Abstract
This work is aimed to formulate and analyze a mathematical modeling, SEIR model, for COVID-19 with the main parameters of vaccination rate, effectiveness of prophylactic and therapeutic vaccines. Global and local stability of the model are investigated and also numerical simulation. Local stability of equilibrium points are classified. A Lyapunov function is constructed to analyze global stability of the disease-free equilibrium. The simulation part is based on two situations, the US and India. In the US circumstance, the result shows that with the rate of vaccination 0.1% per day of the US population and at least 20% effectiveness of both prophylactic and therapeutic vaccines, the reproductive numbers R0 are reduced from 2.99 (no vaccine) to less than 1. The same result happens in India case where the maximum reproductive number R0 in this case is 3.38. To achieve the same infected level of both countries, the simulation shows that with the same vaccine's efficiency the US needs a higher vaccination rate per day. Without vaccines for this pandemic, the model shows that a few percentages of the populations will suffering from the disease in the long term.
Highlights
Coronavirus disease is a severe acute respiratory disease caused by a coronavirus 2 (SARS-CoV-2) that is a new member of the genus Beta coronavirus and family Coronaviridae [1, 2]
Many researches have been studied by adapting SEIR model to forecast dynamics of endemic and epidemic such as Dengue Fever [13, 14, 15], Ebola [16, 17], Middle East Respiratory Syndrome (MERS) [18, 19]
The equilibrium point related to the US and India situations can be computed by using Equation (7)
Summary
Coronavirus disease is a severe acute respiratory disease caused by a coronavirus 2 (SARS-CoV-2) that is a new member of the genus Beta coronavirus and family Coronaviridae [1, 2]. A mathematical model can predict the future situation of an outbreak and evaluate the best strategy to control spreading diseases. Compartment model is an interesting tool for COVID-19 situation It is a powerful mathematical model for understanding the complex dynamics of epidemics. Many researches have been studied by adapting SEIR model to forecast dynamics of endemic and epidemic such as Dengue Fever [13, 14, 15], Ebola [16, 17], Middle East Respiratory Syndrome (MERS) [18, 19],. SEIR model have been adapted by adding strategy parameters such as social distancing and face mask using to control and predict COVID-19 situation in several researches [25, 26, 27, 28, 29, 30]. We applied recorded parameters of US and India circumstances to our model and predicted the potential of COVID-19 in both countries when vaccines come out
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