Network models to evaluate vaccine strategies towards herd immunity in COVID-19

Assessing the impacts of vaccination and viral evolution in contact networks

A key lesson learned with COVID-19 is that public health measures were very different from country to country. In this study, we provide an analysis of epidemic dynamics using three well-known stochastic network models-small-world networks (Watts-Strogatz), random networks (Erdös-Rényi), and scale-free networks (Barabási-Albert)-to assess the impact of different viral strains, lockdown strategies, and vaccination campaigns. We highlight the significant role of highly connected nodes in the spread of infections, particularly within Barabási-Albert networks. These networks experienced earlier and higher peaks in infection rates, but ultimately had the lowest total number of infections, indicating their rapid transmission dynamics. We also found that intermittent lockdown strategies, particularly those with 7-day intervals, effectively reduce the total number of infections, serving as viable alternatives to prolonged continuous lockdowns. When simulating vaccination campaigns, we observed a bimodal distribution leading to two distinct outcomes: pandemic contraction and pandemic expansion. For WS and ER networks, rapid mass vaccination campaigns significantly reduced infection rates compared to slower campaigns; however, for BA networks, differences between vaccination strategies were minimal. To account for the evolution of a virus into a more transmissible strain, we modeled vaccination scenarios that varied vaccine efficacy against the wild-type virus and noted a decline in this efficacy over time against a second variant. Our results showed that vaccination coverage above 40% significantly flattened infection peaks for the wild-type virus, while at least 80% coverage was required to similarly reduce peaks for variant 2. Furthermore, the effect of vaccine efficacy on reducing the peak of variant 2 infection was minimal. Although vaccination strategies targeting hub nodes in scale-free networks did not substantially reduce the total number of infections, they were effective in increasing the probability of preventing pandemic outbreaks. These findings underscore the need to consider the network structure for effective pandemic control.

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.

An agent-based nested model integrating within-host and between-host mechanisms to predict an epidemic

The COVID-19 pandemic has remarkably heightened concerns regarding the prediction of communicable disease spread. This study introduces an innovative agent-based modeling approach. In this model, the quantification of human-to-human transmission aligns with the dynamic variations in the viral load within an individual, termed "within-host" and adheres to the susceptible-infected-recovered (SIR) process, referred to as "between-host." Variations in the viral load over time affect the infectivity between individual agents. This model diverges from the traditional SIR model, which employs a constant transmission probability, by incorporating a dynamic, time-dependent transmission probability influenced by the viral load in a host agent. The proposed model retains the time-integrated transmission probability characteristic of the conventional SIR model. As observed in this model, the overall epidemic size remains consistent with the predictions of the standard SIR model. Nonetheless, compared to predictions based on the classical SIR process, notable differences existed in the peak number of the infected individuals and the timing of this peak. These nontrivial differences are induced by the direct correlation between the time-evolving transmission probability and the viral load within a host agent. The developed model can inform targeted intervention strategies and public health policies by providing detailed insights into disease spread dynamics, crucial for effectively managing epidemics.

Population-Level Immunity for Transient Suppression of COVID-19 Waves in Japan from April 2021 to September 2022

Multiple COVID-19 waves have been observed worldwide, with varying numbers of positive cases. Population-level immunity can partly explain a transient suppression of epidemic waves, including immunity acquired after vaccination strategies. In this study, we aimed to estimate population-level immunity in 47 Japanese prefectures during the three waves from April 2021 to September 2022. For each wave, characterized by the predominant variants, namely, Delta, Omicron, and BA.5, the estimated rates of population-level immunity in the 10-64-years age group, wherein the most positive cases were observed, were 20%, 35%, and 45%, respectively. The number of infected cases in the BA.5 wave was inversely associated with the vaccination rates for the second and third injections. We employed machine learning to replicate positive cases in three Japanese prefectures to validate the reliability of our model for population-level immunity. Using interpolation based on machine learning, we estimated the impact of behavioral factors and vaccination on the fifth wave of new positive cases that occurred during the Tokyo 2020 Olympic Games. Our computational results highlighted the critical role of population-level immunity, such as vaccination, in infection suppression. These findings underscore the importance of estimating and monitoring population-level immunity to predict the number of infected cases in future waves. Such estimations that combine numerical derivation and machine learning are of utmost significance for effective management of medical resources, including the vaccination strategy.

Benefits of near-universal vaccination and treatment access to manage COVID-19 burden in the United States

BACKGROUND

As we continue the fourth year of the COVID-19 epidemic, SARS-CoV-2 infections still cause high morbidity and mortality in the United States. During 2020-2022, COVID-19 was one of the leading causes of death in the United States and by far the leading cause among infectious diseases. Vaccination uptake remains low despite this being an effective burden reducing intervention. The development of COVID-19 therapeutics provides hope for mitigating severe clinical outcomes. This modeling study examines combined strategies of vaccination and treatment to reduce the burden of COVID-19 epidemics over the next decade.

METHODS

We use a validated mathematical model to evaluate the reduction of incident cases, hospitalized cases, and deaths in the United States through 2033 under various levels of vaccination and treatment coverage. We assume that future seasonal transmission patterns for COVID-19 will be similar to those of influenza virus and account for the waning of infection-induced immunity and vaccine-induced immunity in a future with stable COVID-19 dynamics. Due to uncertainty in the duration of immunity following vaccination or infection, we consider three exponentially distributed waning rates, with means of 365 days (1 year), 548 days (1.5 years), and 730 days (2 years). We also consider treatment failure, including rebound frequency, as a possible treatment outcome.

RESULTS

As expected, universal vaccination is projected to eliminate transmission and mortality. Under current treatment coverage (13.7%) and vaccination coverage (49%), averages of 81,000-164,600 annual reported deaths, depending on duration of immunity, are expected by the end of this decade. Annual mortality in the United States can be reduced below 50,000 per year with 52-80% annual vaccination coverage and below 10,000 annual deaths with 59-83% annual vaccination coverage, depending on duration of immunity. Universal treatment reduces hospitalizations by 88.6% and deaths by 93.1% under current vaccination coverage. A reduction in vaccination coverage requires a comparatively larger increase in treatment coverage in order for hospitalization and mortality levels to remain unchanged.

CONCLUSIONS

Adopting universal vaccination and universal treatment goals in the United States will likely lead to a COVID-19 mortality burden below 50,000 deaths per year, a burden comparable to that of influenza virus.

Benefits of near-universal vaccination and treatment access to manage COVID-19 burden in the United States

Background

As we enter the fourth year of the COVID-19 pandemic, SARS-CoV-2 infections still cause high morbidity and mortality in the United States. During 2020-2022, COVID-19 was one of the leading causes of death in the United States and by far the leading cause among infectious diseases. Vaccination uptake remains low despite this being an effective burden reducing intervention. The development of COVID-19 therapeutics provides hope for mitigating severe clinical outcomes. This modeling study examines combined strategies of vaccination and treatment to reduce the burden of COVID-19 epidemics over the next decade.

Methods

We use a validated mathematical model to evaluate the reduction of incident cases, hospitalized cases, and deaths in the United States through 2033 under various levels of vaccination and treatment coverage. We assume that future seasonal transmission patterns for COVID-19 will be similar to those of influenza virus. We account for the waning of infection-induced immunity and vaccine-induced immunity in a future with stable COVID-19 dynamics. Due to uncertainty in the duration of immunity following vaccination or infection, we consider two exponentially-distributed waning rates, with means of 365 days (one year) and 548 days (1.5 years). We also consider treatment failure, including rebound frequency, as a possible treatment outcome.

Results

As expected, universal vaccination is projected to eliminate transmission and mortality. Under current treatment coverage (13.7%) and vaccination coverage (49%), averages of 89,000 annual deaths (548-day waning) and 120,000 annual deaths (365-day waning) are expected by the end of this decade. Annual mortality in the United States can be reduced below 50,000 per year with >81% annual vaccination coverage, and below 10,000 annual deaths with >84% annual vaccination coverage. Universal treatment reduces hospitalizations by 88% and deaths by 93% under current vaccination coverage. A reduction in vaccination coverage requires a comparatively larger increase in treatment coverage in order for hospitalization and mortality levels to remain unchanged.

Conclusions

Adopting universal vaccination and universal treatment goals in the United States will likely lead to a COVID-19 mortality burden below 50,000 deaths per year, a burden comparable to that of influenza virus.

A hybrid compartmental model with a case study of COVID-19 in Great Britain and Israel

Given the severe impact of COVID-19 on several societal levels, it is of crucial importance to model the impact of restriction measures on the pandemic evolution, so that governments are able to make informed decisions. Even though there have been countless attempts to propose diverse models since the rise of the outbreak, the increase in data availability and start of vaccination campaigns calls for updated models and studies. Furthermore, most of the works are focused on a very particular place or application and we strive to attain a more general model, resorting to data from different countries. In particular, we compare Great Britain and Israel, two highly different scenarios in terms of vaccination plans and social structure. We build a network-based model, complex enough to model different scenarios of government-mandated restrictions, but generic enough to be applied to any population. To ease the computational load we propose a decomposition strategy for our model.

Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model

In this paper, we present a fractional-order mathematical model in the Caputo sense to investigate the significance of vaccines in controlling COVID-19. The Banach contraction mapping principle is used to prove the existence and uniqueness of the solution. Based on the magnitude of the basic reproduction number, we show that the model consists of two equilibrium solutions that are stable. The disease-free and endemic equilibrium points are locally stably when R0<1 and R0>1 respectively. We perform numerical simulations, with the significance of the vaccine clearly shown. The changes that occur due to the variation of the fractional order α are also shown. The model has been validated by fitting it to four months of real COVID-19 infection data in Thailand. Predictions for a longer period are provided by the model, which provides a good fit for the data.

Optimizing two-dose vaccine resource allocation to combat a pandemic in the context of limited supply: The case of COVID-19

The adequate vaccination is a promising solution to mitigate the enormous socio-economic costs of the ongoing COVID-19 pandemic and allow us to return to normal pre-pandemic activity patterns. However, the vaccine supply shortage will be inevitable during the early stage of the vaccine rollout. Public health authorities face a crucial challenge in allocating scarce vaccines to maximize the benefits of vaccination. In this paper, we study a multi-period two-dose vaccine allocation problem when the vaccine supply is highly limited. To address this problem, we constructed a novel age-structured compartmental model to capture COVID-19 transmission and formulated as a nonlinear programming (NLP) model to minimize the total number of deaths in the population. In the NLP model, we explicitly take into account the two-dose vaccination procedure and several important epidemiologic features of COVID-19, such as pre-symptomatic and asymptomatic transmission, as well as group heterogeneity in susceptibility, symptom rates, severity, etc. We validated the applicability of the proposed model using a real case of the 2021 COVID-19 vaccination campaign in the Midlands of England. We conducted comparative studies to demonstrate the superiority of our method. Our numerical results show that prioritizing the allocation of vaccine resources to older age groups is a robust strategy to prevent more subsequent deaths. In addition, we show that releasing more vaccine doses for first-dose recipients could lead to a greater vaccination benefit than holding back second doses. We also find that it is necessary to maintain appropriate non-pharmaceutical interventions (NPIs) during the vaccination rollout, especially in low-resource settings. Furthermore, our analysis indicates that starting vaccination as soon as possible is able to markedly alleviate the epidemic impact when the vaccine resources are limited but are currently available. Our model provides an effective tool to assist policymakers in developing adaptive COVID-19 likewise vaccination strategies for better preparedness against future pandemic threats.

Prioritizing vaccination based on analysis of community networks

Many countries that had early access to COVID-19 vaccines implemented vaccination strategies that prioritized health care workers and the elderly. As barriers to access eased, vaccine prioritization strategies have been relaxed. However, these strategies are still an important tool for decision makers to manage new variants, plan for future booster shots, or stage mass vaccinations. This paper explores the impact of vaccine prioritization strategies using networks that represent communities with different demographics and connectivity. The impact of vaccination is compared to non-medical intervention to reduce transmission. Several sources of uncertainty are considered, including vaccine willingness and mask effectiveness. This paper finds that while prioritization strategies can have a large impact on reducing deaths and peak hospitalization, selecting the best strategy depends on community characteristics and the desired objective. Additionally, in some cases random vaccination performs as well as more targeted prioritization strategies. Understanding these trade-offs is important when planning vaccine distribution.

Impulsive Neural Control to Schedule Antivirals and Immunomodulators for COVID-19

New SARS-CoV-2 variants escaping the effect of vaccines are an eminent threat. The use of antivirals to inhibit the viral replication cycle or immunomodulators to regulate host immune responses can help to tackle the viral infection at the host level. To evaluate the potential use of these therapies, we propose the application of an inverse optimal neural controller to a mathematical model that represents SARS-CoV-2 dynamics in the host. Antiviral effects and immune responses are considered as the control actions. The variability between infected hosts can be large, thus, the host infection dynamics are identified based on a Recurrent High-Order Neural Network (RHONN) trained with the Extended Kalman Filter (EKF). The performance of the control strategies is tested by employing a Monte Carlo analysis. Simulation results present different scenarios where potential antivirals and immunomodulators could reduce the viral load.

Dynamics and strategies evaluations of a novel reaction-diffusion COVID-19 model with direct and aerosol transmission

The COVID-19 epidemic has infected millions of people and cast a shadow over the global economic recovery. To explore the epidemic's transmission law and provide theoretical guidance for epidemic prevention and control. In this paper, we investigate a novel SEIR-A reaction-diffusion COVID-19 system with direct and aerosol transmission. First, the solution's positivity and boundedness for the system are discussed. Then, the system's the basic reproduction number is defined. Further, the uniform persistence of disease when R 0 > 1 is explored. In addition, the system equilibrium's global stability based on R 0 is demonstrated. Next, the system's NSFD scheme is investigated and the discrete system's positivity, boundedness, and global properties are studied. Meantime, global sensitivity analysis on threshold R 0 is investigated. Interestingly, the effects of three strategies, including vaccination, receiving treatment, and wearing a mask, are evaluated numerically. The results suggest that the above three strategies can effectively control the peak and final scale of infection and shorten the duration of the epidemic. Finally, theoretical simulations and instance predictions are used to give several key indicators of the epidemic, including threshold R 0 , peak, time to peak, time to clear cases, and final size. The instance prediction results are as follows: (1) The basic reproduction numbers of Yangzhou and Putian in China are R 0 = 2.5107 and R 0 = 1.8846 , respectively. (2) This epidemic round in Yangzhou will peak at 56 new daily confirmed cases on the 9th day (August 5), and Putian will peat at 37 new daily confirmed cases on the 6th day (September 15). (3) The final scale of infections in Yangzhou and Putian reached 570 and 205 cases, respectively. (4) The Yangzhou epidemic is expected to be completely cleared on the 25th day (August 21). In addition, the Putian epidemic will continue for 15 days and be cleared on September 24. The analysis results mean that we should improve our immunity by actively vaccinating, reducing the possibility of aerosol transmission by wearing masks. In particular, people should maintain proper social distance, and the government should strengthen medical investment and COVID-19 project research.

Estimation of mRNA COVID-19 Vaccination Effectiveness in Tokyo for Omicron Variants BA.2 and BA.5: Effect of Social Behavior

The variability of the COVID-19 vaccination effectiveness (VE) should be assessed with a resolution of a few days, assuming that the VE is influenced by public behavior and social activity. Here, the VE for the Omicron variants (BA.2 and BA.5) is numerically derived for Japan’s population for the second and third vaccination doses. We then evaluated the daily VE variation due to social behavior from the daily data reports in Tokyo. The VE for the Omicron variants (BA.1, BA.2, and BA.5) are derived from the data of Japan and Tokyo with a computational approach. In addition, the effect of the different parameters regarding human behavior on VE was assessed using daily data in Tokyo. The individual VE for the Omicron BA.2 in Japan was 61% (95% CI: 57–65%) for the second dose of the vaccination from our computation, whereas that for the third dose was 86% (95% CI: 84–88%). The individual BA.5 VE for the second and third doses are 37% (95% CI: 33–40%) and 63% (95% CI: 61–65%). The reduction in the daily VE from the estimated value was closely correlated to the number of tweets related to social gatherings on Twitter. The number of tweets considered here would be one of the new candidates for VE evaluation and surveillance affecting the viral transmission.

Nonlinear time-series forecasts for decision support: short-term demand for ICU beds in Santiago, Chile, during the 2021 COVID-19 pandemic

In Chile, due to the explosive increase of new Coronavirus disease 2019 (COVID-19) cases during the first part of 2021, the ability of health services to accommodate new incoming cases was jeopardized. It has become necessary to be able to manage intensive care unit (ICU) capacity, and for this purpose, monitoring both the evolution of new cases and the demand for ICU beds has become urgent. This paper presents short-term forecast models for the number of new cases and the number of COVID-19 patients admitted to ICUs in the Metropolitan Region in Chile.

Projecting the impact of Covid-19 variants and vaccination strategies in disease transmission using a multilayer network model in Costa Rica

For countries starting to receive steady supplies of vaccines against SARS-CoV-2, the course of Covid-19 for the following months will be determined by the emergence of new variants and successful roll-out of vaccination campaigns. To anticipate this scenario, we used a multilayer network model developed to forecast the transmission dynamics of Covid-19 in Costa Rica, and to estimate the impact of the introduction of the Delta variant in the country, under two plausible vaccination scenarios, one sustaining Costa Rica's July 2021 vaccination pace of 30,000 doses per day and with high acceptance from the population and another with declining vaccination pace to 13,000 doses per day and with lower acceptance. Results suggest that the introduction and gradual dominance of the Delta variant would increase Covid-19 hospitalizations and ICU admissions by [Formula: see text] and [Formula: see text], respectively, from August 2021 to December 2021, depending on vaccine administration and acceptance. In the presence of the Delta variant, new Covid-19 hospitalizations and ICU admissions are estimated to increase around [Formula: see text] and [Formula: see text], respectively, in the same period if the vaccination pace drops. Our results can help decision-makers better prepare for the Covid-19 pandemic in the months to come.

Modelling vaccination strategies for COVID-19

Mathematical models have been used to guide strategies for COVID-19 vaccine distribution. But with the emergence of new SARS-CoV-2 variants and waning immunity, how should vaccine distribution be prioritized?

COVID-19 vaccination strategies depend on the underlying network of social interactions

Since the onset of the coronavirus disease 2019 (COVID-19) pandemic, different mitigation and management strategies limiting economic and social activities have been implemented across many countries. Despite these strategies, the virus continues to spread and mutate. As a result, vaccinations are now administered to suppress the pandemic. Current COVID-19 epidemic models need to be expanded to account for the change in behaviour of new strains, such as an increased virulence and higher transmission rate. Furthermore, models need to account for an increasingly vaccinated population. We present a network model of COVID-19 transmission accounting for different immunity and vaccination scenarios. We conduct a parameter sensitivity analysis and find the average immunity length after an infection to be one of the most critical parameters that define the spread of the disease. Furthermore, we simulate different vaccination strategies and show that vaccinating highly connected individuals first is the quickest strategy for controlling the disease.