### Analisis Dinamik Model Matematika Penyebaran COVID-19 Pada Populasi SEIR

Ester Meyliana, Ari Kusumastuti, Juhari Juhari

#### Abstract

This study discusses the dynamic analysis of the mathematical model of the spread of COVID-19 using daily cases in Indonesia which are classified into four variables, namely, Susceptible (S), Exposed (E), Infected (I), and Recovered (R) which are then analyzed dynamically by calculate the equilibrium point and look for stability properties. The two equilibrium points of this model are the disease-free equilibrium point  and the endemic equilibrium point . Then, it is linearized around the equilibrium point using the given parameters. Linearization around the equilibrium point  produces four eigenvalues, one of which is positive. Linearization around the equilibrium point  yields two negative real eigenvalues and a pair of complex eigenvalues with negative real parts. Phase portraits and numerical simulations have shown that all variables S, E, I, and R will be asymptotically stable locally towards the equilibrium point, namely the endemic equilibrium point . Thus, based on the dynamic analysis obtained, it is shown that the disease-free equilibrium point  is unstable and the endemic equilibrium point is locally asymptotically stable.

#### Keywords

Dynamic Analysis; Mathematical Model of the Spread of COVID-19; Equilibrium Points; Phase Portrait

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DOI: https://doi.org/10.18860/jrmm.v1i4.14458

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