This paper studies a class of power-law kinetics, PL-ILK, for whose subset, PL-TIK, analogues of the Deficiency Zero Theorem and the Deficiency One Theorem (DOT) for mass action systems are valid. The DOT also includes the necessary and sufficient condition of Boros for uniqueness in the non-weakly reversible case. To our knowledge, this is the first set of kinetics beyond mass action kinetics (MAK) for which the DOT has been shown to be valid. A further interesting property of PL-TIK is a certain "robustness" relative to dependence of linkage classes: existence of a positive equilibrium for each linkage class implies the existence of a positive equilibrium for the whole network. For MAK systems, the PL-ILK property is equivalent to the reactant deficiency of the linkage class containing the zero complex being one, and zero for all other linkage classes. As shown in the Supplementary Materials, an initial survey of MAK and BST systems already reveals numerous examples with PL-ILK kinetics.

Background Responses of subnational government units are crucial in the containment of the spread of pathogens in a country. To mitigate the impact of the COVID-19 pandemic, the Philippine national government through its Inter-Agency Task Force on Emerging Infectious Diseases outlined different quarantine measures wherein each level has a corresponding degree of rigidity from keeping only the essential businesses open to allowing all establishments to operate at a certain capacity. Other measures also involve prohibiting individuals at a certain age bracket from going outside of their homes. The local government units (LGUs)–municipalities and provinces–can adopt any of these measures depending on the extent of the pandemic in their locality. The purpose is to keep the number of infections and mortality at bay while minimizing the economic impact of the pandemic. Some LGUs have demonstrated a remarkable response to the COVID-19 pandemic. The purpose of this study is to identify notable non-pharmaceutical interventions of these outlying LGUs in the country using quantitative methods. Methods Data were taken from public databases such as Philippine Department of Health, Philippine Statistics Authority Census, and Google Community Mobility Reports. These are normalized using Z-transform. For each locality, infection and mortality data (dataset Y) were compared to the economic, health, and demographic data (dataset X) using Euclidean metric d=(x−y)2, where x∈X and y∈Y. If a data pair (x,y) exceeds, by two standard deviations, the mean of the Euclidean metric values between the sets X and Y, the pair is assumed to be a ‘good’ outlier. Results Our results showed that cluster of cities and provinces in Central Luzon (Region III), CALABARZON (Region IV-A), the National Capital Region (NCR), and Central Visayas (Region VII) are the ‘good’ outliers with respect to factors such as working population, population density, ICU beds, doctors on quarantine, number of frontliners and gross regional domestic product. Among metropolitan cities, Davao was a ‘good’ outlier with respect to demographic factors. Conclusions Strict border control, early implementation of lockdowns, establishment of quarantine facilities, effective communication to the public, and monitoring efforts were the defining factors that helped these LGUs curtail the harm that was brought by the pandemic. If these policies are to be standardized, it would help any country’s preparedness for future health emergencies.

Background 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. Objective The study aims to determine an optimal and equitable allocation of COVID-19 vaccines in the Philippines that will minimize the projected number of additional COVID-19 deaths while satisfying the priority groups for immediate vaccination. Methods In this study, a linear programming model is formulated to determine an allocation of vaccines such that COVID-19 deaths are minimized while the prioritization framework set by the government is satisfied. Data used were collected up to November 2020. Total vaccine supply, vaccine effectiveness, vaccine cost, and projected deaths are analyzed. Results of the model are also compared to other allocation approaches. Results Results of the model show that a vaccine coverage of around 60-70% of the population can be enough for a community with limited supplies, and an increase in vaccine supply is beneficial if the initial coverage is less than the specified target range. Additionally, among the vaccines considered in the study, the one with 89.9% effectiveness and a 183 Philippine peso price per dose projected the lowest number of deaths. Compared with other model variations and common allocation approaches, the model has achieved both an optimal and equitable allocation. Conclusions Having a 100% coverage for vaccination with a 100% effectiveness rate of vaccine is ideal for all countries. However, some countries have limited resources. Therefore, the results of our study can be used by policymakers to determine an optimal and equitable distribution of COVID-19 vaccines for a country/community.

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.