Search Results (90)

We present a robust, data-efficient framework for early outbreak assessment using multiscale analysis and Computational Singular Perturbation (CSP). This framework overcomes the shortcomings of the standard compartmental epidemiological models, which often struggle with parameter identifiability during the early stages of a pandemic, limiting their predictive utility considerably when data is sparse. Rather than relying on curve-fitting population profiles, which are sensitive to uncertainty, our approach isolates the dominant “explosive time scale that characterizes the outbreak’s intensity and duration. Using a calibrated SEIRD model, CSP allows for the identification of the paths that drive the process during the outbreak phase and the critical transition from accelerating to decelerating growth, which serves as a reliable precursor to the epidemic peak. This framework is assessed against the 4th, 5th, and 6th waves of the COVID-19 pandemic in Greece during 2021, covering periods dominated by the Delta and Omicron variants. Using only early-stage data from short calibration windows, CSP diagnostic tools revealed distinct dynamical drivers for each wave; e.g., a transition from the 4th wave that was driven by transmission intensity (Delta variant dominance) to the 6th wave that was driven by rapid exposure-to-infection turnover and reduced opposition from recovery mechanisms (Omicron variant dominance). Furthermore, it is demonstrated that the timing of the outbreak’s weakening can be accurately predicted, demonstrating robustness with results obtained from longer observation windows. These findings position multiscale analysis as a powerful, pathogen-agnostic early-warning system, capable of disentangling complex epidemic mechanisms and assessing intervention efficacy in real-time. Full article

In this study, a fractional-order epidemic compartmental model is formulated using the Caputo derivative to account for the memory effects of the chikungunya virus. Based on Banach contractions, fixed-point theorems are used to prove existence and uniqueness, and fundamental properties such as positivity and boundedness are established. Normalized forward sensitivity indices are employed to evaluate the relative impact of model parameters on the transmission dynamics and control of the disease. To reduce the spreading of infection, an optimal control problem is formulated by introducing time-dependent control measures with four control strategies that include public health prevention, treatment enhancement, and vector-control measures. Necessary conditions for optimality are derived using Pontryagin’s Maximum Principle. The predictor–corrector Adams–Bashforth–Moulton scheme is applied across different fractional orders and effectively reduces infection levels. The influence of the fractional order $\xi$ on the epidemic dynamics is investigated, showing that lower values of $\xi$ slow disease progression through a memory effect inherent in the Caputo operator. Moreover, an artificial neural network (ANN) trained via the Levenberg–Marquardt algorithm independently validates the numerical solutions. Full article

During the 2020–2021 period, increasingly complex models have been developed to understand the impact of containment measures, to predict pandemic trends, and then to optimally allocate the few vaccines available. The objective of this study is to demonstrate the application of a time-varying age-dependent SIRD model for developing a vaccination strategy and for better allocating resources. We used a time-varying age-dependent SIRD model to identify the best vaccination strategy considering the percentages of each age group to be vaccinated. Italian public data were used to estimate the model and perform simulations. Simulations were carried out every 15 days from 27 December 2020 to 27 June 2021. Our projections suggest vaccinating those over 89 before other age groups, following a decreasing pattern, to minimise deaths. The cost function of infected individuals returns more unstable results. In general, to minimise infected individuals, it is necessary to assign vaccines to the over-89 and under-30 age groups. Optimal allocation of the limited available vaccine dose is useful to mitigate transmission and to reduce the mortality associated with it. The application of the mathematical model can be very useful at the beginning of an epidemic caused by a new pathogen, a time when it is important to make optimal use of scarce resources, such as vaccines, to best limit the epidemic by using a standardised approach. Full article

Understanding the heterogeneous spread of tuberculosis (TB), particularly multidrug-resistant (MDR) forms and the role of subclinical infection, is critical for achieving the WHO End TB strategy. This study develops a novel compartmental model that explicitly incorporates incipient and subclinical TB together with MDR forms, and links them to case detection and treatment pathways. The key innovation lies in integrating a sensitivity-based identifiability analysis with a Bayesian MCMC framework to quantify parameter uncertainty and correlations directly from regional surveillance data. Applied to five high-burden regions of the Russian Federation (2009–2020), the approach reveals strong heterogeneity in epidemic drivers: wide credible intervals for contagiousness, the rate of progression to bacterio-positive (BE+) states, and detection rates. The probabilistic forecasts up to 2025 are validated against 2021–2023 data. The region-specific differences in these correlated parameters dictate transmission dynamics, and improving detection of BE+ cases is the most effective lever for control. Full article

Standard epidemiological models often treat human behavior as static, failing to capture the dynamic feedback loops that shape epidemic waves. To address this, we developed a compartmental model of COVID-19 that couples the disease dynamics with two co-evolving behavioral games governed by imitation dynamics: an altruistic self-isolation game for infected individuals and a self-interested vaccination game for susceptible individuals. Our simulations reveal a fundamental behavioral paradox: strong adherence to self-isolation, while effective at reducing peak infections, diminishes the perceived risk of disease, thereby undermining the incentive to vaccinate. This dynamic highlights a critical trade-off between managing acute crises through non-pharmaceutical interventions and achieving long-term population immunity. We conclude that vaccination has a powerful stabilizing effect that can prevent the recurrent waves often driven by behavioral responses to non-pharmaceutical interventions. Public health policy must therefore navigate the tension between encouraging short-term mitigation behaviors and communicating the long-term benefits of vaccination to ensure lasting population resilience. Full article

In this research article, we propose a fuzzy fractional-order SEI$R_i{U}_i$HR model to describe the transmission dynamics of COVID-19, comprising susceptible, exposed, infected, reported, unreported, hospitalized, and recovered compartments. The uncertainty in initial conditions is represented using fuzzy numbers, and the fuzzy Laplace transform combined with the Adomian decomposition method is employed to solve nonlinear differential equations and also to derive approximate analytical series of solutions. In addition to fuzzy lower and upper bound solutions, a model is introduced to provide a representative trajectory under uncertainty. A key feature of the proposed model is its inherent symmetry in compartmental transitions and structural formulation, which show the difference in reported and unreported cases. Numerical experiments are conducted to compare fuzzy and normal (non-fuzzy) solutions, supported by 3D visualizations. The results reveal the influence of fractional-order and fuzzy parameters on epidemic progression, demonstrating the model’s capability to capture realistic variability and to provide a flexible framework for analyzing infectious disease dynamics. Full article

Accurate, efficient, and explainable modeling of the dynamics of acute respiratory infections (ARIs) remains, in many aspects, a significant challenge. While compartmental models such as SIR (Susceptible–Infected–Recovered) remain widely used for that purpose due to their simplicity, they cannot capture the complicated multiscale nature of disease progression which unites individual-level interactions affecting the initial phase of an outbreak and mass action laws governing the disease transmission in its general phase. Individual-based models (IBMs) offer a detailed representation capable of capturing these transmission nuances but have high computational demands. In this work, we explore hybrid and surrogate approaches to accelerate forecasting of acute respiratory infection dynamics performed via detailed epidemic models. The hybrid approach combines IBMs and compartmental models, dynamically switching between them with the help of statistical and ML-based methods. The surrogate approach, on the other hand, replaces IBM simulations with trained autoencoder approximations. Our results demonstrate that the usage of machine learning techniques and hybrid modeling allows us to obtain a significant speed–up compared to the original individual-based model—up to 1.6–2 times for the hybrid approach and up to ${10}^4$ times in case of a surrogate model—without compromising accuracy. Although the suggested approaches cannot fully replace the original model, under certain scenarios they make forecasting with fine-grained epidemic models much more feasible for real-time use in epidemic surveillance. Full article

A compartmental, deterministic model was used to explore the effects of temperature dependency in mosquito mortality on the likelihood of epidemics and the size of outbreaks of Chikungunya virus under Florida temperature conditions. Two known vectors, Aedes albopictus and Ae. aegypti, were included, with similar structure but allowing mortality and abundance parameters to vary between them. The mortality relationship with temperature had a central optimal survival region, with increasing mortality outside these regions. The central temperature and the annual mean temperature were most influential in the likelihood of an epidemic, although the variance explained was low. The central temperature, annual mean temperature and day of virus infection influenced the size of the outbreaks. Regression models including two-way interactions explained more of the variance in outcomes than the main effects models, but there was still substantial variance left unexplained. Given the model structure, higher order interactions would be required to explain most of the variance. Full article

In this study, we develop and analyze an extended SEIR-type compartmental model that incorporates vaccination and treatment to describe the dynamics of acute respiratory infection transmission. The model subdivides the infectious population into several symptomatic stages and an asymptomatic class, which allows the evaluation of control strategies across different levels of infection severity. The basic reproduction number ${\mathcal{R}}_0$ is analytically derived, and its sensitivity to vaccination and treatment rates is examined to assess the impact of public health interventions on epidemic control. Numerical simulations demonstrate that the joint implementation of vaccination and treatment can markedly reduce disease prevalence and lead to infection elimination when ${\mathcal{R}}_0<1$. The results emphasize the critical role of parameter interactions in determining disease persistence and show that combining both interventions produces stronger epidemiological effects than either one alone. Machine learning techniques, specifically Support Vector Machines (SVMs), are employed to classify epidemiological outcomes and support parameter estimation. The biological markers evaluated were not effective discriminants of infection status, underscoring the importance of integrating mechanistic modeling with data-driven approaches. This combined framework enhances the understanding of epidemic dynamics and improves the predictive capacity for decision-making in public health. Full article

Background: Monkeypox (Mpox) is a re-emerging zoonotic disease caused by the monkeypox virus (MPXV). Transmission occurs primarily through direct contact with lesions or contaminated materials, with sexual transmission playing a significant role in recent outbreaks. In 2022, Mpox triggered a major global outbreak and was declared a Public Health Emergency of International Concern (PHEIC) by the World Health Organization (WHO), prompting renewed interest in effective control strategies. Methods: This study developed a compartmental SEIR-based model to assess the epidemiological impact of key interventions, including vaccination and isolation, while incorporating critical epidemiological parameters. Sensitivity analyses were conducted to examine (1) disease dynamics in relation to the basic reproduction number, and (2) how different parameters influence the curve of symptomatic infections. Real-world continental-scale data were used to validate the model and identify the parameters that most significantly affect epidemic progression and potential control of Mpox. Results: Results showed that the basic reproduction number was most influenced by the recovery rate, vaccination rate, vaccine effectiveness, and transmission rates of symptomatic and asymptomatic individuals. In contrast, the progression of symptomatic cases was highly sensitive to the case fatality rate and incubation rate. Conclusions: These findings highlight the importance of integrated public health strategies combining vaccination, isolation, and early transmission control to mitigate future Mpox outbreaks. Full article

This study presents an extended approach to compartmental modeling of infectious disease spread, focusing on regional heterogeneity within affected areas. Using classical SIS, SIR, and SEIR frameworks, we simulate the dynamics of COVID-19 across two major regions of Ukraine—Dnipropetrovsk and Kharkiv—during the period 2020–2024. The proposed mathematical model incorporates regionally distributed subpopulations and applies a system of differential equations solved using the classical fourth-order Runge–Kutta method. The simulations are validated against real-world epidemiological data from national and international sources. The SEIR model demonstrated superior performance, achieving maximum relative errors of 4.81% and 5.60% in the Kharkiv and Dnipropetrovsk regions, respectively, outperforming the SIS and SIR models. Despite limited mobility and social contact data, the regionally adapted models achieved acceptable accuracy for medium-term forecasting. This validates the practical applicability of extended compartmental models in public health planning, particularly in settings with constrained data availability. The results further support the use of these models for estimating critical epidemiological indicators such as infection peaks and hospital resource demands. The proposed framework offers a scalable and computationally efficient tool for regional epidemic forecasting, with potential applications to future outbreaks in geographically heterogeneous environments. Full article

Consider an evolving epidemic in which each person is either (S) susceptible and healthy; (E) exposed, contagious but asymptomatic; (I) infected, symptomatic, and quarantined; or (R) recovered, healthy, and susceptible. The inference problem, given (i) who is showing symptoms (I) and who is not (S, E, R) and (ii) the distribution of meetings among people each day, is to predict the number of infected people (state I) in future days (e.g., 1 through 20 days out into the future) for the purpose of planning resources (e.g., needles, medicine, staffing) and policy responses (e.g., masking). Each prediction horizon has different uses. For example, staffing may require forecasts of only a few days, while logistics (i.e., which supplies to order) may require a two- or three-week horizon. Our algorithm and system EpiInfer is a non-Markovian approach to forecasting infection rates. It is non-Markovian because it looks at infection rates over the past several days in order to make predictions about the future. In addition, it makes use of the following information: (i) the distribution of the number of meetings per person and (ii) the transition probabilities between states and uses those estimates to forecast future infection rates. In both simulated and real data, EpiInfer performs better than the standard (in epidemiology) differential equation approaches as well as general-purpose neural network approaches. Compared to ARIMA, EpiInfer is better starting with 6-day forecasts, while ARIMA is better for shorter forecast horizons. In fact, our operational recommendation would be to use ARIMA (1,1,1) for short predictions (5 days or less) and then EpiInfer thereafter. Doing so would reduce relative Root Mean Squared Error (RMSE) over any state of the art method by up to a factor of 4. Predictions of this accuracy could be useful for people, supply, and policy planning. Full article

Background/Objectives: The COVID-19 pandemic highlighted the critical need for accurate predictive models to guide public health interventions and optimize healthcare resource allocation. This study evaluates how the complexity of compartmental infectious disease models influences their forecasting accuracy and utility for pandemic resource planning. Methods: We analyzed a range of compartmental models, including simple susceptible-infected-recovered (SIR) models and more complex frameworks incorporating asymptomatic carriers and deaths. These models were calibrated and tested using real-world COVID-19 data from the United States to assess their performance in predicting symptomatic and asymptomatic infection counts, peak infection timing, and resource demands. Both adaptive models (updating parameters with real-time data) and non-adaptive models were evaluated. Results: Numerical results show that while more complex models capture detailed disease dynamics, simpler models often yield better forecast accuracy, especially during early pandemic stages or when predicting peak infection periods. Adaptive models provided the most accurate short-term forecasts but required substantial computational resources, making them less practical for long-term planning. Non-adaptive models produced stable long-term forecasts useful for strategic resource allocation, such as hospital bed and ICU planning. Conclusions: Model selection should align with the pandemic stage and decision-making horizon. Simpler models are effective for rapid early-stage interventions, adaptive models excel in short-term operational forecasting, and non-adaptive models remain valuable for long-term resource planning. These findings can inform policymakers on selecting appropriate modeling approaches to improve pandemic response effectiveness. Full article

Campylobacteriosis has been described as an ever-changing disease and health issue that is rather dangerous for different population groups all over the globe. The World Health Organization (WHO) reports that 33 million years of healthy living are lost annually, and nearly one in ten persons have foodborne illnesses, including Campylobacteriosis. This explains why there is a need to develop new policies and strategies in the management of diseases at the intergovernmental level. Within this framework, an advanced stochastic fractional delayed model for Campylobacteriosis includes new stochastic, memory, and time delay factors. This model adopts a numerical computational technique called the Grunwald–Letnikov-based Nonstandard Finite Difference (GL-NSFD) scheme, which yields an exponential fitted solution that is non-negative and uniformly bounded, which are essential characteristics when working with compartmental models in epidemic research. Two equilibrium states are identified: the first is an infectious Campylobacteriosis-free state, and the second is a Campylobacteriosis-present state. When stability analysis with the help of the basic reproduction number $R_0$ is performed, the stability of both equilibrium points depends on the $R_0$ value. This is in concordance with the actual epidemiological data and the research conducted by the WHO in recent years, with a focus on the tendency to increase the rate of infections and the necessity to intervene in time. The model goes further to analyze how a delay in response affects the band of Campylobacteriosis spread, and also agrees that a delay in response is a significant factor. The first simulations of the current state of the system suggest that certain conditions can be achieved, and the eradication of the disease is possible if specific precautions are taken. The outcomes also indicate that enhancing the levels of compliance with the WHO-endorsed SOPs by a significant margin can lower infection rates significantly, which can serve as a roadmap to respond to this public health threat. Unlike most analytical papers, this research contributes actual findings and provides useful recommendations for disease management approaches and policies. Full article

Environmental transmission is a critical driver of cholera dynamics and a key factor influencing model-based inference and forecasting. This study focuses on stable parameter estimation and forecasting of cholera outbreaks using a compartmental SIRB model informed by three formulations of the environmental transmission rate: (1) a pre-parameterized periodic function, (2) a temperature-driven function, and (3) a flexible, data-driven time-dependent function. We apply these methods to the 1991–1997 cholera epidemic in Peru, estimating key parameters; these include the case reporting rate and human-to-human transmission rate. We assess practical identifiability via parametric bootstrapping and compare the performance of each transmission formulation in fitting epidemic data and forecasting short-term incidence. Our results demonstrate that while the data-driven approach achieves superior in-sample fit, the temperature-dependent model offers better forecasting performance due to its ability to incorporate seasonal trends. The study highlights trade-offs between model flexibility and parameter identifiability and provides a framework for evaluating cholera transmission models under data limitations. These insights can inform public health strategies for outbreak preparedness and response. Full article