key: cord-0959437-otqs17bw authors: Buhat, C. A. H.; Lutero, D. S.; Olave, Y. H.; Quindala, K. M.; Recreo, M. G. P.; Talabis, D. A. S.; Torres, M. C.; Tubay, J. M.; Rabajante, J. F. title: Optimal Allocation of COVID-19 Vaccines in the Philippines date: 2021-02-18 journal: nan DOI: 10.1101/2021.02.12.21251640 sha: ce56206c413729b4af0801bad19cf8140ef4a632 doc_id: 959437 cord_uid: otqs17bw Vaccine allocation is a national concern especially for countries such as the Philippines that have limited resources in acquiring COVID-19 vaccines. As such, certain groups are suggested to be prioritized for vaccination to protect the most vulnerable before vaccinating others. Our model suggests an allocation of vaccines such that COVID-19 deaths are minimized while the prioritization framework is satisfied. Results of the model show that a vaccine coverage of at least 50 to 70% of the population can be enough for a community with limited supplies, and an increase in vaccine supply is beneficial if initial coverage is less than the specified target range. Also, among the vaccines considered in the study, the one with 89.9% effectiveness and has a 183 Philippine peso (Php) price per dose projected the least number of deaths. Compared to other model variations and common allocation approaches, the model has achieved both an optimal and equitable allocation. This will be helpful for policymakers in determining a vaccine distribution for a resource-constrained community. The coronavirus disease 2019 (COVID-19) is a novel beta-coronavirus that was initially identified to cause respiratory problems among people from a province in China in late 2019 [1] . It is a viral infection transmitted through respiratory particles, fomites, and other biological matter [2] . Beta-coronaviruses have caused outbreaks in the recent decades, with COVID-19 being characterized as a pandemic by the World Health Organization on the first quarter of 2020 [3, 4] . The Philippines is one of the countries greatly affected by this pandemic [5] . Its government placed the country under community lockdown since March 2020 as a measure to control the spread of the virus [6] . The continuous lockdown contributed to the increase in unemployment rate (10.4 percent as of December 2020) [7] , decrease in remittance inflow (14-20 percent) [8] , and decrease in GDP (9.5 percent decline in 2020) [9] . Bringing back jobs is crucial for a sustainable recovery of the economy [10] . All these will be possible when the COVID-19 spread is controlled. Vaccination is considered to be an effective tool in preventing the spread of and deaths due to infectious diseases [11, 12] . Vaccine development takes years to complete from clinical trials to manufacturing [13] . Vaccinating huge groups is another problem entirely. Vaccines have specific storage and shipment requirements to maintain its effectiveness [14] . Once vaccines are available for COVID-19, frontline workers should be vaccinated first followed by the elderly and people with preexisting conditions, according to various government protocols [15] . The Philippine government plans to follow the same prioritization of people for vaccination but with the addition of indigenous people and uniformed personnel in the list [16] . The plan is also to prioritize those from the cities to expedite the recovery of the local economy [17] . Distribution of vaccines will be done through local government units (LGU). Since the vaccines are limited, proper allocation of doses for each LGU is important. An optimal allocation can be found by looking at the problem as an optimization problem that minimizes the number of deaths and follows the prioritization approved by the government. In this paper, a linear programming (LP) model is formulated to determine the optimal allocation of vaccines for every city or province in the country. The succeeding parts of the paper presents the model formulation where the parameters and assumptions of the model are discussed, followed by the results and discussion where the optimal allocation for different cases are presented together with the sensitivity analysis and parameter analysis. The LP for vaccine allocation model in this paper aims to minimize deaths while satisfying the prioritization of certain groups for vaccination as suggested by the government. The formulation of the objective function and constraints are presented. Throughout the paper, we denote the city or province where the individuals are residing as locality i. The objective function value is interpreted as the projected additional COVID-19 deaths after the rollout of vaccines. It is formulated as a summation of multiplicative expressions involving the following parameters. To estimate the number of individuals for vaccination in each locality i, the locality population size N i , total current locality COVID-19 cases C i , number of individuals for vaccination m i , and the effectiveness rate of the vaccine eff are needed. The estimate is given by In the model, N i is based on the forecasted 2020 population of the Philippines from the 2015 Philippine Statistics Authority Census [18] while C i is the total COVID-19 cases in the Philippines (as of 10 November 2020) from the DOH Data Drop [19] . For the decision variable m i , individuals that have already been previously infected are assumed to either be expired cases or recovered cases. For the recovered cases, they obtain a certain degree of immunity to COVID-19 [20] . This suggests that infected individuals can be excluded from the individuals for vaccination, which should be less than N i − C i , to further stretch the distribution of vaccines in many localities [21] . The maximum outbreak size [22] is computed by multiplying the number of individuals susceptible to the virus to where R 0i is the maximum reproduction number recorded per locality i. In the model, the maximum reproduction number recorded per locality i as of 11 November 2020 from [23] are used. Note that some localities recorded very high maximum reproduction number despite its small number of cases due to its small population [24] . Thus, we set max{R 0i } = 4 to be the maximum reproduction number to be considered in this study [25] . A scaling contact coefficient described as is included to incorporate the contact rate with effect of interventions, and population density δ i of each locality i [26] . The coefficient gives the probability of contact in the population, which is nonlinearly proportional to the population density in that locality. This coefficient characterizes the heterogeneous distribution of cases in spatial scale, which relaxes the well-mixing (homogeneity) assumption in the epidemiological model. [27, 28] . This heterogeneity in infected cases as well as deaths can be observed in Philippine setting as shown in our data dashboard (https://datastudio.google.com/s/uCv8ZX2rI8w). The following are parameters needed for the constraints of the LP model: Due to the initial limited amount of vaccines that the country can obtain, priority groups were set by the Philippine government. These include the frontline health workers and uniformed personnel, due to their higher risk of exposure while on duty, and the senior citizens and indigent population, due to their vulnerability and by the principle of equity [29, 21] . To cater the priority groups set by the government, G i is set to be the number of individuals belonging to the priority group per locality i. This is set to be the minimum number of individuals for vaccination per locality. A crucial factor for resource-constrained countries is the vaccination expense [30] . Some countries are considering multiple vaccines. Total expenses should be less than or equal to the allotted budget B. In the Philippines, the approved national budget for vaccines is 72.5 billion Philippine pesos (PHP) [31] which will cover vaccine dosage costs as well as cost of training per vaccinator (1200 PHP) and cost of other peripherals such as masks, face shield, alcohol and cotton balls (1924 PHP for 2 doses), both of which are good for 350 people [32] . The total vaccination cost is defined as where P is the price per complete dose of the COVID-19 vaccine. 2 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The linear programming (LP) model formulated to determine the optimal distribution of vaccines among localities in the Philippines is described below. where d i is the COVID-19 fatality rate per locality i, and V is the total available complete doses of vaccine for allocation across the country. The aim of this model is to find an optimal allocation that minimizes the projected number of additional COVID-19 deaths in each locality i such that (i) the total number of vaccines for allocation in each locality i will not exceed the total number of available vaccines, (ii) the individuals for vaccination per locality i will not include the number of individuals that have already been infected, (iii) all members of the priority groups in each locality i will be vaccinated, and (iv) the total cost of vaccines that will be used will not exceed the budget allocation. The LP model was used to compute for the optimal allocation under different approaches that minimizes COVID-19 deaths while satisfying the prioritization set by the government. Sensitivity analysis, effects of changes in levels of vaccine supply, vaccine effectiveness, and costs of vaccine were also studied. Budget is a huge consideration in a vaccination program so it is only fitting to study the effects of budget in vaccine allocation. The approaches where budget is considered (limited supplies and budget) and when it is not (limited supplies only) are explored in this section, with the latter approach being the basis for Sections 3.2 and 3.3. For both approaches, it is assumed that the total number of vaccines for allocation is equal to 50% of the total population, and that the effectiveness rate of the vaccine is 90%, with 2379 PHP as its cost per complete dose (similar to a market-available vaccine of 90% efficacy). 3 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint Results show that the total number of complete vaccinations to be distributed across the country is 30,361,078 when budget is considered and 54,973,950 when it is not, with corresponding deaths of 17,053 and 6,795, respectively. This translates to an average of 562 and 123 deaths per million vaccines, respectively. The more realistic scenario where budget and supplies are limited is shown in Figures 1.b, 1 .d. This case has less vaccine allocation ergo more deaths, hence, supporting the need for greater budget to achieve less deaths. Furthermore, notice from Figure 1 that localities with the greater share of vaccines still resulted in large projected deaths. This can be explained by the population density and fatality risk in the locality which drives the increase in projected deaths. Sensitivity analysis on the vaccine supply shows that, ceteris paribus, for every 1,000,000 units of increase in vaccine supply, deaths will only decrease by 112. If additional vaccines will be acquired, the best option for every unit of increase in supply should be to allocate it to Manila since for every 1000 additional vaccine allocations in Manila, projected deaths will decrease by around 5. Total vaccine supply, vaccine effectiveness, vaccine cost, and projected deaths are seen as important factors that influence vaccine allocation. Pairwise comparison of different levels of these factors are presented. Other approaches in allocating the vaccine are also studied and discussed below. The total vaccines to be allocated are varied from 20-100% of the total population, and the effectiveness rate of vaccines from 50-100% in the LP model without budget consideration. Note that 20% is assumed in the model to be the minimum total vaccines for allocation to accommodate all priority groups [29] , and 50% to satisfy the minimum efficacy rate for COVID-19 vaccines [33] . Figure 2 shows that the greater the number of people for vaccination coupled with a high vaccine effectiveness rate, the lesser the number of additional deaths that might occur. This is an expected result. The ideal setup in a nationwide vaccination program is to maximize both factors. Unfortunately, not all countries have the resources to provide 100% coverage using the vaccine with the highest effectiveness rate. However in the heat map, notice the blue and red regions. Assume that the blue squares represent the low projected deaths and the red squares represent the high projected deaths. With low coverage of vaccination, even if there is 100% effectiveness, it will result to a red square (high number of cases). But as the coverage increases, the less minimum effectiveness necessary to achieve a blue square (low number of cases). In fact, according to the results of [34] , to stop an ongoing epidemic, it is recommended that the minimum efficacy of the vaccine should be 60% when coverage is 100%, and at least 80% when coverage falls to 75%, to reduce the peak of the epidemic. Both cases fall under the blue region, among other efficacy-coverage combinations, which are feasible in the Philippines since protection and interventions will still be implemented even after vaccination [35] . We further investigate the behavior of the percentage of vaccinated population and vaccine effectiveness as they increase. . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint From Figure 3 .a, the projected deaths slowed down at around 20-40% and after 50-70%, the effect of increasing in percentage of population vaccinated is minimal. This explains the low decrease in deaths from Section 3.2, despite the huge increase in units of vaccine supply. A reason for this is since 50-70% is near the 1 − 1 R 0 threshold for immunization coverage of the country, assuming that R 0 is at a maximum [36] . This makes for a good target for countries with insufficient resources to vaccinate all of its constituents. Meanwhile, in Figure 3 .b, the vaccine effectiveness increases have been shown to have a linear relationship with the projected deaths. That is, a vaccine with a higher effectiveness rate always generate lower deaths. Vaccine effectiveness rates should be maximized as much as possible when deciding on what vaccine should be procured. Also, notice the change in slope as the objective function value decreases, which implies that the higher the objective function value (additional deaths), the less the effect of increasing the effectiveness of the vaccine, which is derivative from the result from Figure 2 where the blue region gets larger as the number of population to be vaccinated increases, and the number of deaths decreases. Another key factor in determining what vaccine to use is the cost of the vaccine. Each vaccine has its own price per dose, required vaccine dose per person, and efficacy rate ( as the effectiveness rate). These factors are used for comparative analysis of the vaccines. Among the vaccines, vaccines 1, 2 and 7 can provide 100% national coverage, i.e., vaccinate all 110 million+ residents of the country. All but vaccine 4 can fulfill the prioritization of certain groups identified by the government. Vaccine 2 generated the lowest projected number of additional deaths compared to the other vaccines. This is due to its high effectiveness rate and significantly low price per dose. Vaccines 3 and 4 can only cover 28% and 16% of the population, respectively, and have high death projections despite having high vaccine effectiveness due to its high cost per dose. Thus, a significant increase in the total budget for vaccination will drastically decrease their additional death projections (see Figure 3 ). Multiple countries use different approaches in distributing vaccines in their community. The table below shows the other approaches for vaccine allocation that can also be adapted, including the one presented in Section 3.1. 6 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint The first approach that considers the allocated budget for vaccines presents the likely scenario in the Philippine setting, while the remaining approaches (without budget constraint), can be viewed as approaches that have equal budget allotment and are thus comparable sans budget constraint. The first two cases in Table 1 are those presented in Section 3.1. The third approach assumes that the R 0 in every locality i is 4 (maximum) to further estimate what to expect if R 0 gets bigger. As expected, there is greater projected deaths even with slight changes in the allocation per locality. If the lower bound is removed as in the fourth approach, it would result in even less deaths. However, this is unequitable since many localities will not receive vaccines. The next three approaches follow allocations based on proportionality, say, if a country will allocate the vaccine based on the population size of the locality, then the vaccine allocation will be proportional to the population of that locality. Note that allocations per locality cannot exceed the N i − C i susceptible population of that province. Allocating vaccines based on population size resulted to the most number of death projections, while allocating based on the number of infections generated the least. None among the three proportion allocations had better results compared to the LP model result without budget consideration. The last approach assumes equal allocation among localities regardless of factors considered in the previous three approaches. This, in turn, results in the most number of additional deaths, and thus, is the least ideal way to allocate the vaccines since it does not consider the difference in fatality rates, infections, dynamics on each locality. Comparing the budget-constrained approaches, the LP model result in the second approach is the best in terms of minimizing the number of deaths and equitable considerations. COVID-19 vaccine allocation is an immediate concern globally. An LP model is used to study vaccine allocation that aims to minimize deaths while satisfying group prioritization for immediate vaccination. Various approaches were studied, all of which assumed using a vaccine with 90% effectiveness rate to be used for at most 50% of the population. Sensitivity analysis shows that if only vaccine supply is limited and budget is not a constraint, Deaths will decrease by 112 for every 1 million vaccines. This figure is less than the average deaths per million vaccines for the non-budget constrained approach. As seen in Section 3.3, when vaccine coverage is between 50 to 70% which is the case for the non-budget constrained approach, decrease in deaths will not be as apparent as when coverage is less than the specified range. Additional vaccines beyond the optimal allocation therefore will be beneficial in decreasing deaths only if the vaccine coverage is less than 50%. Various vaccines were also studied in terms of their associated costs and effectiveness, and determined that the vaccine with 89.9 % effectiveness and 183 PHP price per dose results to the lowest projected deaths. We then compared our result to various model variations and common allocation approaches, upon which our model achieved both optimal and a more equitable allocation. Among the approaches that countries can adapt, the approach using our vaccine allocation model projects the least amount of deaths while upholding equitable considerations. Although proportional allocation according to number of infections can 7 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; be done more conveniently, allocation will not yield minimal deaths. Our model thus can be used by policymakers since minimization of casualties is a humane priority. Furthermore, our model provides insight on the localities that should be prioritized when additional vaccine doses become available. Using our model can help policymakers in distributing COVID-19 vaccines, especially if their resources are limited. The model can be applied not just to countries but also to communities, assuming the situations and health systems are similar. By having an optimal and equitable distribution of vaccines, resources are well-utilized and not wasted. Having sufficient data, the model can also be adapted to other similar infectious diseases, and can be used as basis in future distributions. Note however, that the study is limited to the use of one vaccine type only, which is not the case in some countries, and should be explored in future extensions of the study. It is also good to incorporate other factors such as new COVID-19 strains, dynamic herd immunity, group-specific infection rates and other dynamics, clinical trial results of vaccines, differential vaccine transportation costs and storage facilities, among other factors. JFR is supported by the Abdus Salam International Centre for Theoretical Physics Associateship Scheme. This research is funded by the UP System through the UP Resilience Institute. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint 12 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint 18 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint Appendix D projected 2020 population size of locality i C i number of recovered/ expired COVID-19 cases in locality i as of 11/10/2020 m i number of vaccinated individuals in locality i eff effectiveness rate of the vaccine R 0i maximum reproduction number recorded in locality i as of 11/11/2020 δ i population density of locality i d i case fatality rate per locality i as of 11/10/2020 V total available complete doses of vaccine for allocation across the country G i number of individuals belonging to the priority group in locality i P price per complete dose of vaccine B total allotted budget for vaccination 26 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted February 18, 2021. ; https://doi.org/10.1101/2021.02.12.21251640 doi: medRxiv preprint Coronavirus disease (COVID-19) Situation Report 1 Philippines 9 Transmission of SARS-CoV-2: implications for infection prevention precautions COVID-19 Vaccine: A comprehensive status report World Health Organization. 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The Scaling of Contact Rates with Population Density for the Infectious Disease Models Optimal Allocation of COVID-19 Test Kits Among Accredited Testing Centers in the Philippines High contagiousness and rapid spread of severe acute respiratory syndrome coronavirus 2 FAQS: Vaccines. 2020. url: https : / / doh . gov . ph / faqs / vaccines# :~: text = Frontline % 5C % 20health % 5C % 20workers%5C%2C%5C%20senior%5C%20citizens,9 Vaccination program in a resource-limited setting: A case study in the Philippines Which COVID-19 vaccine is most cost-friendly for PH government? DOH: 50 % vaccine efficacy is OK Vaccine Efficacy Needed for a COVID-19 Coronavirus Vaccine to Prevent or Stop an Epidemic as the Sole Intervention Here's Why Vaccinated People Still Need to Wear a Mask Herd Immunity": A Rough Guide Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. City Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Iloilo (excluding Iloilo City) Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Alloc. Misamis Oriental (excluding Cagayan de Oro City)