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

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.

Multi-state SVIRD Model with Continuous-time Markov Chain Assumption on the Spread of Infectious Diseases

“…In contrast, Klein and Moeschberger (2003) and Commenges (1999) describe how to overcome incomplete observations in a study. Jones (1994); Zuhairoh, Rosadi, and Effendie (2021) discuss the multi-state modeling process using discretetime Markov assumptions, and Haberman and Pitacco (1999) describes how multi-state models are used in long-term care insurance. Haberman and Pitacco (1999), explains how to use the maximum likelihood method to estimate transition intensity in a multi-state model, which is then assessed to produce a transition intensity function.…”

COVID-19 Epidemics Monitored Through the Logarithmic Growth Rate and SIR Model

“…Some used the simpler SIR model, where S was assumed to be the entire population, to estimate the mean infectious time τ and R0 and concluded that R0 was 1.23, a very low value [4]. Some have also used the SIRD model, which separates Dead (D) from recovered people [5,6]. Jacobian matrices representing this model were devised according to each idea and R0 was estimated as the largest eigenvalue of the next generation matrix [7].…”

Data-driven analysis and prediction of COVID-19 infection in Southeast Asia by using a phenomenological model

“…The phenomenological model of Ebola disease has been previously studied by Pell et al (2018) by using a logistic growth model that produces short-term forecasting and determination of basic reproductive numbers. Determination of the basic reproduction number is significant to determine the level of disease spread, as done by Zuhairoh et al (2021). At the same time, the Richards model has been previously studied by Hsieh (2009Hsieh ( , 2010 in SARS and H1N1 disease outbreaks.…”

“…The COVID-19 case in Southeast Asia was first detected in Thailand on January 13, 2020. Until April 21, 2021, the confirmed cases of COVID-19 in Southeast Asia reached 3,172,104 cumulative cases, with 64,182 deaths and 2,814,972 cases recovered.…”