The optimal vaccination strategy to control COVID-19:a modeling study in Wuhan City,China

Background: Reaching optimal vaccination rates is an essential public health strategy to control the coronavirus disease 2019 (COVID-19) pandemic. This study aimed to simulate the optimal vaccination strategy to control the disease by developing an age-specific model based on the current transmission patterns of COVID-19 in Wuhan City, China.Methods: We collected two indicators of COVID-19, including illness onset data and age of confirmed case in Wuhan City, from December 2, 2019, to March 16, 2020. The reported cases were divided into four age groups: group 1, ≤ 14 years old;group 2, 15 to 44 years old;group 3, 44 to 64 years old;and group 4, ≥ 65 years old. An age-specific susceptible-exposed-symptomatic-asymptomatic-recovered/removed model was developed to estimate the transmissibility and simulate the optimal vaccination strategy. The effective reproduction number (R_(eff)) was used to estimate the transmission interaction in different age groups.Results: A total of 47 722 new cases were reported in Wuhan City from December 2, 2019, to March 16, 2020. Before the travel ban of Wuhan City, the highest transmissibility was observed among age group 2 (R_(eff) = 4.28), followed by group 2 to 3 (R_(eff) = 2.61), and group 2 to 4 (R_(eff) = 1.69). China should vaccinate at least 85% of the total population to interrupt transmission. The priority for controlling transmission should be to vaccinate 5% to 8% of individuals in age group 2 per day (ultimately vaccinated 90% of age group 2), followed by 10% of age group 3 per day (ultimately vaccinated 90% age group 3). However, the optimal vaccination strategy for reducing the disease severity identified individuals ≥ 65 years old as a priority group, followed by those 45-64 years old.Conclusions: Approximately 85% of the total population (nearly 1.2 billion people) should be vaccinated to build an immune barrier in China to safely consider removing border restrictions. Based on these results, we concluded that 90% of adults aged 15-64 years should first be vaccinated to prevent transmission in China.

GLOBAL STABILITY OF AN AGE-STRUCTURED SIR EPIDEMIC MODEL WITH PULSE VACCINATION STRATEGY

This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age （duration since infection）. The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infectiomfree situation if the impulsive period T and proportion p satisfy Ro（p,T） 〈 1. Optimal problem is discussed： Pulse vaccination strategy with minimal costs at given R0（p, T） 〈 1.

Modeling and Analysis of COVID-19 Optimizated Vaccination Strategies with Age Structure

The rational and effective implementation of epidemic prevention and control measures is crucial to controlling the spread of COVID-19, and vaccination is a key part to be considered in the development of epidemic prevention and control strategies. In order to give full play to the greater role of vaccination strategies in epidemic prevention and control, more accurate and efficient vaccination strategies should be explored. Based on the classical SEIR dynamic model, this paper established a COVID-19 dynamic model of population age structure in the form of population grouping and combined with the transmission characteristics of the COVID-19 epidemic. An optimization model with the goal of minimizing daily infection was established to analyze the optimization studies on infection-related specificity of vaccination for different age groups under the condition of limited daily vaccine supply at the early stage of the epidemic, and to obtain the priority of vaccination strategies for Chinese age groups. And the effect of the heterogeneity of infection rate and hospitalization rate on the priority of vaccine allocation.

13-Valent pneumococcal conjugate vaccines vaccination innovative strategy in Weifang City,China:a case study

The World Health Organization(WHO)prioritizes pneumococcal disease as a vaccine-preventable disease and recommends the inclusion of pneumococcal conjugate vaccines(PCV)in national immunization programs worldwide.However,PCV is not included in the National Immunization Program in China and has low vaccination coverage due to its high cost.To address this,Weifang City implemented an innovative strategy for a 13-valent PCV(PCV13)on June 1,2021.This strategy aimed to provide one dose of PCV13 free of charge for children aged 6 months to 2 years in registered households and to adopt a commercial insurance model with one dose of PCV13 free of charge in 2023 for children over 2 years old.The Health Commission of Weifang and other departments conducted a comprehensive investigation and considered various factors,such as vaccine efectiveness,safety,accessibility,vaccine price,and immunization schedules,for eligible children(under 5 years old).Stakeholder opinions were also solicited before implementing the policy.The Commission negotiated with various vaccine manufacturers to maximize its negotiating power and reduce vaccine prices.The implementation plan was introduced under the Healthy Weifang Strategy.Following the implementation of this strategy,the full course of vaccination coverage increased signifcantly from 0.67 to 6.59%.However,vaccination coverage is still lower than that in developed countries.Weifang’s PCV13 vaccination innovative strategy is the frst of its kind in Chinese mainland and is an active pilot of non-immunization program vaccination strategies.To further promote PCV13 vaccination,Weifang City should continue to implement this strategy and explore appropriate fnancing channels.Regions with higher levels of economic development can innovate the implementation of vaccine programs,broaden fnancing channels,improve accessibility to vaccination services,and advocate for more localities to incorporate PCV13 into locally expanded immunization programs or people-benefting projects.A monitoring and evaluation system should also be established to evaluate implementation efects.

Mathematical models for assessing vaccination scenarios in several provinces in Indonesia

To mitigate casualties from the COVID-19 outbreak,this study aims at assessing the optimal vaccination scenarios,considering several existing healthcare conditions and assumptions,by developing SIQRD(Susceptible-Infected-Quarantine-Recovery-Death)models for Jakarta,West Java,and Banten,in Indonesia.The models include an age-structured dynamic transmission model that naturally allows for different treatments among different age groups of the population.The simulation results show that the timing and period of the vaccination should be well planned and prioritizing particular age groups will give a significant impact on the total number of casualties.

A MULTI-GROUP SVEIR EPIDEMIC MODEL WITH DISTRIBUTED DELAY AND VACCINATION

In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.

Analysis of an Age Structured SEIRS Epidemic Model with Varying Total Population Size and Vaccination

This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.