Mathematical Models for Assessing Vaccination Scenarios in Several Provinces in Indonesia

To mitigate more casualties from the COVID-19 outbreak, this study assessed optimal vaccination scenarios, considering some existing healthcare conditions and some assumptions, by developing SIQRD (Susceptible-Infected-Quarantine-Recovery-Death) models for Jakarta, West Java, and Banten, in Indonesia. The models included an age-structured dynamic transmission model that naturally could give different treatments among age groups of population. The simulation results show that the timing and periods length of the vaccination should be well planned and prioritizing particular age groups will give significant impact on the total number of casualties.

Modeling COVID-19 Transmissions and Evaluation of Large Scale Social Restriction in Jakarta, Indonesia

This paper presents mathematical modeling and quantitative evaluation of Large Scale Social Restriction (LSSR) in Jakarta between 10 April and 4 June 2020. The special capital region of Jakarta is the only province among 34 provinces in Indonesia with an average Testing Positivity Rate (TPR) below 5% recommended by the World Health Organization (WHO). The transmission model is based on a discrete-time compartmental epidemiological model incorporating suspected cases. The quantitative evaluation is measured based on the estimation of the time-varying effective reproduction number ([R]t). Our results show the LSSR has been successfully suppressed the spread of COVID-19 in Jakarta, which was indicated by [R]t < 1. However, once the LSSR was relaxed, the effective reproduction number increased significantly. The model is further used for short-term forecasting to mitigate the course of the pandemic.

Data-driven modeling and forecasting of COVID-19 outbreak for public policy making

This paper presents a data-driven approach for COVID-19 outbreak modeling and forecasting, which can be used by public policy and decision makers to control the outbreak through Non-Pharmaceutical Interventions (NPI). First, we apply an extended Kalman filter (EKF) to a discrete-time stochastic augmented compartmental model to estimate the time-varying effective reproduction number [R]t. We use daily confirmed cases, active cases, recovered cases, deceased cases, Case-Fatality-Rate (CFR), and infectious time as inputs for the model. Furthermore, we define a Transmission Index (TI) as a ratio between the instantaneous and the maximum value of the effective reproduction number. The value of TI shows the disease transmission in a contact between a susceptible and an infectious individual due to current measures such as physical distancing and lock-down relative to a normal condition. Based on the value of TI, we forecast different scenarios to see the effect of relaxing and tightening public measures. Case studies in three countries are provided to show the practicability of our approach.

A Compartmental Epidemic Model Incorporating Probable Cases to Model COVID-19 Outbreak in Regions with Limited Testing Capacity

We propose a new compartmental epidemic model taking into account people who has symptoms with no confirmatory laboratory testing (probable cases). We prove well-posedness of the model and provide an explicit expression for the basic reproduction number ([R]0). We use the model together with an extended Kalman filter (EKF) to estimate the time-varying effective reproduction number ([R]t) of COVID-19 in West Java province, Indonesia, where laboratory testing capacity is limited. Based on our estimation, the value of [R]t is higher when the probable cases are taken into account. This correction can be used by decision and policy makers when considering re-opening policy and evaluation of measures.

Superspreading in Early Transmissions of COVID-19 in Indonesia

We estimate the basic reproduction number[R] 0 and the overdispersion parameter[K] at two regions in Indonesia: Jakarta-Depok and Batam. Based on the first 1288 confirmed cases in both regions, we find a high degree of individual-level variation in the transmission. The basic reproduction number[R] 0 is estimated at 6.79 and 2.47, while the overdispersion parameter[K] of a negative-binomial distribution is estimated at 0.06 and 0.2 for Jakarta-Depok and Batam, respectively. This suggests that superspreading events played a key role in the early stage of the outbreak, i.e., a small number of infected individuals are responsible for large amounts of COVID-19 transmission.

A new estimation method for COVID-19 time-varying reproduction number using active cases

We propose a new method to estimate the time-varying effective (or instantaneous) reproduction number of the novel coronavirus disease (COVID-19). The method is based on a discrete-time stochastic augmented compartmental model that describes the virus transmission. A two-stage estimation method, which combines the Extended Kalman Filter (EKF) to estimate the reported state variables (active and removed cases) and a low pass filter based on a rational transfer function to remove short term fluctuations of the reported cases, is used with case uncertainties that are assumed to follow a Gaussian distribution. Our method does not require information regarding serial intervals, which makes the estimation procedure simpler without reducing the quality of the estimate. We show that the proposed method is comparable to common approaches, e.g., age-structured and new cases based sequential Bayesian models. We also apply it to COVID-19 cases in the Scandinavian countries: Denmark, Sweden, and Norway, where we see a delay of about four days in predicting the epidemic peak.