Determination of Basic Reproduction Numbers using Transition Intensities Multi-state SIRD Model for COVID-19 in Indonesia

Abstract

Abstract The most important quantity in infectious disease epidemiology is the basic reproduction number (R 0). R 0 is the expected value of the number of infections per unit time. This paper aims to model the spread of COVID-19 in Indonesia using the multi-state SIRD model and then determine the transition intensities to construct R 0. The estimation of the transition intensity uses the maximum likelihood approach with the assumption of a homogeneous time Markov chain with an exponential distribution of transition intensity and the number of transitions in a Poisson distribution. The results of the transition intensity estimation are used to construct R 0 with the next generation matrix method. From the multi-state SIRD model, the largest transition is shown in the individual healing process, namely the movement from an infected to susceptible state, while the smallest transition is the transition from susceptible to dead. The R 0 obtained is 1.079708 (> 1) meaning that the number of individuals infected with COVID-19 will increase until it reaches a stable point. Transition intensities is an effective way of determining R 0 where the dynamics of disease transmission depends on the number of individuals transition between states and the total waiting time in a certain state. R 0 > 1 states that the COVID-19 pandemic in Indonesia has not been over yet.