Compartmental Epidemiological Models Research Articles

A deterministic compartment model for analyzing tuberculosis dynamics considering vaccination and reinfection

Tuberculosis is a pressing global health concern, particularly pervasive in many developing nations. This study investigates the influence of treatment failure on tuberculosis control strategies, incorporating vaccination interventions using a deterministic compartmental epidemiological model. Mathematical analysis unveils disease-free and endemic equilibrium points, with the control reproduction number determined using next-generation methods. Identifying endemic equilibrium points and determining the control reproduction number provide essential metrics for assessing the effectiveness of control strategies and guiding policy decisions. The model exhibits a backward bifurcation phenomenon, leading to multiple endemic equilibria despite a reproduction number below one due to reinfection. Sensitivity analysis using Latin Hypercube Sampling/Partial Rank Correlation Coefficient elucidates parameter impacts on the control reproduction number. Vaccination efficacy is crucial for quality and validity, with superior quality and longer validity yielding more significant effects. While reinfection may not directly affect the reproduction number, its influence is pivotal in determining tuberculosis persistence or extinction. This study underscores the intricate interplay of factors in tuberculosis control strategies, providing insights vital for effective interventions and policy formulation.

Estimating vaccine efficacy during open-label follow-up of COVID-19 vaccine trials based on population-level surveillance data

While rapid development and roll out of COVID-19 vaccines is necessary in a pandemic, the process limits the ability of clinical trials to assess longer-term vaccine efficacy. We leveraged COVID-19 surveillance data in the U.S. to evaluate vaccine efficacy in U.S. Government-funded COVID-19 vaccine efficacy trials with a three-step estimation process. First, we used a compartmental epidemiological model informed by county-level surveillance data, a “population model”, to estimate SARS-CoV-2 incidence among the unvaccinated. Second, a ”cohort model” was used to adjust the population SARS-CoV-2 incidence to the vaccine trial cohort, taking into account individual participant characteristics and the difference between SARS-CoV-2 infection and COVID-19 disease. Third, we fit a regression model estimating the offset between the cohort-model-based COVID-19 incidence in the unvaccinated with the placebo-group COVID-19 incidence in the trial during blinded follow-up. Counterfactual placebo COVID-19 incidence was estimated during open-label follow-up by adjusting the cohort-model-based incidence rate by the estimated offset. Vaccine efficacy during open-label follow-up was estimated by contrasting the vaccine group COVID-19 incidence with the counterfactual placebo COVID-19 incidence. We documented good performance of the methodology in a simulation study. We also applied the methodology to estimate vaccine efficacy for the two-dose AZD1222 COVID-19 vaccine using data from the phase 3 U.S. trial (ClinicalTrials.gov # NCT04516746). We estimated AZD1222 vaccine efficacy of 59.1% (95% uncertainty interval (UI): 40.4%–74.3%) in April, 2021 (mean 106 days post-second dose), which reduced to 35.7% (95% UI: 15.0%–51.7%) in July, 2021 (mean 198 days post-second-dose). We developed and evaluated a methodology for estimating longer-term vaccine efficacy. This methodology could be applied to estimating counterfactual placebo incidence for future placebo-controlled vaccine efficacy trials of emerging pathogens with early termination of blinded follow-up, to active-controlled or uncontrolled COVID-19 vaccine efficacy trials, and to other clinical endpoints influenced by vaccination.

A dynamic game of lymphatic filariasis prevention by voluntary use of insecticide treated nets

Lymphatic filariasis (LF) has been targeted for elimination as a public health concern by 2030 with a goal to keep the prevalence of LF infections under the 1% threshold. While mass drug administration (MDA) is a primary strategy recommended by WHO, the use of insecticide treated nets (ITN) plays a crucial role as an alternative strategy when MDA cannot be used. In this paper, we use imitation dynamics to incorporate human behavior and voluntary use of ITN into the compartmental epidemiological model of LF transmission. We find the equilibrium states of the dynamics and the ITN usage as it depends on epidemiological parameters and the cost of ITNs. We investigate the conditions under which the voluntary use of ITNs can keep the LF prevalence under the 1% threshold. We found that when the cost of using the ITNs is about 105 smaller than the perceived cost of LF, then the voluntary use of ITNs will eliminate LF as a public health concern. Furthermore, when the ITNs are given away for free, our model predicts that over 80% of the population will use them which would eliminate LF completely in regions where Anopheles are the primary vectors.

A compartmental deterministic epidemiological model with non-linear differential equations for analyzing the co-infection dynamics between COVID-19, HIV, and Monkeypox diseases

One of the realities of the COVID-19 worldwide pandemic is the occurrence of infected individuals with COVID-19 and two other diseases, Monkeypox and HIV. This study presents a compartmental deterministic epidemiological model with non-linear differential equations to study the transmission dynamics of the co-infection of the three diseases. Rigorous analysis of the model shows that the disease-free equilibrium was locally and globally asymptotically stable when the associated reproduction number of the diseases was not up to unity, showing that the spread of the diseases and their co-circulation can be effectively controlled in this circumstance. Real-life data about the diseases are collated and fitted to the model through which values of key parameters of the model were estimated. These parameters’ values were used to carry out numerical simulations of the model using MATLAB and validate the qualitative results obtained earlier from the model. The numerical simulation of the model was used to explore the interactions and dynamics resulting from the co-infection of COVID-19, HIV, and Monkeypox in humans, including the reciprocal impacts of each of the diseases on the other two, their patterns of coexistence and their effects on the host. We developed a tool to help predict the co-infection of the three diseases. Through the insights gained in this study, recommendations were made to policymakers in the healthcare sector on how to combat effectively and adequately the co-infection of the three diseases in the human population and mitigate their disease burden.

The Predicted Potential Impact of COVID-19 Pandemic on Tuberculosis Epidemic in Tamil Nadu, South India.

To estimate the prevalence and incidence of TB before and during the COVID-19 pandemic in Tamil Nadu, south India. In the present study, the effect of COVID-19 epidemiology on the TB epidemic was assessed by the SEIR (Susceptible-Exposed-Infected-Recovered), a compartmental epidemiological model. The model input parameters on compartments of TB and incidence of COVID-19 were collected from the published literature. Based on the data collected, point prevalence and incidence of TB per 100,000 population is calculated with and without COVID-19. A prediction was conducted up to 2025, trend analysis was performed, and a trend chi-square test and chi-square test of independence were used to test the difference between the prevalence with and without COVID-19. R software 2000 (R 4.0.0) was used for analysis. The TB prevalence without and with COVID-19 decreases from 289 in 2020 to 271 in 2025 and from 289 in 2020 to 269 in 2025, respectively. Similarly, the incidence of TB was decreasing from 144 in 2020 to 135 in 2025 without COVID-19 and 143 in 2020 to 134 in 2025 with COVID-19. Though the TB burden is decreasing over the years, the trend was not statistically significant (p > 0.05). With respect to the district level, the prevalence and incidence of TB with and without COVID-19 is also found to be decreasing over the years. It was also found that the difference in the prevalence and incidence of TB with and without COVID-19 was not statically significant. The results of our study shows that there was an annual decline of around 2% from 2020 to 2025 in the trend of the prevalence and incidence of TB with and without COVID-19. Overall, there is a reduction, but it was not significant, and there is no significant effect of COVID-19 on TB in Tamil Nadu.

MORE POWERFUL HSIC-BASED INDEPENDENCE TESTS, EXTENSION TO SPACE-FILLING DESIGNS AND FUNCTIONAL DATA

The Hilbert-Schmidt independence criterion (HSIC) is a dependence measure based on reproducing kernel Hilbert spaces. This measure can be used for the global sensitivity analysis of numerical simulators whose objective is to identify the most influential inputs on the output(s) of the code. For this purpose, HSIC-based sensitivity measures and independence tests can be used for the ranking and screening of inputs, respectively. In this framework, this work proposes several improvements in the use of HSIC to increase their application spectrum and make the associated independence tests more powerful. First, we introduce a new method to perform the tests in a non-asymptotic framework. This method is much less central-processing-time expensive than the one based on permutation, while remaining as efficient. Then, the use of HSIC-based independence tests is extended to the case of some space-filling designs, where the independent and identically distributed condition of the observations is lifted. For this, a new procedure based on conditional randomization test is used. In addition, we also propose a more powerful test that relies on a well-chosen parameterization of the HSIC statistics: the kernel bandwidth parameter is optimized instead of the standard choices. Numerical studies are performed to assess the efficiency of these procedures and compare it to existing tests in the literature. Finally, HSIC-based indices for functional outputs are defined: they rely on appropriate and relevant kernels for this type of data. Illustrations are provided on temporal outputs of an analytical function and a compartmental epidemiological model.

Systems Biology Approaches to Understanding COVID-19 Spread in the Population.

In essence, the COVID-19 pandemic can be regarded as a systems biology problem, with the entire world as the system, and the human population as the element transitioning from one state to another with certain transition rates. While capturing all the relevant features of such a complex system is hardly possible, compartmental epidemiological models can be used as an appropriate simplification to model the system's dynamics and infer its important characteristics, such as basic and effective reproductive numbers of the virus. These measures can later be used as response variables in feature selection methods to uncover the main factors contributing to disease transmissibility. We here demonstrate that a combination of dynamic modeling and machine learning approaches can represent a powerful tool in understanding the spread, not only of COVID-19, but of any infectious disease of epidemiological proportions.

Control Strategies for the COVID-19 Infection Wave in India: A Mathematical Model Incorporating Vaccine Effectiveness

The waning effectiveness of the coronavirus disease-2019 (COVID-19) vaccines and the emergence of new variants have given rise to the possibility of future outbreaks of the infection. COVID-19 has caused more than 43 million reported cases and 526,000 deaths in India so far, and the disease spread is active again despite mass vaccinations. In this article, we present a compartmental epidemiological model incorporating vaccinations with dose-dependent effectiveness. We study a possible sudden outbreak of SARS-CoV2 variants in India, bring out the associated predictions for various vaccination rates, and point out optimum control measures. Our model simulation numbers for the total infected are close to the seroprevalance data in August 2021, and our results show that second dose vaccine effectiveness is the most sensitive parameter in the future evolution of the disease. A combination of vaccination and social distancing is the key to tackling the current situation and for the coming few months. Our simulation shows that social distancing measures show better control over disease spread than higher vaccination rates, and disease spread does not appear to rise sharply in the near future unless a new variant emerges.

Pharmaceutical and non-pharmaceutical interventions for controlling the COVID-19 pandemic.

Disease spread can be affected by pharmaceutical interventions (such as vaccination) and non-pharmaceutical interventions (such as physical distancing, mask-wearing and contact tracing). Understanding the relationship between disease dynamics and human behaviour is a significant factor to controlling infections. In this work, we propose a compartmental epidemiological model for studying how the infection dynamics of COVID-19 evolves for people with different levels of social distancing, natural immunity and vaccine-induced immunity. Our model recreates the transmission dynamics of COVID-19 in Ontario up to December 2021. Our results indicate that people change their behaviour based on the disease dynamics and mitigation measures. Specifically, they adopt more protective behaviour when mandated social distancing measures are in effect, typically concurrent with a high number of infections. They reduce protective behaviour when vaccination coverage is high or when mandated contact reduction measures are relaxed, typically concurrent with a reduction of infections. We demonstrate that waning of infection and vaccine-induced immunity are important for reproducing disease transmission in autumn 2021.

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.

Spatial-temporal simulation for hospital infection spread and outbreaks of Clostridioides difficile

Validated and curated datasets are essential for studying the spread and control of infectious diseases in hospital settings, requiring clinical information on patients’ evolution and their location. The literature shows that approaches based on Artificial Intelligence (AI) in the development of clinical-support systems have benefits that are increasingly recognized. However, there is a lack of available high-volume data, necessary for trusting such AI models. One effective method in this situation involves the simulation of realistic data. Existing simulators primarily focus on implementing compartmental epidemiological models and contact networks to validate epidemiological hypotheses. Nevertheless, other practical aspects such as the hospital building distribution, shifts or safety policies on infections has received minimal attention. In this paper, we propose a novel approach for a simulator of nosocomial infection spread, combining agent-based patient description, spatial-temporal constraints of the hospital settings, and microorganism behavior driven by epidemiological models. The predictive validity of the model was analyzed considering micro and macro-face validation, parameter calibration based on literature review, model alignment, and sensitive analysis with an expert. This simulation model is useful in monitoring infections and in the decision-making process in a hospital, by helping to detect spatial-temporal patterns and predict statistical data about the disease.

A Mathematical Model for the COVID-19 Pandemic in Tokyo through Changing Point Calculus

The great social and economic impact that the COVID-19 pandemic has had on a global level has encouraged the development of new mathematical models that make it possible to better manage this and future pandemics. Here, we propose an extension of the classical epidemiological compartmental model SIR, the SEIAMD model (Susceptible–Exposed–Identified–Asymptomatic–iMmunized–Deceased), which considers the appearance of new virus variants, the use of vaccines, the existence of nonidentified asymptomatic individuals, and the loss of immunity acquired by infection or vaccination. Using an optimization model coded in Python that allows us to determine the change points that represent different behaviors of infected people, the SEIAMD model calculates, from official data, the different effective contact rates that were observed during the first seven waves of the COVID-19 pandemic in Tokyo due to the application of Non-Pharmaceutical Interventions (NPIs) and social habits. The closeness of the results obtained with our model and the real data, as well as the accuracy of predictions and observations, confirm the suitability of our model for studying the evolution of the COVID-19 pandemic in Tokyo.

Relating quanta conservation and compartmental epidemiological models of airborne disease outbreaks in buildings

We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition.

Fast and Accurate Maximum-Likelihood Estimation of Multi-Type Birth-Death Epidemiological Models from Phylogenetic Trees.

Multi-type birth-death (MTBD) models are phylodynamic analogies of compartmental models in classical epidemiology. They serve to infer such epidemiological parameters as the average number of secondary infections Re and the infectious time from a phylogenetic tree (a genealogy of pathogen sequences). The representatives of this model family focus on various aspects of pathogen epidemics. For instance, the birth-death exposed-infectious (BDEI) model describes the transmission of pathogens featuring an incubation period (when there is a delay between the moment of infection and becoming infectious, as for Ebola and SARS-CoV-2), and permits its estimation along with other parameters. With constantly growing sequencing data, MTBD models should be extremely useful for unravelling information on pathogen epidemics. However, existing implementations of these models in a phylodynamic framework have not yet caught up with the sequencing speed. Computing time and numerical instability issues limit their applicability to medium data sets (≤ 500 samples), while the accuracy of estimations should increase with more data. We propose a new highly parallelizable formulation of ordinary differential equations for MTBD models. We also extend them to forests to represent situations when a (sub-)epidemic started from several cases (e.g., multiple introductions to a country). We implemented it for the BDEI model in a maximum likelihood framework using a combination of numerical analysis methods for efficient equation resolution. Our implementation estimates epidemiological parameter values and their confidence intervals in two minutes on a phylogenetic tree of 10,000 samples. Comparison to the existing implementations on simulated data shows that it is not only much faster but also more accurate. An application of our tool to the 2014 Ebola epidemic in Sierra-Leone is also convincing, with very fast calculation and precise estimates. As MTBD models are closely related to Cladogenetic State Speciation and Extinction (ClaSSE)-like models, our findings could also be easily transferred to the macroevolution domain.

Bringing back the people in modelling epidemics

The emergence of COVID-19 favoured the development at Université de Montréal of an educational initiative aimed at promoting modelling and simulation in teaching and learning postsecondary mathematics. In our learning activities, modelling is not reduced to curve fitting; software is used and questions are asked to get a deeper understanding of the structure of a situation. In particular, compartmental epidemiological models were the topic of activities using digital tools (Insight Maker and Excel) that generated interest among teachers and students. With the possibilities offered by such tools of reflecting more adequately the complexity of the situation, we considered it relevant to model the perceptions related to significant effects of nonpharmaceutical interventions (NPIs) as well as the apparent social divide in behaviours regarding mandated measures and its effect on the epidemic. A study carried out on these aspects, based on data collected in Québec, led us to develop a new model which could form the basis for a new activity and be explored and further refined by students. This work leads to considering a social dimension to the teaching of modelling with differential equations and to include this teaching in the development of critical thinking.

Epidemic modeling using differential equations with implementation in R

The COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach the principles of mathematical modeling in epidemiology. Compartmental epidemiological models, such as the SIR (susceptible-infected-recovered), are widely used by researchers and educators to study and teach infectious disease dynamics, particularly for COVID-19. The SIR model is considered a fundamental mathematical model for the spread of epidemic disease and employs Ordinary Differential Equations to determine the number of individuals in each compartment of a population at a given time. In this note, we demonstrate how to build a basic SIR model. We show how to simulate, plot, and interpret the results using numerical simulation with R, a popular programming language widely used in data analysis and scientific research.

A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation

A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation

Modeling the spread of an infectious disease with fly-in-fly-out work method

The article discusses problems related to building models for the spread of infectious diseases. It explores the relevance of epidemiological modeling in various public spheres, including how production processes can impact disease spread. The article analyzes the possibilities of using compartmental epidemiological models for epidemiological modeling, taking into account population migration and geography. It also considers methods for constructing compartmental models that account for mortality due to the disease. The article proposes an approach to constructing compartmental models that considers population heterogeneity, dividing it into non-overlapping subsets based on contact intensity indicators. Additionally, the article describes a method for modeling migrating subsets within this approach. The article demonstrates the results of constructed epidemiological models for the spread of infection between localities, taking into account migration fly-in-fly-out worker groups. It compares models with different interactions between individuals of subsets and shows that the order of infection spread between subsets affects epidemic dynamics but not the total number of affected individuals. The article also demonstrates that direct contact can accelerate epidemic transmission between subsets compared to transmission through migrating groups. The proposed approach can be used to implement an epidemic simulation system that accounts for migration, geographical factors, and the nature of participant interaction in the production process.

COVID-19 transmission dynamics and the impact of vaccination: modelling, analysis and simulations.

Despite the lifting of COVID-19 restrictions, the COVID-19 pandemic and its effects remain a global challenge including the sub-Saharan Africa (SSA) region. Knowledge of the COVID-19 dynamics and its potential trends amidst variations in COVID-19 vaccine coverage is therefore crucial for policy makers in the SSA region where vaccine uptake is generally lower than in high-income countries. Using a compartmental epidemiological model, this study aims to forecast the potential COVID-19 trends and determine how long a wave could be, taking into consideration the current vaccination rates. The model is calibrated using South African reported data for the first four waves of COVID-19, and the data for the fifth wave are used to test the validity of the model forecast. The model is qualitatively analysed by determining equilibria and their stability, calculating the basic reproduction number and investigating the local and global sensitivity analysis with respect to . The impact of vaccination and control interventions are investigated via a series of numerical simulations. Based on the fitted data and simulations, we observed that massive vaccination would only be beneficial (deaths averting) if a highly effective vaccine is used, particularly in combination with non-pharmaceutical interventions. Furthermore, our forecasts demonstrate that increased vaccination coverage in SSA increases population immunity leading to low daily infection numbers in potential future waves. Our findings could be helpful in guiding policy makers and governments in designing vaccination strategies and the implementation of other COVID-19 mitigation strategies.

Between lives and economy: COVID-19 containment policy in open economies

This paper studies containment policies for combating a pandemic in an open-economy context. It does so via quantitative analyses using a model that incorporates a standard epidemiological compartmental model in a general equilibrium multi-country, multi-sector Ricardian model of international trade with input–output linkages. We quantitatively evaluate the long-run welfare and real-income losses due to the short-run pandemic shocks, and we study the role of trade in these effects. We devise a novel approach to computing national optimal policies. We find that (1) the long-run welfare and real-income losses due to just two years of pandemic shocks are substantial; (2) international trade helps buffer both the welfare and real-income losses, and it also saves lives; (3) the computed optimal policies indicate that most countries should have tightened their containment measures relative to what was done; and (4) compared to the case of autarky, the optimal policy under trade is generally more stringent.