With a limited number of vaccines and healthcare capacity shortages, particularly in low- and middle-income countries, vaccination programs should seek the most efficient strategy to reduce the negative impact of the COVID-19 pandemics. This study aims at assessing several scenarios of delivering the vaccine to people in Indonesia. We develop a model for several scenarios of delivering vaccines: without vaccination, fair distribution, and targeted distribution to five and eight districts with the highest COVID-19 incidence in West Java, one of the most COVID-19-affected regions in Indonesia. We calculate the needs of vaccines and healthcare staff for the program, then simulate the model for the initial 4-month and one-year scenarios. A one-year vaccination program would require 232,000 inoculations per day by 4833 vaccinators. Targeted vaccine allocation based on the burden of COVID-19 cases could benefit the COVID-19 vaccination program by lowering at least 5000 active cases. The benefits would increase by improving the number of vaccines and healthcare staff. Amidst lacking available vaccines, targeted vaccine allocation based on the burden of COVID-19 cases could increase the benefit of the COVID-19 vaccination program but still requires progressive efforts to improve healthcare capacity and vaccine availability for optimal protection for people.

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Generating dynamic operators are constructed here from the cumulative case function to recover all state dynamics of a Susceptible–Exposed–Infectious–Recovered (SEIR) model for COVID-19 transmission. In this study, recorded and unrecorded EIRs and a time-dependent infection rate are taken into account to accommodate immeasurable control and intervention processes. Generating dynamic operators are built and implemented on the cumulative cases. All infection processes, which are hidden in this cumulative function, can be recovered entirely by implementing the generating operators. Direct implementation of the operators on the cumulative function gives all recorded state dynamics. Further, the unrecorded daily infection rate is estimated from the ratio between IFR and CFR. The remaining dynamics of unrecorded states are directly obtained from the generating operators. The simulations are conducted using infection data provided by Worldometers from ten selected countries. It is shown that the higher number of daily PCR tests contributed directly to reducing the effective reproduction ratio. The simulations of all state dynamics, infection rates, and effective reproduction ratios for several countries in the first and second waves of transmissions are presented. This method directly measures daily transmission indicators, which can be effectively used for the day-to-day control of the epidemic.

Consideration of human mobility is essential for understanding the behavior of COVID-19 spread, especially when millions of people travel across borders around Eid al-Fitr. This study aims to grasp the effect of mass exodus between regions on active cases of COVID-19 through a mathematical perspective. We constructed a multiregional SIQRD (susceptible–infected–quarantined–recovered–death) model that accommodates the direct transfer of people from one region to others. The mobility rate was estimated using the proposed Dawson-like function, which requires data from an origin–destination matrix. Assuming that only susceptible, inapparently infected, and recovered individuals travel around Eid al-Fitr, the rendered model well-depicted the actual data at that time, giving either a significant spike or decline in the number of active cases due to the mass exodus. Most agglomerated regions such as Jakarta and Depok City experienced a fall in active case numbers, both in actual data and in the simulated model. However, most rural areas experienced the opposite, such as Bandung District and Cimahi City. This study confirmed that most travelers journeyed from big cities to the rural regions, and it scientifically demonstrated that mass mobility affects COVID-19 transmission between areas.

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 (Rt). Our results show the LSSR has been successfully suppressed the spread of COVID-19 in Jakarta, which was indicated by Rt<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.

When it comes to understanding the spread of COVID-19, recent studies have shown that pathogens can be transmitted in two ways: direct contact and airborne pathogens. While the former is strongly related to the distancing behavior of people in society, the latter are associated with the length of the period in which the airborne pathogens remain active. Considering those facts, we constructed a compartmental model with a time-dependent transmission rate that incorporates the two sources of infection. This paper provides an analytical and numerical study of the model that validates trivial insights related to disease spread in a responsive society. As a case study, we applied the model to the COVID-19 spread data from a university environment, namely, the Institut Teknologi Bandung, Indonesia, during its early reopening stage, with a constant number of students. The results show a significant fit between the rendered model and the recorded cases of infections. The extrapolated trajectories indicate the resurgence of cases as students’ interaction distance approaches its natural level. The assessment of several strategies is undertaken in this study in order to assist with the school reopening process.

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 (Rt). Our results show the LSSR has been successfully suppressed the spread of COVID-19 in Jakarta, which was indicated by Rt < 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.

The inclusion of the human mobility aspect is essential for understanding the behavior of COVID-19 spread, especially when millions of people travel across borders near Eid Al-Fitr. This study aims at grasping the effect of mass exodus among regions on the active cases of COVID-19 in a mathematical perspective. We construct a multi-region SIQRD (Susceptible-Infected-Quarantined-Recovered-Death) model that accommodates the direct transfer of people from one region to another. The mobility rate is estimated using the proposed Dawson-like function, which requires the Origin-Destination Matrix data. Assuming only susceptible, unapparent infected, and recovered individuals travel near Eid Al-Fitr, the rendered model is well-depicting the actual data at that time, giving either a significant spike or decline in the number of active cases due to the mass exodus. Most agglomerated regions like Jakarta and Depok City experienced the fall of active cases number, both in actual data and the simulated model. However, most rural areas experienced the opposite, like Bandung District and Cimahi City. This study should confirm that most travelers originated from big cities to the rural regions and scientifically justifies that massive mobility affects the COVID-19 transmission among areas.