A mathematical COVID-19 model considering asymptomatic and symptomatic classes with waning immunity

Anggriani, Nursanti; Ndii, Meksianis Z.; Amelia, Rika; Suryaningrat, Wahyu; Aji Pratama, Mochammad Andhika

The spread of COVID-19 to more than 200 countries has shocked the public. Therefore, understanding the dynamics of transmission is very important. In this paper, the COVID-19 mathematical model has been formulated, analyzed, and validated using incident data from West Java Province, Indonesia. The model made considers the asymptomatic and symptomatic compartments and decreased immunity. The model is formulated in the form of a system of differential equations, where the population is divided into seven compartments, namely Susceptible Population ( S 0 ) , Exposed Population ( E ) , Asymptomatic Infection Population ( I A ) , Symptomatic Infection Population ( Y S ) , Recovered Population ( Z ) , Susceptible Populations previously infected ( Z 0 ) , and Quarantine population ( Q ) . The results show that there has been an outbreak of COVID-19 in West Java Province, Indonesia. This can be seen from the basic reproduction number of this model, which is 3.180126127 ( R 0 > 1 ) . Also, the numerical simulation results show that waning immunity can increase the occurrence of outbreaks; and a period of isolation can slow down the process of spreading COVID-19. So if a strict social distancing policy is enforced like a quarantine, the outbreak will lessen.