Assessing the impact of vaccination in a COVID-19 compartmental model

How Does Vaccine-Induced Immunity Compare to Infection-Acquired Immunity in the Dynamics of COVID-19?

Five years into the COVID-19 pandemic, the availability of effective vaccines has substantially reduced new cases, hospitalizations, and mortality. However, the waning of immunity has been a topic of particular interest in relation to disease control. The objective of this study is to investigate the impact of the decline in vaccine-induced immunity (ω1) and infection-acquired immunity (ω2) on disease dynamics. For this purpose, we use a compartmental model with seven compartments that accounts for differential morbidity, vaccination, and waning immunity. A compartmental model divides a population into distinct groups depending on their disease status. The temporal changes in the compartments are represented through ordinary differential equations (ODEs). The model is mathematically analyzed to show that a backward bifurcation (i.e., a perverse outcome) may occur when the vaccinated reproduction number (Rv) is equal to unity. Both local and global sensitivity analysis on the reproduction number reveal that the vaccine efficacy, waning of vaccine-induced immunity, vaccine coverage rate, coefficients of transmissibility, and the recovery rate for mild infections are the most sensitive parameters. The global sensitivity analysis on the cumulative number of infections shows that ω1 and ω2 are both pivotal parameters, while ω2 has a higher influence. Simulations on infections and mortality suggest that the changes in ω2 result in dynamics that are more pronounced compared to the dynamics resulting from the changes in ω1, thus indicating the importance of the duration of infection-acquired immunity in disease spread.

Balancing mitigation strategies for viral outbreaks

Control and prevention strategies are indispensable tools for managing the spread of infectious diseases. This paper examined biological models for the post-vaccination stage of a viral outbreak that integrate two important mitigation tools: social distancing, aimed at reducing the disease transmission rate, and vaccination, which boosts the immune system. Five different scenarios of epidemic progression were considered: (ⅰ) the "no control" scenario, reflecting the natural evolution of a disease without any safety measures in place, (ⅱ) the "reconstructed" scenario, representing real-world data and interventions, (ⅲ) the "social distancing control" scenario covering a broad set of behavioral changes, (ⅳ) the "vaccine control" scenario demonstrating the impact of vaccination on epidemic spread, and (ⅴ) the "both controls concurrently" scenario incorporating social distancing and vaccine controls simultaneously. By comparing these scenarios, we provided a comprehensive analysis of various intervention strategies, offering valuable insights into disease dynamics. Our innovative approach to modeling the cost of control gave rise to a robust computational algorithm for solving optimal control problems associated with different public health regulations. Numerical results were supported by real data for the Delta variant of the COVID-19 pandemic in the United States.

Investigating the impact of vaccine hesitancy on an emerging infectious disease: a mathematical and numerical analysis

Throughout the last two centuries, vaccines have been helpful in mitigating numerous epidemic diseases. However, vaccine hesitancy has been identified as a substantial obstacle in healthcare management. We examined the epidemiological dynamics of an emerging infection under vaccination using an SVEIR model with differential morbidity. We mathematically analyzed the model, derived R 0 , and provided a complete analysis of the bifurcation at R 0 = 1 . Sensitivity analysis and numerical simulations were used to quantify the tradeoffs between vaccine efficacy and vaccine hesitancy on reducing the disease burden. Our results indicated that if the percentage of the population hesitant about taking the vaccine is 10%, then a vaccine with 94% efficacy is required to reduce the peak of infections by 40%. If 60% of the population is reluctant about being vaccinated, then even a perfect vaccine will not be able to reduce the peak of infections by 40%.

Exploring the dynamics of monkeypox transmission with data-driven methods and a deterministic model

Introduction

Mpox (formerly monkeypox) is an infectious disease that spreads mostly through direct contact with infected animals or people's blood, bodily fluids, or cutaneous or mucosal lesions. In light of the global outbreak that occurred in 2022-2023, in this paper, we analyzed global Mpox univariate time series data and provided a comprehensive analysis of disease outbreaks across the world, including the USA with Brazil and three continents: North America, South America, and Europe. The novelty of this study is that it delved into the Mpox time series data by implementing the data-driven methods and a mathematical model concurrently-an aspect not typically addressed in the existing literature. The study is also important because implementing these models concurrently improved our predictions' reliability for infectious diseases.

Methods

We proposed a traditional compartmental model and also implemented deep learning models (1D- convolutional neural network (CNN), long-short term memory (LSTM), bidirectional LSTM (BiLSTM), hybrid CNN-LSTM, and CNN-BiLSTM) as well as statistical time series models: autoregressive integrated moving average (ARIMA) and exponential smoothing on the Mpox data. We also employed the least squares method fitting to estimate the essential epidemiological parameters in the proposed deterministic model.

Results

The primary finding of the deterministic model is that vaccination rates can flatten the curve of infected dynamics and influence the basic reproduction number. Through the numerical simulations, we determined that increased vaccination among the susceptible human population is crucial to control disease transmission. Moreover, in case of an outbreak, our model showed the potential for epidemic control by adjusting the key epidemiological parameters, namely the baseline contact rate and the proportion of contacts within the human population. Next, we analyzed data-driven models that contribute to a comprehensive understanding of disease dynamics in different locations. Additionally, we trained models to provide short-term (eight-week) predictions across various geographical locations, and all eight models produced reliable results.

Conclusion

This study utilized a comprehensive framework to investigate univariate time series data to understand the dynamics of Mpox transmission. The prediction showed that Mpox is in its die-out situation as of July 29, 2023. Moreover, the deterministic model showed the importance of the Mpox vaccination in mitigating the Mpox transmission and highlighted the significance of effectively adjusting key epidemiological parameters during outbreaks, particularly the contact rate in high-risk groups.

Forecasting the effects of vaccination on the COVID-19 pandemic in Malaysia using SEIRV compartmental models

OBJECTIVES

This study aimed to develop susceptible-exposed-infectious-recovered-vaccinated (SEIRV) models to examine the effects of vaccination on coronavirus disease 2019 (COVID-19) case trends in Malaysia during Phase 3 of the National COVID-19 Immunization Program amidst the Delta outbreak.

METHODS

SEIRV models were developed and validated using COVID-19 case and vaccination data from the Ministry of Health, Malaysia, from June 21, 2021 to July 21, 2021 to generate forecasts of COVID-19 cases from July 22, 2021 to December 31, 2021. Three scenarios were examined to measure the effects of vaccination on COVID-19 case trends. Scenarios 1 and 2 represented the trends taking into account the earliest and latest possible times of achieving full vaccination for 80% of the adult population by October 31, 2021 and December 31, 2021, respectively. Scenario 3 described a scenario without vaccination for comparison.

RESULTS

In scenario 1, forecasted cases peaked on August 28, 2021, which was close to the peak of observed cases on August 26, 2021. The observed peak was 20.27% higher than in scenario 1 and 10.37% lower than in scenario 2. The cumulative observed cases from July 22, 2021 to December 31, 2021 were 13.29% higher than in scenario 1 and 55.19% lower than in scenario 2. The daily COVID-19 case trends closely mirrored the forecast of COVID-19 cases in scenario 1 (best-case scenario).

CONCLUSIONS

Our study demonstrated that COVID-19 vaccination reduced COVID-19 case trends during the Delta outbreak. The compartmental models developed assisted in the management and control of the COVID-19 pandemic in Malaysia.

Modeling the effects of Prophylactic behaviors on the spread of SARS-CoV-2 in West Africa

Various general and individual measures have been implemented to limit the spread of SARS-CoV-2 since its emergence in China. Several phenomenological and mechanistic models have been developed to inform and guide health policy. Many of these models ignore opinions about certain control measures, although various opinions and attitudes can influence individual actions. To account for the effects of prophylactic opinions on disease dynamics and to avoid identifiability problems, we expand the SIR-Opinion model of Tyson et al. (2020) to take into account the partial detection of infected individuals in order to provide robust modeling of COVID-19 as well as degrees of adherence to prophylactic treatments, taking into account a hybrid modeling technique using Richard's model and the logistic model. Applying the approach to COVID-19 data from West Africa demonstrates that the more people with a strong prophylactic opinion, the smaller the final COVID-19 pandemic size. The influence of individuals on each other and from the media significantly influences the susceptible population and, thus, the dynamics of the disease. Thus, when considering the opinion of susceptible individuals to the disease, the view of the population at baseline influences its dynamics. The results are expected to inform public policy in the context of emerging and re-emerging infectious diseases.

Sensitivity of endemic behaviour of COVID-19 under a multi-dose vaccination regime, to various biological parameters and control variables

For an infectious disease such as COVID-19, we present a new four-stage vaccination model (unvaccinated, dose 1 + 2, booster, repeated boosters), which examines the impact of vaccination coverage, vaccination rate, generation interval, control reproduction number, vaccine efficacies and rates of waning immunity upon the dynamics of infection. We derive a single equation that allows computation of equilibrium prevalence and incidence of infection, given knowledge about these parameters and variable values. Based upon a 20-compartment model, we develop a numerical simulation of the associated differential equations. The model is not a forecasting or even predictive one, given the uncertainty about several biological parameter values. Rather, it is intended to aid a qualitative understanding of how equilibrium levels of infection may be impacted upon, by the parameters of the system. We examine one-at-a-time sensitivity analysis around a base case scenario. The key finding which should be of interest to policymakers is that while factors such as improved vaccine efficacy, increased vaccination rates, lower waning rates and more stringent non-pharmaceutical interventions might be thought to improve equilibrium levels of infection, this might only be done to good effect if vaccination coverage on a recurrent basis is sufficiently high.

Disease spreading modeling and analysis: a survey

MOTIVATION

The control of the diffusion of diseases is a critical subject of a broad research area, which involves both clinical and political aspects. It makes wide use of computational tools, such as ordinary differential equations, stochastic simulation frameworks and graph theory, and interaction data, from molecular to social granularity levels, to model the ways diseases arise and spread. The coronavirus disease 2019 (COVID-19) is a perfect testbench example to show how these models may help avoid severe lockdown by suggesting, for instance, the best strategies of vaccine prioritization.

RESULTS

Here, we focus on and discuss some graph-based epidemiological models and show how their use may significantly improve the disease spreading control. We offer some examples related to the recent COVID-19 pandemic and discuss how to generalize them to other diseases.

HIV and COVID-19 co-infection: A mathematical model and optimal control

A new mathematical model for COVID-19 and HIV/AIDS is considered to assess the impact of COVID-19 on HIV dynamics and vice-versa. Investigating the epidemiologic synergy between COVID-19 and HIV is important. The dynamics of the full model is driven by that of its sub-models; therefore, basic analysis of the two sub-models; HIV-only and COVID-19 only is carried out. The basic reproduction number is computed and used to prove local and global asymptotic stability of the sub-models' disease-free and endemic equilibria. Using the fmincon function in the Optimization Toolbox of MATLAB, the model is fitted to real COVID-19 data set from South Africa. The impact of intervention measures, namely, COVID-19 and HIV prevention interventions and COVID-19 treatment are incorporated into the model using time-dependent controls. It is observed that HIV prevention measures can significantly reduce the burden of co-infections with COVID-19, while effective treatment of COVID-19 could reduce co-infections with opportunistic infections such as HIV/AIDS. In particular, the COVID-19 only prevention strategy averted about 10,500 new co-infection cases, with similar number also averted by the HIV-only prevention control.