crisis, the scientific community has acted fast to better understand the epidemiological, biological, immunological, and virological aspects of the SARS-CoV-2. Mathematical models have played a significant role to support public health preparedness and response efforts against the ongoing COVID-19 pandemic [ 2 – 6 , 19 , 21 , 23 , 30 , 32 – 34 , 39 , 50 , 55 , 68 , 84 , 86 , 88 , 89 , 91 ]. From the start of the pandemic, modelers have attempted to forecast the spread of COVID-19 in terms of the expected number of infections, deaths, hospital beds, intensive care units, and other health-care resources.…”

A New Threshold Reveals The Uncertainty About The Effect of School Opening On Diffusion of Covid-19.

“…see, e.g. [17], [12]. Here, for seek of simplicity we assume that the timet at which the vaccination program begins corresponds to t = 0.…”

Transmission dynamics of novel coronavirus SARS-CoV-2 among healthcare workers, a case study in Iran

“…For example, In [ 16 ], the authors SIER epidemic model to obtain the optimal control gain under vaccination. In [ 40 ], the authors investigate the stability of the COVID-19 SE(Is)(Ih)AR model under combined antiviral controls and vaccination. The authors obtained the equilibrium point, and then its stability is investigated.…”