Dinamika dan Stabilitas Populasi pada Model Penyebaran COVID-19 dengan Vaksinasi dan Migrasi Penduduk

Abstract

This article discusses the mathematical model of the spread of COVID-19 by considering vaccination and population migration. The former model is analyzed by determining the equilibrium point, basic reproduction number, analyzing the stability of the equilibrium point, sensitivity analysis, and accompanied by numerical simulation. Analysis of the stability of disease-free and endemic equilibrium points using the Routh-Hurwitz Criteria and the Castillo-Chaves and Song theorems. The results of the analysis show that there are two equilibrium points, namely a disease-free equilibrium point (T1), which is locally asymptotically stable when R0 1, and an endemic equilibrium point (T2), which is locally asymptotically stable when R0 1. Furthermore, the sensitivity analysis showed that the most sensitive parameters to changes in the basic reproduction number were the emigration rate parameter (m2) and the infection probability parameter after contact between infected and susceptible individuals without vaccination (h). In addition, the numerical simulation results show that the sensitive parameter values, namely m2, h, zse, g, and # have a significant effect on the basic reproduction numbers. Suppressing the chance of infection in susceptible individuals and the rate of contact between susceptible and exposed individuals, as well as increasing the number of individuals who emigrate and who are vaccinated, can reduce the transmission of COVID-19.

Keywords

• basic reproduction number
• covid-19
• equilibrium point
• migration
• mathematical model
• vaccination