Modeling and Prediction of COVID-19 with a Large Scale Social Distancing

Abstract

Coronavirus 2019 (COVID-19), yang kasusnya dimulai di Cina, dalam kurun waktu dua bulan telah menyebar dengan cepat ke lebih dari 114 negara dan territorial. Pemahaman tentang dinamika penularan Covid-19 sangat penting untuk menentukan kebijakan dan strategi dalam pengobatan dan pengendalian penyebaran penyakit ini. Dalam makalah ini, disusun model matematika yang menggambarkan dinamika penularan penyakit menggunakan model matematika deterministik dengan menggunakan data penyebaran COVID-19 di Jakarta, Indonesia dari 3 Maret 2020, hingga 10 April 2020. Model berbentuk Sistem persamaan diferensial yang selanjutnya dilakukan analisis matematika dan simulasi numerik. Hasil simulasi menunjukkan bahwa tanpa intervensi, angka reproduksi penyebaran Covid-19 di Provisi Jakarta sekitar 1,658 dan jika Pembatasan Sosial Berskala Besar (PSBB) diimplementasikan, maka angka reproduksinya turun menjadi 1,40. Lebih lanjut, epidemi diperkirakan akan berakhir sekitar akhir November 2020 dengan kasus puncak pada pertengahan Juni 2020 dengan jumlah orang yang dikonfirmasi positif terinfeksi mencapai sekitar 9.000 jiwa. Dari hasil pemodelan ini, disimpulkan bahwa untuk meminimalkan penularan penyakit, perlu menerapkan kebijakan dan kontrol yang lebih ketat.
 [Coronavirus disease 2019 (COVID-19) which was initiated in China, has spread rapidly in more than 114 countries and territories over the last two months. An understanding of the dynamics of Covid-19 transmission is very important to determine policies and strategies in the treatment and control of the spread of this disease. In this paper, we formulated a mathematical model that describes the transmission dynamics of the disease using a deterministic mathematical model and the model is validated against data from Jakarta, Indonesia from March 3, 2020, to April 10, 2020. Mathematical analysis and numerical simulations are presented. We found that without intervention, the reproduction number is around 1.658 and the reproduction number declines to 1.40 if large scale social distancing is implemented. Furthermore, the end time of epidemic is predicted to be around the end of November 2020 with peak cases around mid-June 2020 and the number of confirmed infected individuals is around 9,000. To minimize the transmission of the diseases, it is necessary to enforce strict policies and controls.]

Optimal Control and Cost-Effectiveness Analysis in An Epidemic Model with Viral Mutation and Vaccine Intervention

“…Now, we calculate the total cost invested and total infected averted in each strategy to analyze the cost-effectiveness. Using the formula (12), we find that Strategy I has the smallest ACER value and Strategy II has the largest ACER value, as seen in Figure 4. The results are also given in Table 1.…”

“…Beside targeting vaccinations, the Government is currently implementing Community Activity Restrictions (PPKM) to control the spread of the COVID-19 outbreak. Many mathematical models of COVID-19 have also been developed, as in [5], [8]- [12].…”

Optimal Control Mathematical Model of Covid-19 With Social Distancing and Therapy Effect Strategies

“…Pontryagin's minimum principle is an optimal control that must be solved, namely state, costate and their transversality, and stationary equations. It states that Hamiltonian equation will be minimized as long as 𝒰 [5]. By using Pontryagin's minimum principle, the constrained optimization problem can be transformed…”

“…for example, [3] focused on applying PPKM to restrict interactions between individuals and quarantine infected people to reduce the number of sufferers during COVID-19. besides that, [4], [5] modeling the transmission of COVID-19 disease to suppress the spread of the disease and reduce the contact rate by implementing PSBB. In [6], focus on modeling the spread of COVID-19 disease by wearing a health mask and quarantine.…”

An epidemic model with viral mutations and vaccine interventions

“…Especially in COVID-19, various models involving intervention strategies have been developed by many researchers. Modeling the spread of COVID-19 with the policies of social isolation, lockdown, or social distancing and travel restrictions have been studied in [21][22][23][24][25][26][27]. Meanwhile, the COVID-19 model that considers vaccination as a treatment intervention can be studied in [28][29][30][31].…”