Effect of vaccine efficacy on disease transmission with age-structured

Mathematical modeling for estimating influenza vaccine efficacy: A case study of the Valencian Community, Spain

Vaccine efficacy and its quantification is a crucial concept for the proper design of public health vaccination policies. In this work we proposed a mathematical model to estimate the efficacy of the influenza vaccine in a real-word scenario. In particular, our model is a SEIR-type epidemiological model, which distinguishes vaccinated and unvaccinated populations. Mathematically, its dynamics is governed by a nonlinear system of ordinary differential equations, where the non-linearity arises from the effective contacts between susceptible and infected individuals. Two key aspects of this study is that we use a vaccine distribution over time that is based on real data specific to the elderly people in the Valencian Community and the calibration process takes into account that over one influenza season a specific proportion of the population becomes infected with influenza. To consider the effectiveness of the vaccine, the model incorporates a parameter, the vaccine attenuation factor, which is related with the vaccine efficacy against the influenza virus. With this framework, in order to calibrate the model parameters and to obtain an influenza vaccine efficacy estimation, we considered the 2016-2017 influenza season in the Valencian Community, Spain, using the influenza reported cases of vaccinated and unvaccinated. In order to ensure the model identifiability, we choose to deterministically calibrate the parameters for different scenarios and we find the one with the minimum error in order to determine the vaccine efficacy. The calibration results suggest that the influenza vaccine developed for 2016-2017 influenza season has an efficacy of approximately 76.7%, and that the risk of becoming infected is five times higher for an unvaccinated individual in comparison with a vaccinated one. This estimation partially agrees with some previous studies related to the influenza vaccine. This study presents a new integrated mathematical approach to study the influenza vaccine efficacy and gives further insight into this important public health topic.

Assessing the medical resources in COVID-19 based on evolutionary game

COVID-19 has brought a great challenge to the medical system. A key scientific question is how to make a balance between home quarantine and staying in the hospital. To this end, we propose a game-based susceptible-exposed-asymptomatic -symptomatic- hospitalized-recovery-dead model to reveal such a situation. In this new framework, time-varying cure rate and mortality are employed and a parameter m is introduced to regulate the probability that individuals are willing to go to the hospital. Through extensive simulations, we find that (1) for low transmission rates (β < 0.2), the high value of m (the willingness to stay in the hospital) indicates the full use of medical resources, and thus the pandemic can be easily contained; (2) for high transmission rates (β > 0.2), large values of m lead to breakdown of the healthcare system, which will further increase the cumulative number of confirmed cases and death cases. Finally, we conduct the empirical analysis using the data from Japan and other typical countries to illustrate the proposed model and to test how our model explains reality.

Exploring Impacts to COVID-19 Herd Immunity Thresholds Under Demographic Heterogeneity that Lowers Vaccine Effectiveness

The COVID-19 pandemic has caused severe health, economic, and societal impacts across the globe. Although highly efficacious vaccines were developed at an unprecedented rate, the heterogeneity in vaccinated populations has reduced the ability to achieve herd immunity. Specifically, as of Spring 2022, the 0-4 year-old population is still unable to be vaccinated and vaccination rates across 5-11 year olds are low. Additionally, vaccine hesitancy for older populations has further stalled efforts to reach herd immunity thresholds. This heterogeneous vaccine landscape increases the challenge of anticipating disease spread in a population. We developed an age-structured Susceptible-Infectious-Recovered-type mathematical model to investigate the impacts of unvaccinated subpopulations on herd immunity. The model considers two types of undervaccination - age-related and behavior-related - by incorporating four age groups based on available FDA-approved vaccines. The model accounts for two different types of vaccines, mRNA (e.g., Pfizer, Moderna) and vector (e.g., Johnson and Johnson), as well as their effectiveness. Our goal is to analyze different scenarios to quantify which subpopulations and vaccine characteristics (e.g., rate or efficacy) most impact infection levels in the United States, using the state of New Mexico as an example.