Influenza Epidemic Model Research Articles

Dynamics analysis of an influenza epidemic model with virus mutation incorporating log-normal Ornstein–Uhlenbeck process

A stochastic influenza epidemic model where influenza virus can mutate into a mutant influenza virus is established to study the influence of environmental disturbance. And the transmission rate of the model is assumed to satisfy log-normal Ornstein–Uhlenbeck process. We verify that there exists a unique global positive solution to the stochastic model. By constructing proper Lyapunov functions, sufficient conditions under which the stationary distribution exists are obtained. In addition, we discuss the extinction of the disease. Furthermore, we get the accurate expression of probability density function near the endemic equilibrium of the stochastic model. Finally, several numerical simulations are carried out to verify theoretical results and examine the influence of environmental noise.

Criteria of existence and stability of an n-coupled system of generalized Sturm-Liouville equations with a modified ABC fractional derivative and an application to the SEIR influenza epidemic model

<abstract><p>The primary objective of this study was to explore the behavior of an n-coupled system of generalized Sturm-Liouville (GSL) and Langevin equations under a modified ABC fractional derivative. We aimed to analyze the dynamics of the system and gain insights into how this operator influences the conditions for the existence and uniqueness of solutions. We established the existence and uniqueness of solutions by employing the Banach contraction principle and Leray-Schauder's alternative fixed-point theorem. We also investigated the Hyers-Ulam stability of the system. This analysis allows us to understand the stability properties of the solutions and evaluate their sensitivity to perturbations. Furthermore, we employed Lagrange's interpolation polynomials to produce a numerical scheme for the influenza epidemic model. By combining theoretical analysis, mathematical principles, and numerical simulations, this study contributes to enriching our understanding of the behavior of the system and offers insights into its dynamics and practical applications in epidemiology.</p></abstract>

Using linear regression metamodels for evaluating interventions in an individual-based influenza epidemic model

Agent-based simulation modeling is frequently used to model and simulate the spread of transmissible diseases such as influenza, COVID-19, and HIV/AIDS in communities. Besides incorporating disease-specific parameters, these models include a set of parameters to observe the effect of different intervention combinations on the course of an epidemic, bringing the opportunity to use these models as virtual laboratories for decision-making. However, these models are primarily large-scale and complex, increasing the runtime of experimentation. As a solution, metamodeling approaches are frequently employed to represent input–output relationships of simulation models. Instead of running the time-consuming agent-based model, policymakers use the metamodel to obtain predicted outcomes in a comparatively short time. In addition to time-saving advantages, metamodels can provide insights into how disease-specific and intervention parameters affect the outcome of interest. In this regard, this study uses an influenza epidemic model, FluTE, as the experimental platform. Instead of using the original agent-based model, we fit linear regression metamodels to quantify the effect of interventions, such as vaccination, quarantine, and school closure, on the influenza attack rate. After validating the metamodel, we observe that the day on which interventions start, ascertainment delay, the daily number of vaccinations administered, isolation and quarantine compliance probabilities, and the number of school closure days stand as the significant intervention policies.

Threshold Dynamics and Probability Density Function of a Stochastic Avian Influenza Epidemic Model with Nonlinear Incidence Rate and Psychological Effect

Threshold Dynamics and Probability Density Function of a Stochastic Avian Influenza Epidemic Model with Nonlinear Incidence Rate and Psychological Effect

Avian–human influenza epidemic model with diffusion, nonlocal delay and spatial homogeneous environment

In this paper, an avian–human influenza epidemic model with diffusion, nonlocal delay and spatial homogeneous environment is investigated. This model describes the transmission of avian influenza among poultry, humans and environment. The behavior of positive solutions to a reaction–diffusion system with homogeneous Neumann boundary conditions is investigated. By means of linearization method and spectral analysis the local asymptotical stability is established. The global asymptotical stability for the poultry sub-system is studied by spectral analysis and by using a Lyapunov functional. For the full system, the global stability of the disease-free equilibrium is studied using the comparison Theorem for parabolic equations. Our result shows that the disease-free equilibrium is globally asymptotically stable, whenever the contact rate for the susceptible poultry is small. This suggests that the best policy to prevent the occurrence of an epidemic is not only to exterminate the asymptomatic poultry but also to reduce the contact rate between susceptible humans and the poultry environment. Numerical simulations are presented to illustrate the main results.

Mean Latin Hypercube Runge-Kutta Method to Solve the Influenza Model

In this study, we propose a suitable solution for a non-linear system of ordinary differential equations (ODE) of the first order with the initial value problems (IVP) that contains multi variables and multi-parameters with missing real data. To solve the mentioned system, a new modified numerical simulation method is created for the first time which is called Mean Latin Hypercube Runge-Kutta (MLHRK). This method can be obtained by combining the Runge-Kutta (RK) method with the statistical simulation procedure which is the Latin Hypercube Sampling (LHS) method. The present work is applied to the influenza epidemic model in Australia in 1919 for a previous study. The comparison between the numerical and numerical simulation results is done, discussed and tabulated. The behavior of subpopulations is shown graphically. MLHRK method can reduce the number of numerical iterations of RK, and the number of LHS simulations, thus it saves time, effort, and cost. As well as it is a faster simulation over the distribution of the LHS. The MLHRK method has been proven to be effective, reliable, and convergent to solve a wide range of linear and nonlinear problems. The proposed method can predict the future behavior of the population under study in analyzing the behavior of some epidemiological models.

Theoretical and numerical results of a stochastic model describing resistance and non-resistance strains of influenza.

In this world, there are several acute viral infections. One of them is influenza, a respiratory disease caused by the influenza virus. Stochastic modelling of infectious diseases is now a popular topic in the current century. Several stochastic epidemiological models have been constructed in the research papers. In the present article, we offer a stochastic two-strain influenza epidemic model that includes both resistant and non-resistance strains. We demonstrate both the existence and uniqueness of the global positive solution using the stochastic Lyapunov function theory. The extinction of our research sickness results from favourable circumstances. Additionally, the infection’s persistence in the mean is demonstrated. Finally, to demonstrate how well our theoretical analysis performs, various noise disturbances are simulated numerically.

Simulation and forecasting of the influenza epidemic process using seasonal autoregressive integrated moving average model

Today's global COVID-19 pandemic has affected the spread of influenza. COVID-19 and influenza are respiratory infections and have several similar symptoms. They are, however, caused by various viruses; there are also some differences in the categories of people most at risk of severe forms of these diseases. The strategies for their treatment are also different. Mathematical modeling is an effective tool for controlling the epidemic process of influenza in specified territories. The results of modeling and forecasts obtained with the help of simulation models make it possible to develop timely justified anti-epidemic measures to reduce the dynamics of the incidence of influenza. The study aims to develop a seasonal autoregressive integrated moving average (SARIMA) model for influenza epidemic process simulation and to investigate the experimental results of the simulation. The work is targeted at the influenza epidemic process and its dynamic in the territory of Ukraine. The subjects of the research are methods and models of epidemic process simulation, which include machine learning methods, in particular the SARIMA model. To achieve the aim of the research, we have used methods of forecasting and have built the influenza epidemic process SARIMA model. Because of experiments with the developed model, the predictive dynamics of the epidemic process of influenza for 10 weeks were obtained. Such a forecast can be used by persons making decisions on the implementation of anti-epidemic and deterrent measures if the forecast exceeds the epidemic thresholds of morbidity. Conclusions. The paper describes experimental research on the application of the SARIMA model to the epidemic process of influenza simulation. Models have been verified by influenza morbidity in the Kharkiv region (Ukraine) in epidemic seasons for the time ranges as follows: 2017-18, 2018-19, 2019-20, and 2020-21. Data were provided by the Kharkiv Regional Centers for Disease Control and Prevention of the Ministry of Health of Ukraine. The forecasting results show a downward trend in the dynamics of the epidemic process of influenza in the Kharkiv region. It is due to the introduction of anti-epidemic measures aimed at combating COVID-19. Activities such as wearing masks, social distancing, and lockdown also contribute to reducing seasonal influenza epidemics.

Numerical solution of a system of Volterra integral equations in application to avian-human influenza epidemic model

In this paper, we propose an efficient multistage method for solving the system of linear and nonlinear Volterra integral equations of the second kind. This numerical method is based on the Gauss-Legendre quadrature rule that obtains several values of unknown function at each step and it will be shown that the order of the convergence is $O(M^{−4})$, where M is the number of the nodes in the time discretization. The method has also the advantages of simplicity of application, less computational time, and useful performance for large intervals. In order to show the efficiency of the method, numerical results for the avian human influenza epidemic model are obtained that are comparable with the fourth order Runge-Kutta method.

Numerical solution for system with Atangana-Baleanu-Caputo derivative: An influenza epidemic model

In this work, we discuss the fractional three strain influenza epidemic model with vaccination for strain 1 and awareness of strain 2. We use Atangana-Baleanu in the Caputo sense. We show that the model has a unique solution, and we perform the numerical simulation with various values of derivative order. It is shown that by decreasing the value of the derivative order, the maximum value also decreases.

Analysis of an individual‐based influenza epidemic model using random forest metamodels and adaptive sequential sampling

AbstractThis study proposes a three‐step procedure for the analysis of input–response relationships of dynamic models, which enables the analyst to develop a better understanding about the dynamics of the system. The main building block of the procedure is a random forest metamodel capturing the input–output relationships. We utilize an active learning approach as the second step to improve the accuracy of the metamodel. In the last step, we develop a novel way to present the information captured by the metamodel as a set of intelligible IF–THEN rules. For illustration, we use the FluTE model, which is an individual‐based influenza epidemic model. We observe that the number of daily applicable vaccines determines the success of an intervention strategy the most. Another critical observation is that when the daily available vaccines are constrained, nonpharmaceutical strategies should be incorporated to reduce the extent of the outbreak.

Interventions to mitigate early spread of SARS-CoV-2 in Singapore: a modelling study

SummaryBackgroundSince the coronavirus disease 2019 outbreak began in the Chinese city of Wuhan on Dec 31, 2019, 68 imported cases and 175 locally acquired infections have been reported in Singapore. We aimed to investigate options for early intervention in Singapore should local containment (eg, preventing disease spread through contact tracing efforts) be unsuccessful.MethodsWe adapted an influenza epidemic simulation model to estimate the likelihood of human-to-human transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in a simulated Singaporean population. Using this model, we estimated the cumulative number of SARS-CoV-2 infections at 80 days, after detection of 100 cases of community transmission, under three infectivity scenarios (basic reproduction number [R0] of 1·5, 2·0, or 2·5) and assuming 7·5% of infections are asymptomatic. We first ran the model assuming no intervention was in place (baseline scenario), and then assessed the effect of four intervention scenarios compared with a baseline scenario on the size and progression of the outbreak for each R0 value. These scenarios included isolation measures for infected individuals and quarantining of family members (hereafter referred to as quarantine); quarantine plus school closure; quarantine plus workplace distancing; and quarantine, school closure, and workplace distancing (hereafter referred to as the combined intervention). We also did sensitivity analyses by altering the asymptomatic fraction of infections (22·7%, 30·0%, 40·0%, and 50·0%) to compare outbreak sizes under the same control measures.FindingsFor the baseline scenario, when R0 was 1·5, the median cumulative number of infections at day 80 was 279 000 (IQR 245 000–320 000), corresponding to 7·4% (IQR 6·5–8·5) of the resident population of Singapore. The median number of infections increased with higher infectivity: 727 000 cases (670 000–776 000) when R0 was 2·0, corresponding to 19·3% (17·8–20·6) of the Singaporean population, and 1 207 000 cases (1 164 000–1 249 000) when R0 was 2·5, corresponding to 32% (30·9–33·1) of the Singaporean population. Compared with the baseline scenario, the combined intervention was the most effective, reducing the estimated median number of infections by 99·3% (IQR 92·6–99·9) when R0 was 1·5, by 93·0% (81·5–99·7) when R0 was 2·0, and by 78·2% (59·0 −94·4) when R0 was 2·5. Assuming increasing asymptomatic fractions up to 50·0%, up to 277 000 infections were estimated to occur at day 80 with the combined intervention relative to 1800 for the baseline at R0 of 1·5.InterpretationImplementing the combined intervention of quarantining infected individuals and their family members, workplace distancing, and school closure once community transmission has been detected could substantially reduce the number of SARS-CoV-2 infections. We therefore recommend immediate deployment of this strategy if local secondary transmission is confirmed within Singapore. However, quarantine and workplace distancing should be prioritised over school closure because at this early stage, symptomatic children have higher withdrawal rates from school than do symptomatic adults from work. At higher asymptomatic proportions, intervention effectiveness might be substantially reduced requiring the need for effective case management and treatments, and preventive measures such as vaccines.FundingSingapore Ministry of Health, Singapore Population Health Improvement Centre.

Influenza epidemic model using dynamic social networks of individuals with cognition maps

The dynamic of infectious disease is the result of the interplay between the spread of pathogens and individuals’ behaviour. This interaction can be modelled through a network of interdependent dynamical blocks with multiple feedback connections. Epidemic outbreaks trigger behavioural responses, at the group and individual levels, which in turn influence the development of the epidemic. The interactions can be modelled through adaptive temporal networks whose nodes represent the individuals interconnected. Here we introduce an individual-based model where the behaviour of each agent is governed by its appreciation of the environment and external stimulus and its appreciation of its environment. It is built as a combination of three interacting blocks: (i) individual behaviour, (ii) social behaviour and (iii) health state.•Here, we introduce an individual-based model.•Individual's behaviour is modelled through the interplay of information of its health state as well as its neighbourhood (infected and recovered neighbours) and global epidemic situation;•Social behaviour is modelled through contact network that aggregates the behaviour and health state of the individuals;•The proposed model allows to use a wide range of alternatives for modelling each of these blocks, that provides flexibility to select the most adequate tool to model each component of the framework.

An influenza epidemic model with dynamic social networks of agents with individual behaviour

There is an interplay between the spread of infectious disease and the behaviour of individuals that can be modelled through a series of interconnected dynamical feedback blocks. Specifically, the outbreak of an infectious disease can trigger behavioural responses, at the group and individual levels, which in turn influences the epidemic evolution. Daily life interactions can be modelled through adaptive co-evolutionary networks whose nodes represent the interconnected individuals. In this paper we introduce an individual-based model where the behaviour of each agent is determined by both external stimuli and perception of its environment. It is built as a combination of three interacting blocks that model the fundamental aspects of an epidemic: i) individual behaviour, ii) social behaviour and iii) health state.

Dynamical analysis of a fractional-order avian-human influenza epidemic model with logistic growth for avian population

In this paper, a fractional order avian-human influenza epidemic model with logistic growth for avian population is investigated. The dynamical behavior of this model is discussed. We first establish the existence, uniqueness, non-negativity and positive invariance of the solution. Then we analyze the existence of various equilibrium points, and some sufficient conditions are derived to ensure the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, we take some numerical simulations to validate the analytical results.

MODELLING THE DYNAMICS OF AVIAN INFLUENZA WITH NONLINEAR RECOVERY RATE AND PSYCHOLOGICAL EFFECT

In this paper, a SI-SEIR type avian influenza epidemic model with psychological effect, nonlinear recovery rate and saturation inhibition effect is formulated to study the transmission and control of avian influenza virus. By setting the basic reproductive number as the threshold parameter and constructing Lyapunov function, Dulac function and using the Li-Muldowney's geometry approach, we prove the local and global stability of disease-free equilibria and endemic equilibrium. Theoretical analysis are carried out to show the role of the saturation inhibition effect, psychological effect and effective medical resources in this model, and numerical simulations are also given to verify the results.

Study on a Stochastic Avian Influenza Epidemic Model with Generalized Incidence Rate

Avian Influenza, with a high mortality rate in human population, is considered to be one of the most significant potential threats to human beings. Based on a recent avian influenza SI-SIR model with logistic growth for birds, we propose a stochastic model with generalized incidence rate. For the stochastic avian-only system, sufficient conditions for the extinction of infected birds are established, and the existence of a unique ergodic stationary distribution is also obtained. For the stochastic avian-human system, a threshold number is established, and hence the extinction of disease is investigated. From the viewpoint of biology, the noise intensity in the infected birds plays a key role in the evolutionary dynamics. Moreover, we also analyze the asymptotic behavior around the endemic equilibrium of the corresponding deterministic model.

Numerical study of an influenza epidemic dynamical model with diffusion

In this paper, a deterministic model is formulated in the aim of performing a thorough investigation of the transmission dynamics of influenza. The main advantage of our model compared to existing models is that it takes into account the effects of hospitalization as well as the diffusion. The proposed model consisting of a dynamical system of partial differential equations with diffusion terms is numerically solved using fast and accurate numerical techniques for partial differential equations. Furthermore, the basic reproduction number that guarantees the local stability of disease-free steady state without diffusion term is calculated. Various numerical simulation for different values of the model input parameters are finally presented in order to show the effect of the effective contact rate on the steady state of the different population compartments.

Observer-based adaptive PI sliding mode control of developed uncertain SEIAR influenza epidemic model considering dynamic population

This paper presents a new Susceptible, Exposed, Infected, Asymptomatic, and Recovered individuals (SEIAR) model for influenza considering a dynamic population. In the given model, the possibility of transmission of asymptomatic individuals (infectious with no visible symptoms) to infected individuals (infectious exhibiting symptoms) is considered. The basic reproduction number and the equilibrium points of the new model are given while the stability of the equilibrium points is analyzed by using the Jacobian matrix. Then a multi-controller scheme consisting of a parallel controller defined by two control inputs (vaccination and antiviral treatment) is given where both of them are based on Proportional-Integral (PI) and sliding mode controllers, which are parameterized adaptively to guarantee the convergence of trajectories to the sliding surface with minimum amount of chattering. The proposed control scheme is able to asymptotically stabilize the SEIAR model in the sense of eradication of the infected and susceptible individuals. Moreover, a (reduced-order) observer is designed to estimate the actual state variables that are used in the implementation of the control signals. By using MATLAB® software, a comprehensive simulation and evaluation of treatment and performance are carried out to support the presented theoretical results.

Developing epidemic forecasting models to assist disease surveillance for influenza with electronic health records

ABSTRACT Seasonal influenza is an important infectious disease monitored by the Centers for Disease Control. Monitoring, early detection, and prediction of influenza outbreaks can accelerate life-saving public health responses. However, ensuring completeness and timeliness of all surveillance systems can be difficult. Current influenza surveillance systems can be supported through the estimation of influenza activity, which we aim to achieve by defining influenza cases through electronic medical records (EMRs) from Chang Gung Memorial Hospital and constructing predictive models for predicting the epidemic trend for influenza. In total, 84,820 influenza cases were matching the case definition in 2010–2015. Using the exponential smoothing model, autoregressive integrated moving average (ARIMA) model, and Prophet model, we trained the models with influenza cases from 2010 to 2014; we then renewed the models at different intervals and compared their capacities. The results show that the ARIMA model performs best in both Linkou and Kaohsiung branches. In conclusion, we successfully constructed an influenza epidemic predictive model based on EMRs, which may be used as a decision support tool for improving influenza surveillance, controlling infection, and managing resources.