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Without vaccines and medicine, non-pharmaceutical interventions (NPIs) such as social distancing, have been the main strategy in controlling the spread of COVID-19. Strict social distancing policies may lead to heavy economic losses, while relaxed social distancing policies can threaten public health systems. We formulate an optimization problem that minimizes the stringency of NPIs during the prevaccination and vaccination phases and guarantees that cases requiring hospitalization will not exceed the number of available hospital beds. The approach utilizes an SEIQR model that separates mild from severe cases and includes a parameter {micro} that quantifies NPIs. Payoff constraints ensure that daily cases are decreasing at the end of the prevaccination phase and cases are minimal at the end of the vaccination phase. Using the penalty method, the constrained minimization is transformed into a non-convex, multi-modal unconstrained optimization problem, which is solved using a metaheuristic algorithm called the improved multi-operator differential evolution. We apply the framework to determine optimal social distancing strategies in the Republic of Korea given different amounts and types of antiviral drugs. The model considers variants, booster shots, and waning of immunity. The optimal {micro} values show that fast administration of vaccines is as important as using highly effective vaccines. The initial number of infections and daily imported cases should be kept minimum especially if the severe bed capacity is low. In Korea, a gradual easing of NPIs without exceeding the severe bed capacity is possible if there are at least seven million antiviral drugs and the effectiveness of the drug in reducing disease severity is at least 86%. Model parameters can be adapted to a specific region or country, or other infectious disease. The framework can also be used as a decision support tool in planning practical and economic policies, especially in countries with limited healthcare resources. Mathematics Subject Classification34A55, 34H05, 90C26, 92-10
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Coronavirus disease 2019 (COVID-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2. Millions of people have fallen sick, and some have died due to this affliction that has spread across the globe. The current pandemic has disrupted normal day-to-day human life, causing a profound social and economic burden. Vaccination is an important control measure that could significantly reduce the incidence of cases and mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered, namely: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission and reporting rates are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.
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IntroductionAt the start of the pandemic, the Philippine capital Metro Manila was placed under a strict lockdown termed Enhanced Community Quarantine (ECQ). When ECQ was eased to General Community Quarantine (GCQ) after three months, healthcare systems were soon faced with a surge of COVID-19 cases, putting most facilities at high or critical risk and prompting a return to a stricter policy. MethodsWe developed a mathematical model considering behavior changes and underreporting to represent the first major epidemic wave in Metro Manila. Key parameters were fitted to the cumulative cases in the capital from March to September 2020. A bi-objective optimization problem was formulated that allows easing of restrictions at an earlier time and minimizes the necessary additional beds to ensure sufficient capacity in healthcare facilities once ECQ was lifted. ResultsIf behavior was changed one to four weeks earlier before GCQ, then the cumulative number of cases can be reduced by up to 55% and the peak delayed by up to four weeks. Increasing the reporting ratio during ECQ threefold may increase the reported cases by 23% but can reduce the total cases, including the unreported, by 61% on June 2020. If GCQ began on May 28, 2020, 48 beds should have been added per day to keep the capacity only at high-risk (75% occupancy). Among the optimal solutions, the peak of cases is lowest if ECQ was lifted on May 20, 2020 and with at least 56 additional beds per day. ConclusionSince infectious diseases are likely to reemerge, the formulated model can be used as a decision support tool to improve existing policies and plan effective strategies that can minimize the socioeconomic impact of strict lockdown measures and ensure adequate healthcare capacity.
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BackgroundEarly vaccination efforts and non-pharmaceutical interventions were insufficient to prevent a surge of coronavirus disease 2019 (COVID-19) cases triggered by the Delta variant. This study aims to understand how vaccination and variants contribute to the spread of COVID-19 so that appropriate measures are implemented. MethodsA compartment model that includes age, vaccination, and infection with the Delta or non-Delta variants was developed. We estimated the transmission rates using maximum likelihood estimation and phase-dependent reduction effect of non-pharmaceutical interventions (NPIs) according to government policies from 26 February to 8 October 2021. We extended our model simulation until 31 December considering the initiation of eased NPIs. Furthermore, we also performed simulations to examine the effect of NPIs, arrival timing of Delta variant, and speed of vaccine administration. ResultsThe estimated transmission rate matrices show distinct pattern, with the transmission rates of younger age groups (0 39 years) much larger than non-Delta. Social distancing (SD) level 2 and SD4 in Korea were associated with transmission reduction factors of 0.64 to 0.69 and 0.70 to 0.78, respectively. The easing of NPIs to a level comparable to SD2 should be initiated not earlier than 16 October to keep the number of severe cases below the capacity of Koreas healthcare system. Simulation results also showed that a surge prompted by the spread of the Delta variant can be prevented if the number of people vaccinated daily was larger. ConclusionsSimulations showed that the timing of easing and intensity of NPIs, vaccination speed, and screening measures are key factors in preventing another epidemic wave. 2 Key MessagesO_LIMaximum likelihood estimation can be utilized to determine the transmission rates of the Delta and non-Delta variants. C_LIO_LIThe phase-dependent NPIs implemented by the Korean government were effectively quantified in the modelling study. C_LIO_LIEven with fast vaccination, resurgence of cases is still possible if NPIs are eased too early or screening measures are relaxed. C_LIO_LIThe model can be used as a guide for policy makers on deciding appropriate SD level that considers not only disease control, but also the socio-economic impact of maintaining strict measures. C_LI
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In this work, we present an approach to determine the optimal location of coronavirus disease (COVID-19) vaccination sites at the municipal level. We assume that each municipality or town is subdivided into smaller administrative units, which we refer to as villages or barangays. The proposed method solves a minimization problem arising from a facility location problem, which is formulated based on the proximity of the vaccination sites to the villages, number of COVID-19 cases, and population densities of the villages. We present a numerical scheme to solve the optimization problem and give a detailed description of the algorithm, which is coded in Python. To make the results reproducible, the codes used in this study are uploaded to a public repository, which also contains complete instructions on how to use them. As an illustration, we apply our method in determining the optimal location of vaccination sites in San Juan, a town in the province of Batangas, in the Philippines. We hope that this study may guide the local government units in coming up with strategic plans for the COVID-19 vaccine rollout.
