COVID-19 optimal vaccination policies: A modeling study on efficacy, natural and vaccine-induced immunity responses

Novel multi-cluster workflow system to support real-time HPC-enabled epidemic science: Investigating the impact of vaccine acceptance on COVID-19 spread

We present MacKenzie, a HPC-driven multi-cluster workflow system that was used repeatedly to configure and execute fine-grained US national-scale epidemic simulation models during the COVID-19 pandemic. Mackenzie supported federal and Virginia policymakers, in real-time, for a large number of "what-if" scenarios during the COVID-19 pandemic, and continues to be used to answer related questions as COVID-19 transitions to the endemic stage of the disease. MacKenzie is a novel HPC meta-scheduler that can execute US-scale simulation models and associated workflows that typically present significant big data challenges. The meta-scheduler optimizes the total execution time of simulations in the workflow, and helps improve overall human productivity. As an exemplar of the kind of studies that can be conducted using Mackenzie, we present a modeling study to understand the impact of vaccine-acceptance in controlling the spread of COVID-19 in the US. We use a 288 million node synthetic social contact network (digital twin) spanning all 50 US states plus Washington DC, comprised of 3300 counties, with 12 billion daily interactions. The highly-resolved agent-based model used for the epidemic simulations uses realistic information about disease progression, vaccine uptake, production schedules, acceptance trends, prevalence, and social distancing guidelines. Computational experiments show that, for the simulation workload discussed above, MacKenzie is able to scale up well to 10K CPU cores. Our modeling results show that, when compared to faster and accelerating vaccinations, slower vaccination rates due to vaccine hesitancy cause averted infections to drop from 6.7M to 4.5M, and averted total deaths to drop from 39.4K to 28.2K across the US. This occurs despite the fact that the final vaccine coverage is the same in both scenarios. We also find that if vaccine acceptance could be increased by 10% in all states, averted infections could be increased from 4.5M to 4.7M (a 4.4% improvement) and total averted deaths could be increased from 28.2K to 29.9K (a 6% improvement) nationwide.

Valuation and comparison of the actual and optimal control strategy in an emerging infectious disease: Implication from a COVID-19 transmission model

To effectively combat emerging infectious diseases like COVID-19, it is crucial to adopt strict prevention and control measures promptly to effectively contain the spread of the epidemic. In this paper, we propose a transmission model to investigate the influence of two control strategies: reducing contact numbers and improving medical resources. We examine these strategies in terms of constant control and time-varying control. Through sensitivity analysis on two reproduction numbers of the model with constant control, we demonstrate that reducing contact numbers is more effective than improving medical resources. Furthermore, these two constant controls significantly influence the peak values and timing of infections. Specifically, intensifying control measures can reduce peak values, albeit at the expense of delaying the peak time. In the model with time-varying control, we initially explore the corresponding optimal control problem and derive the characteristic expression of optimal control. Subsequently, we utilize real data from January 10th to April 12th, 2020, in Wuhan city as a case study to perform parameter estimation by using our proposed improved algorithm. Our findings illustrate that implementing optimal control measures can effectively reduce infections and deaths, and shorten the duration of the epidemic. Then, we numerically explore that implementing control measures promptly and increasing intensity to reduce contact numbers can make actual control be more closer to optimized control. Finally, we utilize the real data from October 31st to November 18th, 2021, in Hebei province as a second case study to validate the feasibility of our proposed suggestions.

Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Modeling the impact of hospital beds and vaccination on the dynamics of an infectious disease

The unprecedented scale and rapidity of dissemination of re-emerging and emerging infectious diseases impose new challenges for regulators and health authorities. To curb the dispersal of such diseases, proper management of healthcare facilities and vaccines are core drivers. In the present work, we assess the unified impact of healthcare facilities and vaccination on the control of an infectious disease by formulating a mathematical model. To formulate the model for any region, we consider four classes of human population; namely, susceptible, infected, hospitalized, and vaccinated. It is assumed that the increment in number of beds in hospitals is continuously made in proportion to the number of infected individuals. To ensure the occurrence of transcritical, saddle-node and Hopf bifurcations, the conditions are derived. The normal form is obtained to show the existence of Bogdanov-Takens bifurcation. To validate the analytically obtained results, we have conducted some numerical simulations. These results will be useful to public health authorities for planning appropriate health care resources and vaccination programs to diminish prevalence of infectious diseases.

Predictive models for health outcomes due to SARS-CoV-2, including the effect of vaccination: a systematic review

BACKGROUND

The interaction between modelers and policymakers is becoming more common due to the increase in computing speed seen in recent decades. The recent pandemic caused by the SARS-CoV-2 virus was no exception. Thus, this study aims to identify and assess epidemiological mathematical models of SARS-CoV-2 applied to real-world data, including immunization for coronavirus 2019 (COVID-19).

METHODOLOGY

PubMed, JSTOR, medRxiv, LILACS, EconLit, and other databases were searched for studies employing epidemiological mathematical models of SARS-CoV-2 applied to real-world data. We summarized the information qualitatively, and each article included was assessed for bias risk using the Joanna Briggs Institute (JBI) and PROBAST checklist tool. The PROSPERO registration number is CRD42022344542.

FINDINGS

In total, 5646 articles were retrieved, of which 411 were included. Most of the information was published in 2021. The countries with the highest number of studies were the United States, Canada, China, and the United Kingdom; no studies were found in low-income countries. The SEIR model (susceptible, exposed, infectious, and recovered) was the most frequently used approach, followed by agent-based modeling. Moreover, the most commonly used software were R, Matlab, and Python, with the most recurring health outcomes being death and recovery. According to the JBI assessment, 61.4% of articles were considered to have a low risk of bias.

INTERPRETATION

The utilization of mathematical models increased following the onset of the SARS-CoV-2 pandemic. Stakeholders have begun to incorporate these analytical tools more extensively into public policy, enabling the construction of various scenarios for public health. This contribution adds value to informed decision-making. Therefore, understanding their advancements, strengths, and limitations is essential.

Exploring the potential of learning methods and recurrent dynamic model with vaccination: A comparative case study of COVID-19 in Austria, Brazil, and China

In order to effectively manage infectious diseases, it is crucial to understand the interplay between disease dynamics and human conduct. Various factors can impact the control of an epidemic, including social interventions, adherence to health protocols, mask-wearing, and vaccination. This article presents the development of an innovative hybrid model, known as the Combined Dynamic-Learning Model, that integrates classical recurrent dynamic models with four different learning methods. The model is composed of two approaches: The first approach introduces a traditional dynamic model that focuses on analyzing the impact of vaccination on the occurrence of an epidemic, and the second approach employs various learning methods to forecast the potential outcomes of an epidemic. Furthermore, our numerical results offer an interesting comparison between the traditional approach and modern learning techniques. Our classic dynamic model is a compartmental model that aims to analyze and forecast the diffusion of epidemics. The model we propose has a recurrent structure with piecewise constant parameters and includes compartments for susceptible, exposed, vaccinated, infected, and recovered individuals. This model can accurately mirror the dynamics of infectious diseases, which enables us to evaluate the impact of restrictive measures on the spread of diseases. We conduct a comprehensive dynamic analysis of our model. Additionally, we suggest an optimal numerical design to determine the parameters of the system. Also, we use regression tree learning, bidirectional long short-term memory, gated recurrent unit, and a combined deep learning method for training and evaluation of an epidemic. In the final section of our paper, we apply these methods to recently published data on COVID-19 in Austria, Brazil, and China from 26 February 2021 to 4 August 2021, which is when vaccination efforts began. To evaluate the numerical results, we utilized various metrics such as RMSE and R-squared. Our findings suggest that the dynamic model is ideal for long-term analysis, data fitting, and identifying parameters that impact epidemics. However, it is not as effective as the supervised learning method for making long-term forecasts. On the other hand, supervised learning techniques, compared to dynamic models, are more effective for predicting the spread of diseases, but not for analyzing the behavior of epidemics.

Optimal age-specific vaccination control for COVID-19: An Irish case study

The outbreak of a novel coronavirus causing severe acute respiratory syndrome in December 2019 has escalated into a worldwide pandemic. In this work, we propose a compartmental model to describe the dynamics of transmission of infection and use it to obtain the optimal vaccination control. The model accounts for the various stages of the vaccination, and the optimisation is focused on minimising the infections to protect the population and relieve the healthcare system. As a case study, we selected the Republic of Ireland. We use data provided by Ireland's COVID-19 Data-Hub and simulate the evolution of the pandemic with and without the vaccination in place for two different scenarios, one representative of a national lockdown situation and the other indicating looser restrictions in place. One of the main findings of our work is that the optimal approach would involve a vaccination programme where the older population is vaccinated in larger numbers earlier while simultaneously part of the younger population also gets vaccinated to lower the risk of transmission between groups. We compare our simulated results with those of the vaccination policy taken by the Irish government to explore the advantages of our optimisation method. Our comparison suggests that a similar reduction in cases may have been possible even with a reduced set of vaccinations available for use.

Modeling a traffic light warning system for acute respiratory infections

The high morbidity of acute respiratory infections constitutes a crucial global health burden. In particular, for SARS-CoV-2, non-pharmaceutical intervention geared to enforce social distancing policies, vaccination, and treatments will remain an essential part of public health policies to mitigate and control disease outbreaks. However, the implementation of mitigation measures directed to increase social distancing when the risk of contagion is a complex enterprise because of the impact of NPI on beliefs, political views, economic issues, and, in general, public perception. The way of implementing these mitigation policies studied in this work is the so-called traffic-light monitoring system that attempts to regulate the application of measures that include restrictions on mobility and the size of meetings, among other non-pharmaceutical strategies. Balanced enforcement and relaxation of measures guided through a traffic-light system that considers public risk perception and economic costs may improve the public health benefit of the policies while reducing their cost. We derive a model for the epidemiological traffic-light policies based on the best response for trigger measures driven by the risk perception of people, instantaneous reproduction number, and the prevalence of a hypothetical acute respiratory infection. With numerical experiments, we evaluate and identify the role of appreciation from a hypothetical controller that could opt for protocols aligned with the cost due to the burden of the underlying disease and the economic cost of implementing measures. As the world faces new acute respiratory outbreaks, our results provide a methodology to evaluate and develop traffic light policies resulting from a delicate balance between health benefits and economic implications.

Impact of vaccine measures on the transmission dynamics of COVID-19

In many nations, efforts to prevent and control COVID-19 have been significantly impeded by the SARS-CoV-2 virus ongoing mutation. The Omicron strain, a more recent and prevalent strain, has had more significant detrimental effects in countries worldwide. To investigate the impact of the Omicron BA.2 strain on vaccine efficacy, we proposed a model with vaccination and immunological decline in this research. Then, we fitted our model based on the number of daily new instances reported by the government in Jilin and Shanghai, China. We estimated the effective reproduction number Re = 4.71 for the Jilin and Re = 3.32 for Shanghai. Additionally, we do sensitivity analysis to identify the critical factors affecting the effective reproduction number Re. It was found that vaccination rate, effectiveness rate, and declining rate had a significant effect on Re. Further, we investigate the relevant parameter thresholds that make Re lower than unity. Finally, rich numerical experiments were then carried out. We observed that even when vaccine efficiency was not high, increasing vaccination rates had a significant effect on early disease transmission, that limiting social distance was the most economical and rational measure to control the spread of disease, and that for a short period, reducing immune decline was not significant in curbing disease transmission.

Analysis of the COVID-19 pandemic using a compartmental model with time-varying parameters fitted by a genetic algorithm

Analyzing the COVID-19 pandemic is a critical factor in developing effective policies to deal with similar challenges in the future. However, many parameters (e.g., the actual number of infected people, the effectiveness of vaccination) are still subject to considerable debate because they are unobservable. To model a pandemic and estimate unobserved parameters, researchers use compartmental models. Most often, in such models, the transition rates are considered as constants, which allows simulating only one epidemiological wave. However, multiple waves have been reported for COVID-19 caused by different strains of the virus. This paper presents an approach based on the reconstruction of real distributions of transition rates using genetic algorithms, which makes it possible to create a model that describes several pandemic peaks. The model is fitted on registered COVID-19 cases in four countries with different pandemic control strategies (Germany, Sweden, UK, and US). Mean absolute percentage error (MAPE) was chosen as the objective function, the MAPE values of 2.168%, 2.096%, 1.208% and 1.703% were achieved for the listed countries, respectively. Simulation results are consistent with the empirical statistics of medical studies, which confirms the quality of the model. In addition to observables such as registered infected, the output of the model contains variables that cannot be measured directly. Among them are the proportion of the population protected by vaccines, the size of the exposed compartment, and the number of unregistered cases of COVID-19. According to the results, at the peak of the pandemic, between 14% (Sweden) and 25% (the UK) of the population were infected. At the same time, the number of unregistered cases exceeds the number of registered cases by 17 and 3.4 times, respectively. The average duration of the vaccine induced immune period is shorter than claimed by vaccine manufacturers, and the effectiveness of vaccination has declined sharply since the appearance of the Delta and Omicron strains. However, on average, vaccination reduces the risk of infection by about 65-70%.

An integrated chance constraints approach for optimal vaccination strategies under uncertainty for COVID-19

Despite concerted efforts by health authorities worldwide to contain COVID-19, the SARS-CoV-2 virus has continued to spread and mutate into new variants with uncertain transmission characteristics. Therefore, there is a need for new data-driven models for determining optimal vaccination strategies that adapt to the new variants with their uncertain transmission characteristics. Motivated by this challenge, we derive an integrated chance constraints stochastic programming (ICC-SP) approach for finding vaccination strategies for epidemics that incorporates population demographics for any region of the world, uncertain disease transmission and vaccine efficacy. An optimal vaccination strategy specifies the proportion of individuals in a given household-type to vaccinate to bring the reproduction number to below one. The ICC-SP approach provides a quantitative method that allows to bound the expected excess of the reproduction number above one by an acceptable amount according to the decision-maker's level of risk. This new methodology involves a multi-community household based epidemiology model that uses census demographics data, vaccination status, age-related heterogeneity in disease susceptibility and infectivity, virus variants, and vaccine efficacy. The new methodology was tested on real data for seven neighboring counties in the United States state of Texas. The results are promising and show, among other findings, that vaccination strategies for controlling an outbreak should prioritize vaccinating certain household sizes as well as age groups with relatively high combined susceptibility and infectivity.

Impact of vaccination on the entire population and dose-response relation of COVID-19

Objective

The objective of this study is to develop a mathematical model for the COVID-19 pandemic including vaccination, the transmissibility of the virus-pathogen dose-response relationship, vaccine efficiency, and vaccination rate.

Methods

The Runge-Kutta (RK-45) method was applied to solve the proposed model with MATLAB code and the calculated results show the dynamics of the individuals in each compartment. The data of total death due to the COVID-19 pandemic in the case of the USA were collected from GitHub and the re-use of this data needs no ethical clearance. The control reproduction number was used to assess the dose-response relationship and critical vaccination coverage.

Results

We have calculated the probability of infection and the infection risk against the different exposure doses and the virus copies, respectively. The results show that the probability of infection increases with the increasing exposure dose for certain virus copies and the risk of infection decreases with the increasing of virus copies for a certain exposure dose. The results also show that the critical vaccination coverage demands increase with an increase in transmission rate and decrease with increasing vaccine efficacy.

Conclusions

It was seen that the critical vaccination coverage corresponding to an increased transmission rate rise sharply in the beginning and then reached a threshold. Moreover, the real data of the total death cases in the USA were compared with the fitted curved of the model which validated the proposed model. Vaccination against COVID-19 is essential to control the pandemic, and achieving high vaccine uptake in the population can reduce the pandemic as fast as possible.

Study of optimal vaccination strategies for early COVID-19 pandemic using an age-structured mathematical model: A case study of the USA

In this paper we study different vaccination strategies that could have been implemented for the early COVID-19 pandemic. We use a demographic epidemiological mathematical model based on differential equations in order to investigate the efficacy of a variety of vaccination strategies under limited vaccine supply. We use the number of deaths as the metric to measure the efficacy of each of these strategies. Finding the optimal strategy for the vaccination programs is a complex problem due to the large number of variables that affect the outcomes. The constructed mathematical model takes into account demographic risk factors such as age, comorbidity status and social contacts of the population. We perform simulations to assess the performance of more than three million vaccination strategies which vary depending on the vaccine priority of each group. This study focuses on the scenario corresponding to the early vaccination period in the USA, but can be extended to other countries. The results of this study show the importance of designing an optimal vaccination strategy in order to save human lives. The problem is extremely complex due to the large amount of factors, high dimensionality and nonlinearities. We found that for low/moderate transmission rates the optimal strategy prioritizes high transmission groups, but for high transmission rates, the optimal strategy focuses on groups with high CFRs. The results provide valuable information for the design of optimal vaccination programs. Moreover, the results help to design scientific vaccination guidelines for future pandemics.

Optimal interventional policy based on discrete-time fuzzy rules equivalent model utilizing with COVID-19 pandemic data

In this paper, a mathematical model of the COVID-19 pandemic is formulated by fitting it to actual data collected during the fifth wave of the COVID-19 pandemic in Coahuila, Mexico, from June 2022 to October 2022. The data sets used are recorded on a daily basis and presented in a discrete-time sequence. To obtain the equivalent data model, fuzzy rules emulated networks are utilized to derive a class of discrete-time systems based on the daily hospitalized individuals' data. The aim of this study is to investigate the optimal control problem to determine the most effective interventional policy including precautionary and awareness measures, the detection of asymptomatic and symptomatic individuals, and vaccination. A main theorem is developed to guarantee the closed-loop system performance by utilizing approximate functions of the equivalent model. The numerical results indicate that the proposed interventional policy can eradicate the pandemic within 1-8 weeks. Additionally, the results show that if the policy is implemented within the first 3 weeks, the number of hospitalized individuals remains below the hospital's capacity.

Modeling the Spread of COVID-19 with the Control of Mixed Vaccine Types during the Pandemic in Thailand

COVID-19 is a respiratory disease that can spread rapidly. Controlling the spread through vaccination is one of the measures for activating immunization that helps to reduce the number of infected people. Different types of vaccines are effective in preventing and alleviating the symptoms of the disease in different ways. In this study, a mathematical model, SVIHR, was developed to assess the behavior of disease transmission in Thailand by considering the vaccine efficacy of different vaccine types and the vaccination rate. The equilibrium points were investigated and the basic reproduction number R0 was calculated using a next-generation matrix to determine the stability of the equilibrium. We found that the disease-free equilibrium point was asymptotically stable if, and only if, R0<1, and the endemic equilibrium was asymptotically stable if, and only if, R0>1. The simulation results and the estimation of the parameters applied to the actual data in Thailand are reported. The sensitivity of parameters related to the basic reproduction number was compared with estimates of the effectiveness of pandemic controls. The simulations of different vaccine efficacies for different vaccine types were compared and the average mixing of vaccine types was reported to assess the vaccination policies. Finally, the trade-off between the vaccine efficacy and the vaccination rate was investigated, resulting in the essentiality of vaccine efficacy to restrict the spread of COVID-19.

A mathematical model reveals the influence of NPIs and vaccination on SARS-CoV-2 Omicron Variant

An SVEIR SARS-CoV-2 Omicron variant model is proposed to provide some insights to coordinate non-pharmaceutical interventions (NPIs) and vaccination. Mathematically, we define the basic reproduction number R 0 and the effective reproduction number R e to measure the infection potential of Omicron variant and formulate an optimal disease control strategy. Our inversion results imply that the sick period of Omicron variant in the United States is longer than that of Delta variant in India. The decrease in the infectious period of the infection with infectiousness implies that the risk of hospitalization is reduced; but the increasing period of the infection with non-infectiousness signifies that Omicron variant lengthens the period of nucleic acid test being negative. Optimistically, Omicron's death rate is only a quarter of Delta's. Moreover, we forecast that the cumulative cases will exceed 100 million in the United States on February 28, 2022, and the daily confirmed cases will reach a peak on February 2, 2022. The results of parameters sensitivity analysis imply that NPIs are helpful to reduce the number of confirmed cases. In particular, NPIs are indispensable even if all the people were vaccinated when the efficiency of vaccine is relatively low. By simulating the relationships of the effective reproduction number R e , the vaccination rate and the efficacy of vaccine, we find that it is impossible to achieve the herd immunity without NPIs while the efficiency of vaccine is lower than 88.7 % . Therefore, the herd immunity area is defined by the evolution of relationships between the vaccination rate and the efficacy of vaccine. Finally, we present that the disease-induced mortality rate demonstrates the periodic oscillation and an almost periodic function is deduced to match the curve. A discussion completes the paper.

COVID-19 vaccination challenges: A mini-review

The emergence of SARS-CoV-2 has led to the infection of many people across the globe, over six million deaths, and has placed an unprecedented burden on public health worldwide. The pandemic has led to the high-speed development and production of vaccines against the COVID-19, as vaccines can end the pandemic. At the beginning of the program, vaccinations were initially targeted only at high-risk groups, such as the elderly, those with comorbidities, or healthcare workers. Although most of the mentioned populations have received the two recommended doses, limited resources have left many authorities with an effective vaccine undersupply. Therefore, policies have been implemented to manage the available doses of the vaccines more efficiently. As there is no universally agreed consensus on this topic, we discuss the different recommendations and guidelines regarding the time interval between the two vaccine doses and explain the different scenarios for applying the two doses.

Stability Analysis of an Extended SEIR COVID-19 Fractional Model with Vaccination Efficiency

This work is aimed at presenting a new numerical scheme for COVID-19 epidemic model based on Atangana-Baleanu fractional order derivative in Caputo sense (ABC) to investigate the vaccine efficiency. Our construction of the model is based on the classical SEIR, four compartmental models with an additional compartment V of vaccinated people extending it SEIRV model, for the transmission as well as an effort to cure this infectious disease. The point of disease-free equilibrium is calculated, and the stability analysis of the equilibrium point using the reproduction number is performed. The endemic equilibrium's existence and uniqueness are investigated. For the solution of the nonlinear system presented in the model at different fractional orders, a new numerical scheme based on modified Simpson's 1/3 method is developed. Convergence and stability of the numerical scheme are thoroughly analyzed. We attempted to develop an epidemiological model presenting the COVID-19 dynamics in Italy. The proposed model's dynamics are graphically interpreted to observe the effect of vaccination by altering the vaccination rate.

Changes in the frequency and clinical features of acute rheumatic fever in the COVID-19 era: a retrospective analysis from a single center

OBJECTIVE:

Coronavirus disease 2019 (COVID-19) pandemic resulted in significant changes in the frequency of many diseases. In this study, we aimed to investigate the changes in the frequency and clinical features of acute rheumatic fever (ARF) in this period and determine the effect of health measures taken against COVID-19 on this change.

METHODS:

The cases with initial attack of ARF between January 2016 and March 2022 in Ataturk University, Division of Pediatric Cardiology, were determined from the clinic’s database, and case per month ratios were calculated for each period, retrospectively. Also the frequency of the clinical manifestations was compared among patients before and during the outbreak.

RESULTS:

Frequency of the major clinical manifestations among patients before and during the outbreak was similar. On average, the number of cases reported per month in the years 2016, 2017, 2018, and 2019 are, respectively, 1.75, 2, 2.25, and 2.58. In the first 3 months of 2020, the average number of cases reported per month was 3.67. After the advent of the pandemic, in the period from April to December 2020 and from January to September 2021, an average of 0.56 and 0.22 cases were reported per month, respectively. The frequency of clinical features between patients diagnosed before and during the outbreak was similar.

CONCLUSIONS:

Our results indicated an important decrease in frequency of ARF, but no change in the clinical features of the disease during the COVID-19 pandemic. It is thought that this is the result of health measures taken for COVID-19. Children with an increased risk of acute rheumatic fever should be encouraged in terms of wearing mask, social distance, and cleaning, especially during the seasons when upper respiratory tract infections are common. Thus, a permanent decrease in the incidence of ARF and its recurrences may be achieved.

The heterogeneous mixing model of COVID-19 with interventions

The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number Rc of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p3 plays a key role in Rc. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

The realistic assessments of public health intervention strategies are of great significance to effectively combat the COVID-19 epidemic and the formation of intervention policy. In this paper, an extended COVID-19 epidemic model is devised to assess the severity of the pandemic and explore effective control strategies. The model is characterized by ordinary differential equations with seven-state variables, and it incorporates some parameters associated with the interventions (i.e., media publicity, home isolation, vaccination and face-mask wearing) to investigate the impacts of these interventions on the spread of the COVID-19 epidemic. Some dynamic behaviors of the model, such as forward and backward bifurcation, are analyzed. Specifically, we calibrate the model parameters using actual COVID-19 infected data in Brazil by Markov Chain Monte Carlo algorithm such that we can study the effects of interventions on a practical case. Through a comprehensive exploration of model design and analysis, model calibration, sensitivity analysis, implementation of optimal control problems and cost-effectiveness analysis, the rationality of our model is verified, and the effective strategies to combat the epidemic in Brazil are revealed. The results show that the asymptomatic infected individuals are the main drivers of COVID-19 transmission, and rapid detection of asymptomatic infections is critical to combat the COVID-19 epidemic in Brazil. Interestingly, the effect of the vaccination rate associated with pharmaceutical intervention on the basic reproduction number is much lower than that of non-pharmaceutical interventions (NPIs). Our study also highlights the importance of media publicity. To reduce the infected individuals, the multi-pronged NPIs have considerable positive effects on controlling the outbreak of COVID-19. The infections are significantly decreased by the early implementation of media publicity complemented with home isolation and face-mask wearing strategy. When the cost of implementation is taken into account, the early implementation of media publicity complemented with a face-mask wearing strategy can significantly mitigate the second wave of the epidemic in Brazil. These results provide some management implications for controlling COVID-19.

A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior

During the broadcast of Coronavirus across the globe, many mathematicians made several mathematical models. This was, of course, in order to understand the forecast and behavior of this epidemic’s spread precisely. Nevertheless, due to the lack of much information about it, the application of many models has become difficult in reality and sometimes impossible, unlike the simple SIR model. In this work, a simple, novel fractional-order discrete model is proposed in order to study the behavior of the COVID-19 epidemic. Such a model has shown its ability to adapt to the periodic change in the number of infections. The existence and uniqueness of the solution for the proposed model are examined with the help of the Picard Lindelöf method. Some theoretical results are established in view of the connection between the stability of the fixed points of this model and the basic reproduction number. Several numerical simulations are performed to verify the gained results.

Risk-based cost-benefit analysis of alternative vaccines against COVID-19 in Brazil: Coronavac vs. Astrazeneca vs. Pfizer

We propose a probabilistic model to quantify the cost-benefit of mass Vaccination Scenarios (VSs) against COVID-19. Through this approach, we conduct a six-month simulation, from August 31st, 2021 to March 3rd, 2022, of nine VSs, i.e., the three primary vaccine brands in Brazil (CoronaVac, AstraZeneca and Pfizer), each with three different vaccination rates (2nd doses per week). Since each vaccine has different individual-level effectiveness, we measure the population-level benefit as the probability of reaching herd immunity (HI). We quantify and categorize the cost-benefit of VSs through risk graphs that show: (i) monetary cost vs. probability of reaching HI; and (ii) number of new deaths vs. probability of reaching HI. Results show that AstraZeneca has the best cost-benefit when prioritizing acquisition costs, while Pfizer is the most cost-beneficial when prioritizing the number of deaths. This work provides helpful information that can aid public health authorities in Brazil to better plan VSs. Furthermore, our approach is not restricted to Brazil, the COVID-19 pandemic, or the mentioned vaccine brands. Indeed, the method is flexible so that this study can be a valuable reference for future cost-benefit analyses in other countries and pandemics, especially in the early stages of vaccination, when data is scarce and uncertainty is high.

COVID-19 waves: variant dynamics and control

The waves of COVID-19 infections driven by its variants continue to nullify the success we achieved through efficacious vaccines, social restrictions, testing and quarantine policies. This paper models the two major variants-driven waves by two sets of susceptible-infected-quarantined-recovered-vaccinated-deceased coupled dynamics that are modulated by the three main interventions: vaccination, quarantine and restrictions. This \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SI^2Q^2R^2VD$$\end{document}SI2Q2R2VD system is used to demonstrate that the second major novel coronavirus wave in the US is caused by the delta variant and the corresponding rapid surge in infectious cases is driven by the unvaccinated pool of the populace. Next, a feedback control based planned vaccination strategy is derived and is shown to be able to suppress the surge in infections effectively.

Modeling of COVID-19 spread with self-isolation at home and hospitalized classes

This work examines the impacts of self-isolation and hospitalization on the population dynamics of the Corona-Virus Disease. We developed a new nonlinear deterministic model eight classes compartment, with self-isolation and hospitalized being the most effective tools. There are (Susceptible S C ( t ) , Exposed E ( t ) , Asymptomatic infected I A ( t ) , Symptomatic infected A S ( t ) , Self-isolation T M ( t ) , Hospitalized T H ( t ) , Healed H ( t ) , and Susceptible individuals previously infected H C ( t ) ). The expression of basic reproduction number R 0 comes from the next-generation matrix method. With suitably constructed Lyapunov functions, the global asymptotic stability of the non-endemic equilibria Σ 0 for R 0 < 1 and that of endemic equilibria Σ ∗ for R 0 > 1 are established. The computed value of R 0 = 3 . 120277403 proves the endemic level of the epidemic. The outbreak will lessen if a policy is enforced like self-isolation and hospitalization. This is related to those policies that can reduce the number of direct contacts between infected and susceptible individuals or waning immunity individuals. Various simulations are presented to appreciate self-isolation at home and hospitalized strategies if applied sensibly. By performing a global sensitivity analysis, we can obtain parameter values that affect the model through a combination of Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods to determine the parameters that affect the number of reproductions and the increase in the number of COVID cases. The results obtained show that the rate of self-isolation at home and the rate of hospitalism have a negative relationship. On the other hand, infections will decrease when the two parameters increase. From the sensitivity of the results, we formulate a control model using optimal control theory by considering two control variables. The result shows that the control strategies minimize the spread of the COVID infection in the population.

Distinct Immune Response at 1 Year Post-COVID-19 According to Disease Severity

Background

Despite the fact of ongoing worldwide vaccination programs for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), understanding longevity, breadth, and type of immune response to coronavirus disease-19 (COVID-19) is still important to optimize the vaccination strategy and estimate the risk of reinfection. Therefore, we performed thorough immunological assessments 1 year post-COVID-19 with different severity.

Methods

We analyzed peripheral blood mononuclear cells and plasma samples at 1 year post-COVID-19 in patients who experienced asymptomatic, mild, and severe illness to assess titers of various isotypes of antibodies (Abs) against SARS-CoV-2 antigens, phagocytic capability, and memory B- and T-cell responses.

Findings

A total of 24 patients (7, 9, and 8 asymptomatic, mild, and severe patients, respectively) and eight healthy volunteers were included in this study. We firstly showed that disease severity is correlated with parameters of immune responses at 1 year post-COVID-19 that play an important role in protecting against reinfection with SARS-CoV-2, namely, the phagocytic capacity of Abs and memory B-cell responses.

Interpretation

Various immune responses at 1 year post-COVID-19, particularly the phagocytic capacity and memory B-cell responses, were dependent on the severity of the prior COVID-19. Our data could provide a clue for a tailored vaccination strategy after natural infection according to the severity of COVID-19.

Effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines for reducing susceptibility to infection with the Delta variant (B.1.617.2) of SARS-CoV-2

Background

From January to May 2021 the alpha variant (B.1.1.7) of SARS-CoV-2 was the most commonly detected variant in the UK. Following this, the Delta variant (B.1.617.2) then became the predominant variant. The UK COVID-19 vaccination programme started on 8th December 2020. Prior to the Delta variant, most vaccine effectiveness studies focused on the alpha variant. We therefore aimed to estimate the effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines in preventing symptomatic and asymptomatic infection with respect to the Delta variant in a UK setting.

Methods

We used anonymised public health record data linked to infection data (PCR) using the Combined Intelligence for Population Health Action resource. We then constructed an SIR epidemic model to explain SARS-CoV-2 infection data across the Cheshire and Merseyside region of the UK. Vaccines were assumed to be effective after 21 days for 1 dose and 14 days for 2 doses.

Results

We determined that the effectiveness of the Oxford-AstraZeneca vaccine in reducing susceptibility to infection is 39% (95% credible interval [34, 43]) and 64% (95% credible interval [61, 67]) for a single dose and a double dose respectively. For the Pfizer-BioNTech vaccine, the effectiveness is 20% (95% credible interval [10, 28]) and 84% (95% credible interval [82, 86]) for a single-dose and a double dose respectively.

Conclusion

Vaccine effectiveness for reducing susceptibility to SARS-CoV-2 infection shows noticeable improvement after receiving two doses of either vaccine. Findings also suggest that a full course of the Pfizer-BioNTech provides the optimal protection against infection with the Delta variant. This reinforces the need to complete the full course programme to maximise individual protection and reduce transmission.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-022-07239-z.

The impact of vaccination on the spread of COVID-19: Studying by a mathematical model

The global spread of COVID-19 has not been effectively controlled, posing a huge threat to public health and the development of the global economy. Currently, a number of vaccines have been approved for use and vaccination campaigns have already started in several countries. This paper designs a mathematical model considering the impact of vaccination to study the spread dynamics of COVID-19. Some basic properties of the model are analyzed. The basic reproductive number ℜ 1 of the model is obtained, and the conditions for the existence of endemic equilibria are provided. There exist two endemic equilibria when ℜ 1 < 1 under certain conditions, which will lead to backward bifurcation. The stability of equilibria are analyzed, and the condition for the backward bifurcation is given. Due to the existence of backward bifurcation, even if ℜ 1 < 1 , COVID-19 may remain prevalent. Sensitivity analysis and simulations show that improving vaccine efficacy can control the spread of COVID-19 faster, while increasing the vaccination rate can reduce and postpone the peak of infection to a greater extent. However, in reality, the improvement of vaccine efficacy cannot be realized in a short time, and relying only on increasing the vaccination rate cannot quickly achieve the control of COVID-19. Therefore, relying only on vaccination may not completely and quickly control COVID-19. Some non-pharmaceutical interventions should continue to be enforced to combat the virus. According to the sensitivity analysis, we improve the model by including some non-pharmaceutical interventions. Combining the sensitivity analysis with the simulation of the improved model, we conclude that together with vaccination, reducing the contact rate of people and increasing the isolation rate of infected individuals will greatly reduce the number of infections and shorten the time of COVID-19 spread. The analysis and simulations in this paper can provide some useful suggestions for the prevention and control of COVID-19.

COVID-19 epidemic in New York City: development of an age group-specific mathematical model to predict the outcome of various vaccination strategies

Background

Since December 14, 2020, New York City (NYC) has started the first batch of COVID-19 vaccines. However, the shortage of vaccines is currently an inevitable problem. Therefore, optimizing the age-specific COVID-19 vaccination is an important issue that needs to be addressed as a priority.

Objective

Combined with the reported COVID-19 data in NYC, this study aimed to construct a mathematical model with five age groups to estimate the impact of age-specific vaccination on reducing the prevalence of COVID-19.

Methods

We proposed an age-structured mathematical model and estimated the unknown parameters based on the method of Markov Chain Monte Carlo (MCMC). We also calibrated our model by using three different types of reported COVID-19 data in NYC. Moreover, we evaluated the reduced cumulative number of deaths and new infections with different vaccine allocation strategies.

Results

Compared with the current vaccination strategy in NYC, if we gradually increased the vaccination coverage rate for only one age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 75–100 age group would be reduced the most, about 72 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0–17 age group would be reduced the most, about 21,591 fewer new infections per increased 100,000 vaccinated individuals. If we gradually increased the vaccination coverage rate for two age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 65–100 age group would be reduced the most, about 36 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0–44 age group would be reduced the most, about 17,515 fewer new infections per increased 100,000 vaccinated individuals. In addition, if we had an additional 100,000 doses of vaccine for 0–17 and 75–100 age groups as of June 1, 2021, then the allocation of 80% to the 0–17 age group and 20% to the 75–100 age group would reduce the maximum numbers of new infections and deaths simultaneously in NYC.

Conclusions

The COVID-19 burden including deaths and new infections would decrease with increasing vaccination coverage rate. Priority vaccination to the elderly and adolescents would minimize both deaths and new infections.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12985-022-01771-9.

Mathematical Modeling to Study Optimal Allocation of Vaccines against COVID-19 Using an Age-Structured Population

Vaccination against the coronavirus disease 2019 (COVID-19) started in early December of 2020 in the USA. The efficacy of the vaccines vary depending on the SARS-CoV-2 variant. Some countries have been able to deploy strong vaccination programs, and large proportions of their populations have been fully vaccinated. In other countries, low proportions of their populations have been vaccinated, due to different factors. For instance, countries such as Afghanistan, Cameroon, Ghana, Haiti and Syria have less than 10% of their populations fully vaccinated at this time. Implementing an optimal vaccination program is a very complex process due to a variety of variables that affect the programs. Besides, science, policy and ethics are all involved in the determination of the main objectives of the vaccination program. We present two nonlinear mathematical models that allow us to gain insight into the optimal vaccination strategy under different situations, taking into account the case fatality rate and age-structure of the population. We study scenarios with different availabilities and efficacies of the vaccines. The results of this study show that for most scenarios, the optimal allocation of vaccines is to first give the doses to people in the 55+ age group. However, in some situations the optimal strategy is to first allocate vaccines to the 15–54 age group. This situation occurs whenever the SARS-CoV-2 transmission rate is relatively high and the people in the 55+ age group have a transmission rate 50% or less that of those in the 15–54 age group. This study and similar ones can provide scientific recommendations for countries where the proportion of vaccinated individuals is relatively small or for future pandemics.

Vaccination Schedule under Conditions of Limited Vaccine Production Rate

The paper is devoted to optimal vaccination scheduling during a pandemic to minimize the probability of infection. The recent COVID-19 pandemic showed that the international community is not properly prepared to manage a crisis of this scale. Just after the vaccines had been approved by medical agencies, the policymakers needed to decide on the distribution strategy. To successfully fight the pandemic, the key is to find the equilibrium between the vaccine distribution schedule and the available supplies caused by limited production capacity. This is why society needs to be divided into stratified groups whose access to vaccines is prioritized. Herein, we present the problem of distributing protective actions (i.e., vaccines) and formulate two mixed-integer programs to solve it. The problem of distributing protective actions (PDPA) aims at finding an optimal schedule for a given set of social groups with a constant probability of infection. The problem of distributing protective actions with a herd immunity threshold (PDPAHIT) also includes a variable probability of infection, i.e., the situation when herd immunity is obtained. The results of computational experiments are reported and the potential of the models is illustrated with examples.

A mental health survey among young front-line clinicians in high-risk areas during the COVID-19 sporadic epidemic in China

BACKGROUND

The sporadic coronavirus disease (COVID-19) epidemic has placed enormous psychological stress on people, especially clinicians. The objective of this study was to examine depression, anxiety, quality of life (QOL), and related social psychological factors among young front-line clinicians in high-risk areas during the COVID-19 sporadic epidemic in China and to provide a reference for formulating reasonable countermeasures.

METHODS

In this cross-sectional study, demographic information, COVID-19-related questions, anxiety (Generalized Anxiety Disorder-7, GAD-7), depression (Patient Health Questionnaire-9, PHQ-9), insomnia (Insomnia Severity Index, ISI), stress (Perceived Stress Scale-10, PSS-10), and QOL (World Health Organization Quality of Life-brief version, WHOQOL-BREF) were collected. Binary logistic regression analysis was used to test the relationships between anxiety and/or depression and other related problems. Multiple linear regression analysis was used to test the relationships among factors influencing QOL.

RESULTS

A total of 146 young front-line clinicians were included. The prevalence rates of depression, anxiety, and anxiety-depression comorbidity were 37.7% (95% CI = 29.7-45.6%), 26.0% (95% CI = 18.8-33.2%), and 24.0% (95% CI = 17.0-31.0%), respectively. Severe stress (OR = 1.258, 95% CI = 1.098-1.442, P < 0.01) and insomnia (OR = 1.282, 95% CI = 1.135-1.447, P < 0.01) were positively correlated with depression. Severe stress (OR = 1.487, 95% CI = 1.213-1.823, P < 0.01) and insomnia (OR = 1.131, 95% CI = 1.003-1.274, P < 0.05) were positively correlated with anxiety. Severe stress (OR = 1.532, 95% CI = 1.228-1.912, P < 0.01) was positively correlated with anxiety-depression comorbidity. However, insomnia (OR = 1.081, 95% CI = 0.963-1.214, P > 0.05) was not correlated with anxiety-depression comorbidity. The belief that the vaccine will stop the COVID-19 pandemic (OR = 0.099, 95% CI = 0.014-0.715, P < 0.05) was negatively correlated with anxiety and anxiety-depression comorbidity (OR = 0.101, 95% CI = 0.014-0.744, P < 0.05). Severe stress (B = -0.068, 95% CI = -0.129 to -0.007, P < 0.05) and insomnia (B = -0.127, 95% CI = -0.188 to -0.067, P < 0.01) were negatively correlated with QOL. The belief that the vaccine could provide protection (B = 1.442, 95% CI = 0.253-2.631, P < 0.05) was positively correlated with QOL.

CONCLUSIONS

The prevalence of depression, anxiety, and even anxiety-depression comorbidity was high among young front-line clinicians in high-risk areas during the COVID-19 sporadic epidemic in China. Various biological and psychological factors as well as COVID-19-related factors were associated with mental health issues and QOL. Psychological intervention should evaluate these related factors and formulate measures for these high-risk groups.

Effect of Vaccination to COVID-19 Disease Progression and Herd Immunity

A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.

Mathematical modeling and optimal control of the COVID-19 dynamics

We are considering a new COVID-19 model with an optimal control analysis when vaccination is present. Firstly, we formulate the vaccine-free model and present the associated mathematical results involved. Stability results forR 0 < 1 are shown. In addition, we frame the model with the vaccination class. We look at the mathematical results with the details of the vaccine model. Additionally, we are considering setting controls to minimize infection spread and control. We consider four different controls, such as prevention, vaccination control, rapid screening of people in the exposed category, and people who are identified as infected without screening. Using the suggested controls, we develop an optimal control model and derive mathematical results from it. In addition, the mathematical model with control and without control is resolved by the forward-backward Runge-Kutta method and presents the results graphically. The results obtained through optimal control suggest that controls can be useful for minimizing infected individuals and improving population health.

Mathematical analysis for the effect of voluntary vaccination on the propagation of Corona virus pandemic

In this manuscript, a new nonlinear model for the rapidly spreading Corona virus disease (COVID-19) is developed. We incorporate an additional class of vaccinated humans which ascertains the impact of vaccination strategy for susceptible humans. A complete mathematical analysis of this model is conducted to predict the dynamics of Corona virus in the population. The analysis proves the effectiveness of vaccination strategy employed and helps public health services to control or to reduce the burden of corona virus pandemic. We first prove the existence and uniqueness and then boundedness and positivity of solutions. Threshold parameter for the vaccination model is computed analytically. Stability of the proposed model at fixed points is investigated analytically with the help of threshold parameter to examine epidemiological relevance of the pandemic. We apply LaSalle's invariance principle from the theory of Lyapunov function to prove the global stability of both the equilibria. Two well known numerical techniques namely Runge-Kutta method of order 4 (RK4), and the Non-Standard Finite Difference (NSFD) method are employed to solve the system of ODE's and to validate our obtained theoretical results. For different coverage levels of voluntary vaccination, we explored a complete quantitative analysis of the model. To draw our conclusions, the effect of proposed vaccination on threshold parameter is studied numerically. It is claimed that Corona virus disease could be eradicated faster if a human community selfishly adopts mandatory vaccination measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effect of vaccination strategy on a disease dynamics.

Epidemic model dynamics and fuzzy neural-network optimal control with impulsive traveling and migrating: Case study of COVID-19 vaccination

To suppress the epidemics caused by a virus such as COVID-19, three effective strategies listing vaccination, quarantine and medical treatments, are employed under suitable policies. Quarantine motions may affect the economic systems and pharmaceutical medications may be recently in the developing phase. Thus, vaccination seems the best hope of the current situation to control COVID-19 epidemics. In this work, the dynamic model of COVID-19 epidemic is developed when the quarantine factor and the antiviral factor are established as free variables. Moreover, the impulsive populations are comprehended for traveling and migrating of individuals. The proposed dynamics with impulsive distractions are employed to generate the online data. Thereafter, the equivalent model is developed by using only the daily data of symptomatic infectious individuals and the optimal vaccination policy is derived by utilizing the closed-loop control topology. The theoretical framework of the proposed schemes validates the reduction of symptomatic infectious individuals by using fewer doses of vaccines comparing with the scheduling vaccination.

Modeling vaccination strategies in an Excel spreadsheet: Increasing the rate of vaccination is more effective than increasing the vaccination coverage for containing COVID-19

We have investigated the importance of the rate of vaccination to contain COVID-19 in urban areas. We used an extremely simple epidemiological model that is amenable to implementation in an Excel spreadsheet and includes the demographics of social distancing, efficacy of massive testing and quarantine, and coverage and rate of vaccination as the main parameters to model the progression of COVID-19 pandemics in densely populated urban areas. Our model predicts that effective containment of pandemic progression in densely populated cities would be more effectively achieved by vaccination campaigns that consider the fast distribution and application of vaccines (i.e., 50% coverage in 6 months) while social distancing measures are still in place. Our results suggest that the rate of vaccination is more important than the overall vaccination coverage for containing COVID-19. In addition, our modeling indicates that widespread testing and quarantining of infected subjects would greatly benefit the success of vaccination campaigns. We envision this simple model as a friendly, readily accessible, and cost-effective tool for assisting health officials and local governments in the rational design/planning of vaccination strategies.

The trade-off between mobility and vaccination for COVID-19 control: a metapopulation modelling approach

November 2020 received a string of encouraging results from leading vaccine developers raising hopes for the imminent availability of an effective and safe vaccine against the SARS-CoV-2. In the present work, we discuss the theoretical impact of introducing a vaccine across a range of scenarios. In particular, we investigate how vaccination coverage, efficacy and delivery time affect the control of the transmission dynamics in comparison to mobility restrictions. The analysis is based on a metapopulation epidemic model structured by risk. We perform a global sensitivity analysis using the Sobol method. Our analysis suggest that the reduction of mobility among patches plays a significant role in the mitigation of the disease close to the effect of immunization coverage of 30% achieved in four months. Moreover, for an immunization coverage between 20% and 50% achieved in the first half of 2021 with a vaccine efficacy between 70% and 95%, the percentage reduction in the total number of SARS-CoV-2 infections is between 30% and 50% by the end of 2021 in comparison with the no vaccination scenario.