A model-based strategy for the COVID-19 vaccine roll-out in the Philippines.

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces 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: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission rate and reporting rate 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.

Risk estimation of lifted mask mandates and emerging variants using mathematical model.

Background: More than half of the population in Korea had a prior COVID-19 infection. In 2022, most nonpharmaceutical interventions, except mask-wearing indoors, had been lifted. And in 2023, the indoor mask mandates were eased. Methods: We developed an age-structured compartmental model that distinguishes vaccination history, prior infection, and medical staff from the rest of the population. Contact patterns among hosts were separated based on age and location. We simulated scenarios with the lifting of the mask mandate all at once or sequentially according to the locations. Furthermore, we investigated the impact of a new variant assuming that it has higher transmissibility and risk of breakthrough infection. Results: We found that the peak size of administered severe patients may not exceed 1100 when the mask mandate is lifted everywhere, and 800 if the mask mandate only remains in the hospital. If the mask mandate is lifted in a sequence (except hospital), then the peak size of administered severe patients may not exceed 650. Moreover, if the new variant has both higher transmissibility and immune reduction, the effective reproductive number of the new variant is approximately 3 times higher than that of the current variant, and additional interventions may be needed to keep the administered severe patients from exceeding 2,000, which is the critical level we set. Conclusion: Our findings showed that the lifting of the mask mandate, except in hospitals, would be more manageable if implemented sequentially. Considering a new variant, we found that depending on the population immunity and transmissibility of the variant, wearing masks and other interventions may be necessary for controlling the disease.

Identifying patterning behavior in a plant infestation of insect pests.

In this study, we developed a mechanistic model formulated as a system of reaction-diffusion equations (RDE) to explore the spatiotemporal dynamics of a theoretical pest with a tillering host plant in a controlled rectangular plant field. Local perturbation analysis, a recently developed method of analysis for wave propagation, was utilized to determine patterning regimes resulting from the local and global behaviors of the slow and fast diffusing components of the RDE system, respectively. Turing analysis was done to show that the RDE system does not exhibit Turing patterns. With bug mortality as the bifurcation parameter, regions with oscillations and stable coexistence of the pest and tillers were identified. Numerical simulations illustrate the patterning regimes in 1D and 2D settings. The oscillations suggest that recurrences in pest infestation is possible. Moreover, simulations showed that patterns produced in the model are strongly influenced by the pests' homogeneous dynamics inside the controlled environment.

Modelling the effects of social distancing, antiviral therapy, and booster shots on mitigating Omicron spread.

As the COVID-19 situation changes because of emerging variants and updated vaccines, an elaborate mathematical model is essential in crafting proactive and effective control strategies. We propose a COVID-19 mathematical model considering variants, booster shots, waning, and antiviral drugs. We quantify the effects of social distancing in the Republic of Korea by estimating the reduction in transmission induced by government policies from February 26, 2021 to February 3, 2022. Simulations show that the next epidemic peak can be estimated by investigating the effects of waning immunity. This research emphasizes that booster vaccination should be administered right before the next epidemic wave, which follows the increasing waned population. Policymakers are recommended to monitor the waning population immunity using mathematical models or other predictive methods. Moreover, our simulations considering a new variant's transmissibility, severity, and vaccine evasion suggest intervention measures that can reduce the severity of COVID-19.

Estimation of monkeypox spread in a nonendemic country considering contact tracing and self-reporting: A stochastic modeling study.

In May 2022, monkeypox started to spread in nonendemic countries. To investigate contact tracing and self-reporting of the primary case in the local community, a stochastic model is developed. An algorithm based on Gillespie's stochastic chemical kinetics is used to quantify the number of infections, contacts, and duration from the arrival of the primary case to the detection of the index case (or until there are no more local infections). Different scenarios were set considering the delay in contact tracing and behavior of infectors. We found that the self-reporting behavior of a primary case is the most significant factor affecting outbreak size and duration. Scenarios with a self-reporting primary case have an 86% reduction in infections (average: 5-7, in a population of 10 000) and contacts (average: 27-72) compared with scenarios with a non-self-reporting primary case (average number of infections and contacts: 27-72 and 197-537, respectively). Doubling the number of close contacts per day is less impactful compared with the self-reporting behavior of the primary case as it could only increase the number of infections by 45%. Our study emphasizes the importance of the prompt detection of the primary case.

Optimal selection of COVID-19 vaccination sites in the Philippines at the municipal level.

In this work, we present an approach to determine the optimal location of coronavirus disease 2019 (COVID-19) vaccination sites at the municipal level. We assume that each municipality is subdivided into smaller administrative units, which we refer to as 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 barangays, the number of COVID-19 cases, and the population densities of the barangays. These objectives are formulated as a single optimization problem. As an alternative decision support tool, we develop a bi-objective optimization problem that considers distance and population coverage. Lastly, we propose a dynamic optimization approach that recalculates the optimal vaccination sites to account for the changes in the population of the barangays that have completed their vaccination program. A numerical scheme that solves the optimization problems is presented and the detailed description of the algorithms, which are coded in Python and MATLAB, are uploaded to a public repository. As an illustration, we apply our method to determine the optimal location of vaccination sites in San Juan, a municipality in the province of Batangas, in the Philippines. We hope that this study may guide the local government units in coming up with strategic and accessible plans for vaccine administration.

Multi-Faceted Analysis of COVID-19 Epidemic in Korea Considering Omicron Variant: Mathematical Modeling-Based Study.

BACKGROUND: The most recent variant of concern, omicron (B.1.1.529), has caused numerous cases worldwide including the Republic of Korea due to its fast transmission and reduced vaccine effectiveness. METHODS: A mathematical model considering age-structure, vaccine, antiviral drugs, and influx of the omicron variant was developed. We estimated transmission rates among age groups using maximum likelihood estimation for the age-structured model. The impact of non-pharmaceutical interventions (NPIs; in community and border), quantified by a parameter µ in the force of infection, and vaccination were examined through a multi-faceted analysis. A theory-based endemic equilibrium study was performed to find the manageable number of cases according to omicron- and healthcare-related factors. RESULTS: By fitting the model to the available data, the estimated values of µ ranged from 0.31 to 0.73, representing the intensity of NPIs such as social distancing level. If µ < 0.55 and 300,000 booster shots were administered daily from February 3, 2022, the number of severe cases was forecasted to exceed the severe bed capacity. Moreover, the number of daily cases is reduced as the timing of screening measures is delayed. If screening measure was intensified as early as November 24, 2021 and the number of overseas entrant cases was contained to 1 case per 10 days, simulations showed that the daily incidence by February 3, 2022 could have been reduced by 87%. Furthermore, we found that the incidence number in mid-December 2021 exceeded the theory-driven manageable number of daily cases. CONCLUSION: NPIs, vaccination, and antiviral drugs influence the spread of omicron and number of severe cases in the Republic of Korea. Intensive and early screening measures during the emergence of a new variant is key in controlling the epidemic size. Using the endemic equilibrium of the model, a formula for the manageable daily cases depending on the severity rate and average length of hospital stay was derived so that the number of severe cases does not surpass the severe bed capacity.

A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, the Philippines.

Despite being one of the first countries to implement mass drug administration (MDA) for elimination of lymphatic filariasis (LF) in 2001 after a pilot study in 2000, the Philippines is yet to eliminate the disease as a public health problem with 6 out of the 46 endemic provinces still implementing MDA for LF as of 2018. In this work, we propose a mathematical model of the transmission dynamics of LF in the Philippines and a control strategy for its elimination using MDA. Sensitivity analysis using the Latin hypercube sampling and partial rank correlation coefficient methods suggests that the infected human population is most sensitive to the treatment parameters. Using the available LF data in Caraga Region from the Philippine Department of Health, we estimate the treatment rates r 1 and r 2 using the least-squares parameter estimation technique. Parameter bootstrapping showed small variability in the parameter estimates. Finally, we apply optimal control theory with the objective of minimizing the infected human population and the corresponding implementation cost of MDA, using the treatment coverage γ as the control parameter. Simulation results highlight the importance of maintaining a high MDA coverage per year to effectively minimize the infected population by the year 2030.

Explicit solution of a Lotka-Sharpe-McKendrick system involving neutral delay differential equations using the r-Lambert W function.

Structured population models, which account for the state of individuals given features such as age, gender, and size, are widely used in the fields of ecology and biology. In this paper, we consider an age-structured population model describing the population of adults and juveniles. The model consists of a system of ordinary and neutral delay differential equations. We present an explicit solution to the model using a generalization of the Lambert W function called the r-Lambert W function. Numerical simulations with varying parameters and initial conditions are done to illustrate the obtained solution. The proposed method is also applied to an insect population model with long larval and short adult phases.