Mathematical modeling of the spread of corona virus disease 19 (COVID-19) with vaccines

Abstract

Coronavirus Disease 2019 (Covid-19) is a new type of disease caused by a virus from the coronavirus group, namely SARS-CoV-2 which is also often called the Corona Virus. In just a few months, COVlD-19 spread between humans very quickly and spread to almost all countries in the world, including Indonesia. The very fast spread has encouraged researchers in the health and epidemiology fields to study the dynamics of the development and transmission of COVlD-19. Many perspectives emerging from these results, not least of researchers in the field of science, especially researchers in the field of mathematical modeling. This article discusses the mathematical model proposed and dynamics of the spread Covid-19 by considering the vaccine. The model is constructed with reference to the split popuasi Seir models into four sub-populations, namely sub-population susceptible, exposed sub-population, sub poplasi infection and sub-populations recover. Furthermore, the model was developed by taking into account the vaccine variable. The vaccine variable is intended to suppress the transmission of Covid-19 disease. The results of the development of the SElR mathematical model will change to SVEIR. Furthermore SVElR models have two equilibrium point that is disease-free equilibrium point and the point of equilibrium endemic by analyzing the model, a basic reproduction number is found, also called a threshold number, which identifies whether the virus is extinct or endemic. Numerical simulation shows that an increase in the vaccine may contribute to slow the spread of COVlD-19, which is expected to prevent the spread of disease outbreaks Covid-19.