Mathematical modeling and simulation of SEIR model for COVID-19 outbreak: A case study of Trivandrum

Abstract

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In this study, we formulated a mathematical model of COVID-19 with the effects of partially and fully vaccinated individuals. Here, the purpose of this study is to solve the model using some numerical methods. It is complex to solve four equations of the SEIR model, so we introduce the Euler and the fourth-order Runge–Kutta method to solve the model. These two methods are efficient and practically well suited for solving initial value problems. Therefore, we formulated a simple nonlinear SEIR model with the incorporation of partially and fully vaccinated parameters. Then, we try to solve our model by transforming our equations into the Euler and Runge–Kutta methods. Here, we not only study the comparison of these two methods, also found out the differences in solutions between the two methods. Furthermore, to make our model more realistic, we considered the capital of Kerala, Trivandrum city for the simulation. We used MATLAB software for simulation purpose. At last, we discuss the numerical comparison between these two methods with real world data.

Keywords

• COVID-19
• mathematical model
• Euler method
• Runge Kutta method
• Trivandrum
• numerical simulation