key: cord-0599702-dzp18hs6 authors: Minoza, Jose Marie Antonio; Bongolan, Vena Pearl; Rayo, Joshua Frankie title: COVID-19 Agent-Based Model with Multi-objective Optimization for Vaccine Distribution date: 2021-01-27 journal: nan DOI: nan sha: ad9540fc2a65ff93b8e6aa049e667cd1628f68b8 doc_id: 599702 cord_uid: dzp18hs6 Now that SARS-CoV-2 (COVID-19) vaccines are developed, it is very important to plan its distribution strategy. In this paper, we formulated a multi-objective linear programming model to optimize vaccine distribution and applied it to the agent-based version of our age-stratified and quarantine-modified SEIR with non-linear incidence rates (ASQ-SEIR-NLIR) compartmental model. Simulations were performed using COVID-19 data from Quezon City and results were analyzed under various scenarios: (1) no vaccination, (2) base vaccination (prioritizing essential workers and vulnerable population), (3) prioritizing mobile workforce, (4) prioritizing elderly, and (5) prioritizing mobile workforce and elderly; in terms of (a) reducing infection rates and (b) reducing mortality incidence. After 10 simulations on distributing 500,000 vaccine courses, results show that prioritizing mobile workforce minimizes further infections by 24.14%, which is better than other scenarios. On the other hand, prioritizing the elderly yields the highest protection (439%) for the Quezon City population compared to other scenarios. This could be due to younger people, when contracted the disease, has higher chances of recovery than the elderly. Thus, this leads to reduction of mortality cases. The COVID-19 pandemic is an ongoing outbreak, caused by severe acute respiratory syndrome coronavirus 2 (so-called SARS-CoV-2). The outbreak was first reported in Wuhan, China in December 2019 [2] . Researchers around the world are working persistently to create a vaccine against COVID-19. As of December 28 2020, there were currently 15 COVID-19 vaccine candidates within Emergency Use Listing (EUL) evaluation at the World Health Organization (WHO) [16] . Now that vaccines are developed, it is very important to plan on how it will be distributed, given that the number of infections continue to rise. Prior to vaccine development, several countries implemented lockdown measures to address the current pandemic. Additionally, health experts recommended face masks and physical distancing as part of the comprehensive strategy to suppress virus transmission. In our previous work on age-stratified and quarantine-modified SEIR with non-linear incidence rates (ASQ-SEIR-NLIR) compartmental model [6, 15, 4] , these factors were considered by introducing the following parameters in the classic SEIR model (see : (i) quarantine Q(t), (ii) age-stratification U, and (iii) α and ε to represent behavioral and disease-resistance factors that disrupt transmission. In agent-based modeling (ABM), a system is modeled as a collection of autonomous decision-making entities called agents. Each agent individually assesses its situation and makes decisions on the basis of a set of rules. [3] The main advantage of using ABM is it could capture the emergent phenomena such as spread of the virus during interaction of agents. Second, developing ABM is flexible enough to design rules within the simulation environment. Thus, we tried to improve our existing model by transforming the ASQ-SEIR-NLIR model into ABM. It is known that during this pandemic, vaccines that will be developed will be limited. Given that COVID-19 pandemic has an incredible impact on global economic growth, there would not be enough purchasing power, especially in third world countries like the Philippines, to acquire vaccines. Thus, we need to devise a strategy for vaccination and identify what should be prioritized to equitably distribute this scarce supply. Combined with the ABM, a resource optimization model was proposed in this study to simulate possible decisions of policy makers and to help them identify appropriate strategies for their constituents. In this study, we converted the ASQ-SEIR-NLIR compartmental model [7, 16, 5] into an agent-based model to simulate people living in a common environment. We also developed a multi-objective linear programming model as a vaccine distribution priority optimization framework that aims to minimize further infections. After combining the two models, we explored different vaccination scenarios and analyzed their effects on the number of infections and the coverage of protection on the population. The primary data used in this study is the Philippines' Department of Health (DOH) COVID-19 Data Drop. Additionally, the published reports from Philippine Statistics Authority (PSA), such as The Women & Men in National Capital Region: 2018 Statistical Handbook First Edition [13] , NCR Gender Factsheet [12] , and 2020 RSET NCR [11] were also used for the vaccination distribution model. The area of interest for this study was Quezon City since it is considered as one of the "coronavirus hotspots" in the Philippines [9] . The ASQ-SEIR-NLIR compartmental model is described by the following equations: The parameters of the classic SEIR model are defined by the following: β is the rate of disease transmission due to infectious population, σ is the rate of progression from exposed to infectious (reciprocal of the incubation period), and γ is the recovery rate of infectious individuals (reciprocal of the infectious period). Additionally, we introduce Q(t) as quarantine factor [16] , which controls interactions between Susceptibles and Infected. U is age-stratified infection expectation [5] that serves as a damping factor for infections. Furthermore, we added Crowley-Martin incidence rates as nonlinear infection rates [7] α and ε, representing the inhibition effect due to susceptible and infectious population, respectively. For this model, it is assumed that all compartments of SEIR are well-mixed and interact homogeneously with each other. The coefficients β, σ and γ are considered immutable properties of the virus while α and ε are properties of the population S and I, respectively. To capture nuances in geographic distribution, we decided to transcribe the ASQ-SEIR-NLIR into an agent-based model. [13] Here in this study, Mesa [6] as an agent-based modeling framework was utilized. The proposed agent-based approach aims to emulate a closed society living in a shared finite environment, could be divided into states or districts and composed of Person agents with attributes corresponding to ASQ-SEIR-NLIR factors. From the classic SEIR, Removal is either via recovery with permanent immunity, or death. In summary: shown in table above was created. These input parameters will be used for initializing Person agents' attributes (see Age Restrictions, will not move and interact with others, having In Lockdown attribute set to true. Susceptible agents contacted with Persons having an Infected status will be under the Exposed status. During the incubation period, the age infection probability (based on Hubei incidence data_ will determine if the agent will be transferred to Infected status. Agents with Infected status could spread the virus until transmission rate probability is hit. Then, agents will be hospitalized and locked down in its current cell position. During the recovery period, an age stratified mortality rate based on the case incidence data will be calculated and will be used as probability for removed status, (recovered with permanent immunity or died). Vaccination of agents will only be implemented once, on a selected vaccination day implementation. A further assumption is 100% efficacy. Vaccines with less than 100% efficacy will have their doses divided, e.g., if a vaccine has only a 50% efficacy, the number of doses (courses) N will be N/2 . In literature, there are various optimization models [1, 8, 15] applied in allocation of healthcare resources, including vaccine distribution. Here in this study, we formulated a linear goal optimization or multi-objective linear programming model for equitable vaccine distribution. Multi-objective linear programming deals with multiple criteria decision making problems involving more than one objective function to be optimized simultaneously, subject to linear equality and inequality constraints. Particularly for this study, our main objective function is to maximize the available vaccine doses to be distributed to minimize the further spread of the virus infection. The formal problem addressed by the optimization model is as follows. Given the following inputs: • N , a limited number of vaccine doses (courses) that can be given to remaining susceptible populations; • L locations where the vaccine will be distributed; • A , age stratified percentage of the population for each L locations; • P, set of prioritization factors for each of the L locations; The model determined the optimal allocation of available vaccines and the corresponding distribution for each location. our goal is to maximize the vaccine to be allocated for each location l and further optimize given with the priority factors P for each location l It is important to determine the areas and priorities to make sure that vaccines are equitably distributed. Fair Priority Model [4] was proposed as an ethical framework for vaccine global allocation. Phase I of the Fair Priority Model would allocate vaccines in order to reduce premature deaths caused by COVID-19 directly or indirectly; Phase II would aim to stem serious economic and social harms; and Phase III would seek to reduce and ultimately end community transmission. Furthermore, vulnerable groups are an important factor to consider for equitable distribution of vaccines. The definition of "most vulnerable" in the society must not be limited to adults 65 years of age or older, persons with pre-existing comorbidities, and the economically deprived. Essential workers i.e in the medical field and other most at risk should be considered. [10] Given the PSA data for Quezon City, we used the following as Priority Factors (PF): Moreover, the mobile workforce could be considered an important group especially this pandemic since various essential areas, such as public market and grocery, were limited for access and supply of necessities were becoming scarce. It is presumed that these workers could help in spreading the disease further, thus it is necessary to prioritized them for minimizing the number of infections. From the NCR Gender Factsheet [11] , the following mobile workforce were considered: agriculture, construction, wholesale and retail trade, transportation and storage, and accommodation and food service activities. It is known that the number of comorbid diseases increases with age. Therefore, prioritizing elderly could help in reducing mortality incidence (providing protection to the population). Since in the Fair Priority Model, Phase I aims to reduce premature deaths and Phase II concerns about reducing serious economic and social deprivations, we analyzed the effect of different combinations of priority factors in terms of following objectives: i. Minimizes the Number of Infections (Phase II) ii. Provides Highest Protection to the Population (Phase I) For model experimentations, we consider the following scenarios: (1) no vaccination (control), (2) base vaccination, (3) prioritizing mobile workforce, (4) prioritizing elderly, and (5) prioritizing mobile workforce and elderly. In this study, we consider the priority factors 1-4, as the base vaccination scenario, being the first concern during the implementation of vaccination distribution. In scenario 3 and 4, priority factor 5 and 6 was added to the base vaccination scenario, respectively. For scenario 5, all priority factors were considered. To measure scenarios in terms of the objective, 10 simulation runs were conducted. In minimizing the number of infections objective, decrease in number of infected agents relative to the control scenario is computed. Meanwhile in providing highest protection to the population, the number of recovered and vaccinated agents relative to the control scenario is calculated. For the simulation of the model, 10 On the other hand, infected agents for Prioritizing Mobility scenario average peaked at 82, complimenting with the results presented in Table 2 . Addressing the challenges to immunization practice with an economic algorithm for vaccine selection Clinical features of patients infected with 2019 novel coronavirus in Wuhan Agent-based modeling: Methods and techniques for simulating human systems An ethical framework for global vaccine allocation Modeling the dynamics of COVID-19 using Q-SEIR model with age-stratified infection probability". medRxiv Utilizing Python for Agent-Based Modeling: The Mesa Framework Protection after Quarantine: Insights from a Q-SEIR Model with Nonlinear Incidence Rates Applied to COVID-19 A linear goal programming model for human resource allocation in a health-care organization Makati, Quezon City remain as virus hotspots The Covid-19 Vaccine-Development Multiverse Philippine Statistics Authority (PSA). 2020 RSET NCR NCR Gender Factsheet The Women & Men in National Capital Region The Epidemiology Workbench: a Tool for Communities to Strategize in Response to COVID-19 and other Infectious Diseases Integer/linear mathematical programming models: a tool for allocating healthcare resources Age-stratified Infection Probabilities Combined with Quarantine-Modified SEIR Model in the Needs Assessments for COVID-19 Status of COVID-19 Vaccines within WHO EUL/PQ evaluation process. Guidance Document The authors would like to thank Prof. Roselle Leah K Rivera, Dr. Jesus Emmanuel Sevilleja, Dr.Romulo de Castro, and Dr. Salvador E. Caoili for their insightful comments during the modelling process. The authors would like to give gratitude to the efforts of undergraduate students, Karina Kylle Ang and Jimuel Celeste, for the development of ABM in the Mesa framework. The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. The authors declare that they have no competing interests. The author(s) received no specific funding for this work.