A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia

• Published in: Chaos, solitons and fractals Vol. 139; p. 110042
• Main Authors: Aldila, Dipo, Khoshnaw, Sarbaz H.A., Safitri, Egi, Anwar, Yusril Rais, Bakry, Aanisah R.Q., Samiadji, Brenda M., Anugerah, Demas A., GH, M. Farhan Alfarizi, Ayulani, Indri D., Salim, Sheryl N.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-10-2020
• Subjects: Asymptomatic cases; Backward bifurcation; Basic reproduction number; COVID-19; Rapid test; Social distancing; COVID-19; Basic reproduction number; Rapid test; 92D30; Asymptomatic cases; Social distancing; Backward bifurcation; 34D05
• ISSN: 0960-0779; 1873-2887; 0960-0779
• DOI: 10.1016/j.chaos.2020.110042

•Epidemic model for COVID-19.•Consider asymptomatic (hidden) cases, limited hospital capacity, social distancing, rapid test assessment, and isolation/quarantine.•Jakarta incidence data used for validation. The data consist of two types of infected individuals: isolated at home, and treated in the hospital.•Backward bifurcation occurs as a consequence of the low capacity of the hospital.•Analyzing the possible impact on the Jakarta government’s plan to “relaxing” the social distancing policy.
The aim of this study is to investigate the effects of rapid testing and social distancing in controlling the spread of COVID-19, particularly in the city of Jakarta, Indonesia. We formulate a modified susceptible exposed infectious recovered compartmental model considering asymptomatic individuals. Rapid testing is intended to trace the existence of asymptomatic infected individuals among the population. This asymptomatic class is categorized into two subclasses: detected and undetected asymptomatic individuals. Furthermore, the model considers the limitations of medical resources to treat an infected individual in a hospital. The model shows two types of equilibrium point: COVID-19 free and COVID-19 endemic. The COVID-19-free equilibrium point is locally and asymptotically stable if the basic reproduction number (R0)is less than unity. In contrast, COVID-19-endemic equilibrium always exists when R0>1. The model can also show a backward bifurcation at R0=1whenever the treatment saturation parameter, which describes the hospital capacity, is larger than a specific threshold. To justify the model parameters, we use the incidence data from the city of Jakarta, Indonesia. The data pertain to infected individuals who self-isolate in their homes and visit the hospital for further treatment. Our numerical experiments indicate that strict social distancing has the potential to succeed in reducing and delaying the time of an outbreak. However, if the strict social distancing policy is relaxed, a massive rapid-test intervention should be conducted to avoid a large-scale outbreak in the future.