Epidemic Model Research Articles

Improving the Method for Simulating the Evolution of SAR-CoV-2 in the Form of Hybrid SIR Models for Predicting New COVID-19 Waves

Improving the Method for Simulating the Evolution of SAR-CoV-2 in the Form of Hybrid SIR Models for Predicting New COVID-19 Waves

Predicting COVID-19 infections using multi-layer centrality measures in population-scale networks

Understanding the spread of SARS-CoV-2 has been one of the most pressing problems of the recent past. Network models present a potent approach to studying such spreading phenomena because of their ability to represent complex social interactions. While previous studies have shown that network centrality measures are generally able to identify influential spreaders in a susceptible population, it is not yet known if they can also be used to predict infection risks. However, information about infection risks at the individual level is vital for the design of targeted interventions. Here, we use large-scale administrative data from the Netherlands to study whether centrality measures can predict the risk and timing of infections with COVID-19-like diseases. We investigate this issue leveraging the framework of multi-layer networks, which accounts for interactions taking place in different contexts, such as workplaces, households and schools. In epidemic models simulated on real-world network data from over one million individuals, we find that existing centrality measures offer good predictions of relative infection risks, and are correlated with the timing of individual infections. We however find no association between centrality measures and real SARS-CoV-2 test data, which indicates that population-scale network data alone cannot aid predictions of virus transmission.

Solving fractional differential equations on a quantum computer: A variational approach

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in terms of time complexity but also has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation costs scale economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering applications, such as the subdiffusion equation, the nonlinear Burgers' equation, and a coupled diffusive epidemic model. We assess quantum hardware performance under realistic noise conditions, further validating the practical utility of our algorithm.

Exact solutions to SIR epidemic models via integrable discretization

An integrable discretization of the SIR model with vaccination is proposed. Through the discretization, the conserved quantities of the continuous model are inherited to the discrete model, since the discretization is based on the intersection structure of the non-algebraic invariant curve defined by the conserved quantities. Uniqueness of the forward/backward evolution of the discrete model is demonstrated in terms of the single-valuedness of the Lambert W function on the positive real axis. Furthermore, the exact solution to the continuous SIR model with vaccination is constructed via the integrable discretization. When applied to the original SIR model, the discretization procedure leads to two kinds of integrable discretization, and the exact solution to the continuous SIR model is also deduced. It is furthermore shown that the discrete SIR model geometrically linearizes the time evolution by using the non-autonomous parallel translation of the line intersecting the invariant curve.

Comparing the Change in R0 for the COVID-19 Pandemic in Eight Countries Using an SIR Model for Specific Periods

The reproduction number, R0, is an important parameter in epidemic models. It is interpreted as the average number of new cases resulted from each infected individual during the course of infection. In this paper, the R0 estimates since the outbreak of COVID-19 till 10 August 2020 for eight countries were computed using the package R{eSIR}. The computed values were examined and compared with the daily R0 estimates obtained by a static SIR model by aligning the days of infection, assuming a fixed number of days for the infected person to become confirmed/recover/die. The results showed that running R{eSIR} to obtain R0 estimates provided an easy mean of exploring epidemic data. Care must be taken in the interpretation of R0 as a measure of severity of the spread of an epidemic. Other factors, such as imported cases, need to be considered.

Optimal control and bifurcation analysis of a delayed fractional-order SIRS model with general incidence rate and delayed control

A fractional-order generalized SIRS model considering incubation period is established in this paper for the transmission of emerging pathogens. The corresponding Hopf bifurcation is discussed by selecting time delay as the bifurcation parameter. In order to control the occurrence of Hopf bifurcation and achieve better dynamic behaviors, a delayed feedback control is adopted to the model. Further, the delayed fractional-order optimal control problem (DFOCP) is proposed and discussed. The parameters of the proposed model are identified through the measurement data of coronavirus disease 2019 (COVID-19). Based on the results of parameter identification, the corresponding DFOCP with delayed control is numerically solved.

Individualized epidemic spreading models predict epilepsy surgery outcomes: A pseudo-prospective study.

Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but up to 50% of patients continue to have seizures one year after the resection. In order to aid presurgical planning and predict postsurgical outcome on a patient-by-patient basis, we developed a framework of individualized computational models that combines epidemic spreading with patient-specific connectivity and epileptogeneity maps: the Epidemic Spreading Seizure and Epilepsy Surgery framework (ESSES). ESSES parameters were fitted in a retrospective study (N = 15) to reproduce invasive electroencephalography (iEEG)-recorded seizures. ESSES reproduced the iEEG-recorded seizures, and significantly better so for patients with good (seizure-free, SF) than bad (nonseizure-free, NSF) outcome. We illustrate here the clinical applicability of ESSES with a pseudo-prospective study (N = 34) with a blind setting (to the resection strategy and surgical outcome) that emulated presurgical conditions. By setting the model parameters in the retrospective study, ESSES could be applied also to patients without iEEG data. ESSES could predict the chances of good outcome after any resection by finding patient-specific model-based optimal resection strategies, which we found to be smaller for SF than NSF patients, suggesting an intrinsic difference in the network organization or presurgical evaluation results of NSF patients. The actual surgical plan overlapped more with the model-based optimal resection, and had a larger effect in decreasing modeled seizure propagation, for SF patients than for NSF patients. Overall, ESSES could correctly predict 75% of NSF and 80.8% of SF cases pseudo-prospectively. Our results show that individualised computational models may inform surgical planning by suggesting alternative resections and providing information on the likelihood of a good outcome after a proposed resection. This is the first time that such a model is validated with a fully independent cohort and without the need for iEEG recordings.

Instabilities and self–organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID–19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread–anchored in physical considerations–lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing–type instabilities, and the concomitant emergence of steady–state patterns under the interplay between three critical model parameters–the saturation parameter, the noise intensity, and the transmission rate. Employing a second–order perturbation analysis to investigate stability, we uncover both diffusion–driven and noise–induced instabilities and corresponding self–organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Numerical Simulation Model of the Infectious Diseases by Comparing Backward Euler Method and Adams-Bash forth 2-Step Method

In this work, the Backward Euler technique and the Adams-Bashforth 2-step method—two numerical approaches for solving the SIR model of epidemiology are compared for performance. An essential resource for comprehending the transmission of infectious illnesses like COVID-19 in the SIR model. While the explicit Adams-Bash forth 2-step approach is well known for its computing efficiency, the implicit Backward Euler method is noted for its stability. The study evaluates the accuracy, strength, and computing cost of the two approaches to determine which approach is best for simulating the spread of infectious illnesses. The SIR Model was easily solved using the Adams Bashforth 2-step analysis and the Backward Euler method. The approaches' solutions are close to the exact requirements. There are important distinctions between the two-step Adams Bashforth and backward Euler procedures. The running time of the Adams Bashforth 2-step backward Euler method is shorter than that of the backward Euler method.

Analysis of SEIQV Epidemic Model on the Spread of Covid-19 in Jember Regency

Covid-19 is a disease that attacks the respiratory system caused by infection with SARSCoV-2. Efforts to prevent the spread of Covid-19 by vaccination. The spread of disease can be modeled into a mathematical equation. The model used in this study is the SEIQV Model. The disease spread model is analyzed by finding the equilibrium point and the stability of the equilibrium point as well as the basic reproduction number. In the Covid-19 distribution model, a bifurcation analysis is carried out which is needed to determine changes in stability and changes in the number of equilibrium points. Then perform a numerical solution using the fourth-order Runge-Kutta method which is simulated using MATLAB.

A Simple Modelling of Microscopic Epidemic Process with Two Vaccine Doses on a Synthesized Human Interaction Network

In this study, we illustrate the incorporation of two vaccine doses into a discrete SIR model to aid in the decision-making process for optimal vaccination strategies. We present a basic model of a human interaction network synthesized to depict social contacts within a population, taking into account the number of connections and the level of interaction among individuals. Under a limited number of available vaccine doses, we explore various vaccination scenarios considering factors such as the distribution of vaccines, the proportion of vaccinated individuals, and the timing of vaccination commencement. Our research demonstrates that the most effective vaccination strategy, which focuses on re-characterized hubs or redefining the individual who has high connectivity, will cover fewer individuals and result in the smallest total number of infected individuals.

Stability analysis of a fractional-order [formula omitted] epidemic model for the COVID-19 pandemic

To explore the impact of the COVID-19 vaccination rate and immune loss rate on the pandemic, this paper proposes a fractional-order SIV1V2S epidemic model with vaccination ineffectiveness and infection differences. And we compare and analyze the dynamic differences between integer-order and Caputo fractional-order operators. First, we show the non-negativity and boundedness of solutions for the Caputo fractional-order model. Based on the basic reproduction number, we use the fractional-order matrix eigenvalue method and the Routh–Hurwitz criterion to determine the local asymptotic stability of disease-free equilibrium points and endemic equilibrium points, construct Lyapunov functions, and use the fractional-order Barbalat’s Lemma to prove the global asymptotic stability of the two equilibrium points. Second, real data from India were used to fit the model parameters and get the optimal fractional-order parameter, and then sensitivity analysis was performed on the basic reproduction number. Further, through numerical simulation of different fractional-order parameter epidemic models, we verify the global asymptotic stability of the equilibrium point of the fractional-order SIV1V2S COVID-19 model. The comparison shows that the fractional-order model is more closely related to actual virus transmission than the integer-order model. In the case of the SIV1V2S model, which only considers vaccination measures, simultaneously increasing the vaccination rate of susceptible individuals and reducing the rate of immunization loss can effectively control epidemic transmission.

Nonrepresentativeness of Human Mobility Data and its Impact on Modeling Dynamics of the COVID-19 Pandemic: Systematic Evaluation.

In recent years, a range of novel smartphone-derived data streams about human mobility have become available on a near-real-time basis. These data have been used, for example, to perform traffic forecasting and epidemic modeling. During the COVID-19 pandemic in particular, human travel behavior has been considered a key component of epidemiological modeling to provide more reliable estimates about the volumes of the pandemic's importation and transmission routes, or to identify hot spots. However, nearly universally in the literature, the representativeness of these data, how they relate to the underlying real-world human mobility, has been overlooked. This disconnect between data and reality is especially relevant in the case of socially disadvantaged minorities. The objective of this study is to illustrate the nonrepresentativeness of data on human mobility and the impact of this nonrepresentativeness on modeling dynamics of the epidemic. This study systematically evaluates how real-world travel flows differ from census-based estimations, especially in the case of socially disadvantaged minorities, such as older adults and women, and further measures biases introduced by this difference in epidemiological studies. To understand the demographic composition of population movements, a nationwide mobility data set from 318 million mobile phone users in China from January 1 to February 29, 2020, was curated. Specifically, we quantified the disparity in the population composition between actual migrations and resident composition according to census data, and shows how this nonrepresentativeness impacts epidemiological modeling by constructing an age-structured SEIR (Susceptible-Exposed-Infected- Recovered) model of COVID-19 transmission. We found a significant difference in the demographic composition between those who travel and the overall population. In the population flows, 59% (n=20,067,526) of travelers are young and 36% (n=12,210,565) of them are middle-aged (P<.001), which is completely different from the overall adult population composition of China (where 36% of individuals are young and 40% of them are middle-aged). This difference would introduce a striking bias in epidemiological studies: the estimation of maximum daily infections differs nearly 3 times, and the peak time has a large gap of 46 days. The difference between actual migrations and resident composition strongly impacts outcomes of epidemiological forecasts, which typically assume that flows represent underlying demographics. Our findings imply that it is necessary to measure and quantify the inherent biases related to nonrepresentativeness for accurate epidemiological surveillance and forecasting.

Compartmental Nonlinear Epidemic Disease Model with Mixed Behavior

Compartmental Nonlinear Epidemic Disease Model with Mixed Behavior

Optimal region-specific social distancing strategies in a complex multi-patch model through reinforcement learning

Although non-pharmaceutical interventions such as social distancing have proven effective in curbing outbreaks, they also carry economic consequences. This poses a dilemma for policymakers striving to find a balance between disease control and economic burden. This delicate balance varies regionally, influenced by non-epidemiological factors such as population movements, socio-demographic characteristics, and the intricacies of social distancing policies. These factors interact in intricate ways, shaping the transmission dynamics of COVID-19. To address this complexity, we propose an innovative approach utilizing deep reinforcement learning (RL). This method assists in tailoring intervention policies for diverse regions, taking into account their unique dynamics. We incorporate South Korea’s social distancing policies and their economic impact into a RL framework with a multi-region epidemic model, offering a comprehensive solution. We integrate official mobility data and GDP specific to each region, employing the proximity policy optimization algorithm to determine the most appropriate region-specific social distancing policy. The algorithm’s reward function considers both outbreak control and economic impacts, providing policymakers with the flexibility to fine-tune the balance between these two factors according to their preferences. This adjustment can be performed across three distinct cost scenarios: High, Base, and Low-cost scenarios. In scenarios with High-costs, social distancing measures are aimed at regions with extensive connectivity and higher transmission rates. When costs are moderate, policies center around the period of peak prevalence, illustrating adaptable strategies in areas characterized by high transmission rates, budget limitations, and population mobility. In situations with Low-costs, these measures encompass most regions, excluding those with low transmission rates. The study’s results support focused interventions in specific regions to balance outbreak control and economic impact mitigation.

A mathematical model for a disease outbreak considering waning-immunity class with nonlinear incidence and recovery rates

In the spread of infectious diseases, intervention levels play a crucial role in shaping interactions between healthy and infected individuals, leading to a nonlinear transmission process. Additionally, the availability of medical resources limits the recovery rate of infected patients, adding further nonlinear dynamics to the healing process. Our research introduces novelty by combining nonlinear incidence and recovery rates alongside waning immunity in an epidemic model. We present a modified SIRW-type model, examining the epidemic problem with these factors. Through analysis, we explore conditions for non-endemic and co-existing cases based on the basic reproduction ratio. The local stability of equilibria is verified using the Routh-Hurwitz criteria, while global stability is assessed using Lyapunov functions for each equilibrium. Furthermore, we investigate bifurcations around both non-endemic and co-existing equilibria. Numerically, we give some simulations to support our analytical findings.

A simple approach for studying stability properties of an SEIRS epidemic model

Abstract In this work, we study stability properties of a well-known integer-order SEIRS model with nonlinear incidence and vertical transmission. Firstly, we introduce a simple approach to the analysis of global asymptotic stability (GAS) of the integer-order model. This approach is based on general quadratic Lyapunov functions and characteristic of quadratic forms associated with real matrices. The result is that the GAS of disease-free and disease-endemic equilibrium points is completely established. This provides an important improvement for results constructed in two previous works. Secondly, we generalize the integer-order SEIRS model by considering it in the context of the Caputo fractional-order derivative. After that, the present approach is utilized to investigate the GAS of the proposed fractional-order model. As an important consequence, not only the GAS but also the uniform stability of the fractional-order model are determined fully. Therefore, the applicability of the approach is shown. Finally, a series of numerical experiments is conducted to illustrate and support the theoretical findings.

Nonlinear Dynamics of a General Stochastic SIR Model with Behavioral and Physical Changes: Analysis and Application to Zoonotic Tuberculosis

This paper presents a comprehensive nonlinear analysis of an innovative stochastic epidemic model that accounts for both behavioral changes and physical discontinuities. Our research begins with the formulation of a perturbed model, integrating two general incidence functions and incorporating a Lévy measure to account for independent jump components. We start by confirming the well-posed nature of the model, ensuring its mathematical soundness and feasibility for further analysis. Following this, we establish a global threshold criterion that serves to distinguish between the eradication and the persistence of an epidemic. This threshold is crucial for understanding the long-term behavior of a disease within a population. To rigorously validate the accuracy of this threshold, we conducted extensive numerical simulations using estimated data on Zoonotic Tuberculosis in Morocco. These simulations provide practical insights and reinforce the theoretical findings of our study. A notable aspect of our approach is its significant advancement over previous works in the literature. Our model not only offers a more comprehensive framework but also identifies optimal conditions under which an epidemic can be controlled or eradicated.

Spatiotemporal Patterns in a Space–Time Discrete SIRS Epidemic Model with Self- and Cross-Diffusion

In this work, a two-dimensional Coupled Map Lattice (CML) method is applied to a continuous Reaction–Diffusion (RD) SIRS epidemic model. The model involves a complex, nonlinear incidence rate and the spatially heterogeneous self- and cross-diffusion coefficients. The CML method applied here results in a space–time discrete counterpart of the model. The basic reproduction number is derived, and the local stability of the fixed points of the discrete model is established. The two typical bifurcations of codimension 1, such as the flip and the Neimark–Sacker (NS) bifurcations, are investigated by utilizing the center manifold theory and the normal form theorem. Furthermore, the codimension-2 fold–flip bifurcation about the endemic fixed point is discussed in detail. Turing instability criterion of the cross-diffusion epidemic model is established by utilizing the CML method under periodic boundary conditions. Finally, the numerical simulations clarify both the effectiveness of all theoretical findings and the effects of time step size and cross-diffusion on the spatiotemporal patterns. The main contribution of this work is the discovery of some interesting Turing and non-Turing patterns which may be induced by flip–Turing instability, NS–Turing instability or fold–flip–Turing instability. Concretely speaking, spiral patterns are observed near the flip bifurcation threshold value and ultimately evolve into an irregular defect pattern. Stripe pattern, labyrinth pattern and circular pattern are observed near the NS bifurcation threshold value. The disorderly interwoven ribbon pattern, mosaic pattern and some irregular oscillatory patterns are observed near the fold–flip bifurcation point. Our results greatly help in predicting the long-term behavior of the space–time discrete SIRS epidemic model under study.

The impact of social interventions on COVID-19 spreading based on multilayer commuter networks

From March to June 2022, Shanghai was struck by a new coronavirus variant, Omicron, resulting in the infected cases of at least 600,000 people. Despite implementing a strict containment policy of city-wide silence (i.e., residents were not allowed to go out unless necessary), the outbreak cannot be effectively prevented within a short period of time. A significant academic and practical question is: how could we prevent and control outbreak of COVID-19 in large, densely populated cities like Shanghai? It is necessary to develop a rational epidemic spreading model for large cities, in order to accurately predict the trend of disease and quantitatively assess the impact of non-pharmaceutical interventions. In this paper, a multilayer commuter metapopulation network model is constructed to capture commuting flows and the size of epidemic outbreak during commuting between districts. The model accurately predicts epidemic spreading in each district of Shanghai. Assuming strict city-wide lockdowns, with each district locked down and limited inter-district commuting as social zones, simulations demonstrate significant suppression of outbreaks due to social-level interventions. For example, a 1-fold increase in PCR (Polymerase Chain Reaction) testing efficiency reduces the size of epidemic outbreak by approximately 70%. Larger districts require stricter controls to prevent exponential growth. Lockdowns effectively prevent epidemic outbreak at low disease rates but less so at high rates. Liberalized policies lead to varied outbreak trends, with economically developed regions peaking earlier due to higher population densities. This study provides a comprehensive framework for quantitatively evaluating the impact of social and regional controls on urban epidemics.