Dynamics Of Epidemic Model Research Articles

Revisiting the discrete--time SIS criss-cross model of epidemic dynamics for a heterogeneous population

Revisiting the discrete--time SIS criss-cross model of epidemic dynamics for a heterogeneous population

Analysis of stochastic epidemic model with awareness decay and heterogeneous individuals on multi-weighted networks.

In the current study, we present a stochastic SAIS (unaware susceptible-aware susceptible-infectious-unaware susceptible) epidemic dynamic model on complex networks with multi-weights. The disease dynamic is influenced by random perturbations to the force of the infection rates, as well as awareness rates. To analyze the problem of extinction, we discuss both the stochastic asymptotic stability in the large and almost surely exponential stability of the trivial solution. Then, we get some sufficient conditions, which guarantee the stochastic persistence of infectious disease. Based on the Erdös-Réyni random graph, the numerical simulations are given. These not only validate our conclusions but also obtain else significative results. Both theoretical results and numerical simulations further reflect that improvement of risk awareness and reduction of decay in awareness are highly effective in preventing disease spread. And then, environmental noises play a significant role in disease transmission.

A tight fit of the SIR dynamic epidemic model to daily cases of COVID-19 reported during the 2021-2022 Omicron surge in New York City: A novel approach.

We describe a novel approach for recovering the underlying parameters of the SIR dynamic epidemic model from observed data on case incidence. We formulate a discrete-time approximation of the original continuous-time model and search for the parameter vector that minimizes the standard least squares criterion function. We show that the gradient vector and matrix of second-order derivatives of the criterion function with respect to the parameters adhere to their own systems of difference equations and thus can be exactly calculated iteratively. Applying our new approach, we estimated a four-parameter SIR model from daily reported cases of COVID-19 during the SARS-CoV-2 Omicron/BA.1 surge of December 2021-March 2022 in New York City. The estimated SIR model showed a tight fit to the observed data, but less so when we excluded residual cases attributable to the Delta variant during the initial upswing of the wave in December. Our analyses of both the real-world COVID-19 data and simulated case incidence data revealed an important problem of weak parameter identification. While our methods permitted for the separate estimation of the infection transmission parameter and the infection persistence parameter, only a linear combination of these two key parameters could be estimated with precision. The SIR model appears to be an adequate reduced-form description of the Omicron surge, but it is not necessarily the correct structural model. Prior information above and beyond case incidence data may be required to sharply identify the parameters and thus distinguish between alternative epidemic models.

Impact of reinfection on dynamics of epidemic model with discrete two-state structure

Impact of reinfection on dynamics of epidemic model with discrete two-state structure

Role of heterogeneity: National scale data-driven agent-based modeling for the US COVID-19 Scenario Modeling Hub

UVA-EpiHiper is a national scale agent-based model to support the US COVID-19 Scenario Modeling Hub (SMH). UVA-EpiHiper uses a detailed representation of the underlying social contact network along with data measured during the course of the pandemic to initialize and calibrate the model. In this paper, we study the role of heterogeneity on model complexity and resulting epidemic dynamics using UVA-EpiHiper. We discuss various sources of heterogeneity that we encounter in the use of UVA-EpiHiper to support modeling and analysis of epidemic dynamics under various scenarios. We also discuss how this affects model complexity and computational complexity of the corresponding simulations. Using round 13 of the SMH as an example, we discuss how UVA-EpiHiper was initialized and calibrated. We then discuss how the detailed output produced by UVA-EpiHiper can be analyzed to obtain interesting insights. We find that despite the complexity in the model, the software, and the computation incurred to an agent-based model in scenario modeling, it is capable of capturing various heterogeneities of real-world systems, especially those in networks and behaviors, and enables analyzing heterogeneities in epidemiological outcomes between different demographic, geographic, and social cohorts. In applying UVA-EpiHiper to round 13 scenario modeling, we find that disease outcomes are different between and within states, and between demographic groups, which can be attributed to heterogeneities in population demographics, network structures, and initial immunity.

Leveraging advances in data-driven deep learning methods for hybrid epidemic modeling

Mathematical modeling of epidemic dynamics is crucial to understand its underlying mechanisms, quantify important parameters, and make predictions that facilitate more informed decision-making. There are three major types of models: mechanistic models including the SEIR-type paradigm, alternative data-driven (DD) approaches, and hybrid models that combine mechanistic models with DD approaches. In this paper, we summarize our work in the COVID-19 Scenario Modeling Hub (SMH) for more than 12 rounds since early 2021 for informed decision support. We emphasize the importance of deep learning techniques for epidemic modeling via a flexible DD framework that substantially complements the mechanistic paradigm to evaluate various future epidemic scenarios. We start with a traditional curve-fitting approach to model cumulative COVID-19 based on the underlying SEIR-type mechanisms. Hospitalizations and deaths are modeled as binomial processes of cases and hospitalization, respectively. We further formulate two types of deep learning models based on multivariate long short term memory (LSTM) to address the challenges of more traditional DD models. The first LSTM is structurally similar to the curve fitting approach and assumes that hospitalizations and deaths are binomial processes of cases. Instead of using a predefined exponential curve, LSTM relies on the underlying data to identify the most appropriate functions, and is capable of capturing both long-term and short-term epidemic behaviors. We then relax the assumption of dependent inputs among cases, hospitalizations, and death. Another type of LSTM that handles all input time series as parallel signals, the independent multivariate LSTM, is developed. Independent multivariate LSTM can incorporate a wide range of data sources beyond traditional case-based epidemiological surveillance. The DD framework unleashes its potential in big data era with previously neglected heterogeneous surveillance data sources, such as syndromic, environment, genomic, serologic, infoveillance, and mobility data. DD approaches, especially LSTM, complement and integrate with the mechanistic modeling paradigm, provide a feasible alternative approach to model today’s complex socio-epidemiological systems, and further leverage our ability to explore different scenarios for more informed decision-making during health emergencies.

Stochastic Modeling of Nonlinear SIS Epidemic Dynamics with Jump Perturbations

Stochastic Modeling of Nonlinear SIS Epidemic Dynamics with Jump Perturbations

Qualitative analysis of solutions for a degenerate partial differential equations model of epidemic spread dynamics

Compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases or in mathematical models of population genetics. In this study, we study a time-dependent Susceptible-Infectious-Susceptible (SIS) Partial Differential Equation (PDE) model that is based on a diffusion-drift approximation of a probability density from a well-known discrete-time Markov chain model. This SIS-PDE model is conservative due to the degeneracy of the diffusion term at the origin. The main results of this article are the qualitative behavior of weak solutions, the dependence of the local asymptotic property of these solutions on initial data, and the existence of Dirac delta function type solutions. Moreover, we study the long-term behavior of solutions and confirm our analysis with numerical computations.

Promoting healthy populations as a pandemic preparedness strategy: a simulation study from Mexico

The underlying health status of populations was a major determinant of the impact of the COVID-19 pandemic, particularly obesity prevalence. Mexico was one of the most severely affected countries during the COVID-19 pandemic and its obesity prevalence is among the highest in the world. It is unknown by how much the COVID-19 burden could have been reduced if systemic actions had been implemented to reduce excess weight in Mexico before the onset of the pandemic. Using a dynamic epidemic model based on nationwide data, we compare actual deaths with those under hypothetical scenarios assuming a lower body mass index in the Mexican population, as observed historically. We also model the number of deaths that would have been averted due to earlier implementation of front-of-pack warning labels or due to increases in taxes on sugar-sweetened beverages and non-essential high-energy foods in Mexico. We estimate that 52.5% (95% prediction interval (PI) 43.2, 61.6%) of COVID-19 deaths were attributable to obesity for adults aged 20-64 and 23.8% (95% PI 18.7, 29.1%) for those aged 65 and over. Had the population BMI distribution remained as it was in 2000, 2006, or 2012, COVID-19 deaths would have been reduced by an expected 20.6% (95% PI 16.9, 24.6%), 9.9% (95% PI 7.3, 12.9%), or 6.9% (95% PI 4.5, 9.5%), respectively. If the food-labelling intervention introduced in 2020 had been introduced in 2018, an expected 6.2% (95% PI 5.2, 7.3%) of COVID-19 deaths would have been averted. If taxes on sugar-sweetened beverages and high-energy foods had been doubled, trebled, or quadrupled in 2018, COVID-19 deaths would have been reduced by an expected 4.1% (95% PI 2.5, 5.7%), 7.9% (95% PI 4.9, 11.0%), or 11.6% (95% PI 7.3, 15.8%), respectively. Public health interventions targeting underlying population health, including non-communicable chronic diseases, is a promising line of action for pandemic preparedness that should be included in all pandemic plans. This study received funding from Bloomberg Philanthropies, awarded to Juan A. Rivera from the National Institute of Public Health; Community Jameel, the UK Medical Research Council (MRC), Kenneth C Griffin, and the World Health Organization.

An Epidemic Model with Infection Age and Vaccination Age Structure.

A model of epidemic dynamics is developed that incorporates continuous variables for infection age and vaccination age. The model analyzes pre-symptomatic and symptomatic periods of an infected individual in terms of infection age. This property is shown to be of major importance in the severity of the epidemic, when the infectious period of an infected individual precedes the symptomatic period. The model also analyzes the efficacy of vaccination in terms of vaccination age. The immunity to infection of vaccinated individuals varies with vaccination age and is also of major significance in the severity of the epidemic. Application of the model to the 2003 SARS epidemic in Taiwan and the COVID-19 epidemic in New York provides insights into the dynamics of these diseases. It is shown that the SARS outbreak was effectively contained due to the complete overlap of infectious and symptomatic periods, allowing for the timely isolation of affected individuals. In contrast, the pre-symptomatic spread of COVID-19 in New York led to a rapid, uncontrolled epidemic. These findings underscore the critical importance of the pre-symptomatic infectious period and the vaccination strategies in influencing the dynamics of an epidemic.

Fractional-Order Epidemic Model for Measles Infection.

In this study, a nonlinear dynamic SEVIQR measles epidemic model is constructed and analyzed using the novel Caputo fractional-order derivative operator. The model's existence and uniqueness are established. In addition, the model equilibria are determined, and the novel Jacobian determinant method recently constructed in the literature of epidemiological modeling of infectious diseases is applied to determine the threshold quantity, ℛ 0. Furthermore, we construct appropriate Lyapunov functions to establish the global asymptotic stability of the disease-free and endemic equilibrium points. Finally, the numerical solution of the model is executed employing the efficient and widely known Adams-type predictor-corrector iterative scheme, and simulation is conducted to investigate the impact of memory index and diverse preventive measures on the occurrence of the disease. Numerical simulation of the model indicates that quarantine, vaccination, and treatment can reduce the numbers of infectious and exposed populations, thereby controlling the disease. Therefore, it is recommended that the government provide financial assistance for vaccine distribution.

The impact of non-pharmaceutical interventions on the spread of COVID-19 in Saudi Arabia: Simulation approach

ObjectivesThis paper aims to measure the impact of the implemented nonpharmaceutical interventions (NPIs) in the Kingdom of Saudi Arabia (KSA) during the pandemic using simulation modeling. MethodsTo measure the impact of NPI, a hybrid agent-based and system dynamics simulation model was built and validated. Data were collected prospectively on a weekly basis. The core epidemiological model is based on a complex Susceptible-Exposed-Infectious-Recovered and Dead model of epidemic dynamics. Reverse engineering was performed on a weekly basis throughout the study period as a mean for model validation which reported on four outcomes: total cases, active cases, ICU cases, and deaths cases. To measure the impact of each NPI, the observed values of active and total cases were captured and compared to the projected values of active and total cases from the simulation. To measure the impact of each NPI, the study period was divided into rounds of incubation periods (cycles of 14 days each). The behavioral change of the spread of the disease was interpreted as the impact of NPIs that occurred at the beginning of the cycle. The behavioral change was measured by the change in the initial reproduction rate (R0). ResultsAfter 18 weeks of the reverse engineering process, the model achieved a 0.4 % difference in total cases for prediction at the end of the study period. The results estimated that NPIs led to 64 % change in The R0. Our breakdown analysis of the impact of each NPI indicates that banning going to schools had the greatest impact on the infection reproduction rate (24 %). ConclusionWe used hybrid simulation modeling to measure the impact of NPIs taken by the KSA government. The finding further supports the notion that early NPIs adoption can effectively limit the spread of COVID-19. It also supports using simulation for building mathematical modeling for epidemiological scenarios.

An integrated optimization control model of combining epidemic and production–inventory models and its numerical simulations

This paper explores the integration and harmonization of an epidemic dynamics model and a resource production–inventory management model, aiming to identify optimal control strategies of epidemic containment. We begin with establishing a generalized optimal control model for epidemic dynamics, which offers a unified framework to verify the sufficient conditions for the existence of the optimal solutions to a class of epidemic optimal control models. Based on the model, a resource production–inventory dynamic model with learning ability is proposed to find optimal strategies of the medical resource management. Subsequently, we propose the optimal control model for a dynamics system of COVID-19 and explore the optimal strategies of the combined applications of vaccine and recommended treatment in comprehensive control of the epidemic. Finally, the viability of effective integration and coordination between the optimal control models of the epidemic dynamics and the resource production–inventory system is verified by numerical simulation and analytical analysis, and a new method is implemented for finding the optimal management strategy for epidemic control. Therefore, this study advances a more comprehensive understanding of the interplay between epidemic dynamics and resource management, illustrating the feasibility and efficacy of integrating multiple models to achieve optimal decisions in both theoretical and practical aspects of epidemic control.

An epidemic dynamics model with limited isolation capacity.

We consider a modified SIR model with a four-dimensional system of ordinary differential equations to consider the influence of a limited isolation capacity on the final epidemic size defined as the total number of individuals who experienced the disease at the end of an epidemic season. We derive the necessary and sufficient condition that the isolation reaches the capacity in a finite time on the way of the epidemic process, and show that the final epidemic size is monotonically decreasing in terms of the isolation capacity. We find further that the final epidemic size could have a discontinuous change at the critical value of isolation capacity below which the isolation reaches the capacity in a finite time. Our results imply that the breakdown of isolation with a limited capacity would cause a drastic increase of the epidemic size. Insufficient capacity of the isolation could lead to an unexpectedly severe epidemic situation, while such a severity would be avoidable with the sufficient isolation capacity.

Phase portraits of an SIR epidemic model

In this paper, we classify the phase portraits of an SIR epidemic dynamics model. Depending on the values of the parameters, this model can exhibit seven different phase portraits. In particular, from a biological point of view we prove that the unique attractors of this model are one or two equilibrium points depending on the values of the parameters and from the phase portraits follow the basins of attraction of these equilibria.

Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes

Vaccines are recognized as an effective way to control the spread of epidemics. It should be noted that the vaccination of a population is influenced not only by the infectiousness of a disease but also the vaccination strategy, such as the cost of vaccination. An accurate prediction model is helpful in forecasting the most likely trend to support smart decisions. In order to solve this problem, a model of epidemic spread dynamics is proposed, which is called the Susceptible–Infected–Vaccinated with vaccine A–Vaccinated with vaccine B–Recovered (SIVAVBR) model. This model assesses the competition between two vaccines in terms of economic cost and protection effectiveness in an open-market economy. The optimization process of individual vaccination decision-making was studied in an evolutionary game. In addition, a novel network containing environmental nodes and individual nodes was used to simulate the increase in infection probability caused by aggregation. Using the mean-field approach, the existence and stability of the disease-free equilibrium point and the endemic equilibrium point were demonstrated. Numerous simulations were further carried out to examine the relationship between the basic reproduction number and epidemic dynamics. The results reveal that immunization hesitation reduces the immunity level of the entire population. It is important to improve vaccine efficiency and affordability for manufacturers to become more competitive. Establishing the core individuals in the network is also a means of quickly occupying the market.

A dynamic approach to supply chain reconfiguration and ripple effect analysis in an epidemic

The COVID-19 pandemic has illustrated the unprecedented challenges of ensuring the continuity of operations in a supply chain as suppliers’ and their suppliers stop producing due the spread of infection, leading to a degradation of downstream customer service levels in a ripple effect. In this paper, we contextualize a dynamic approach and propose an optimal control model for supply chain reconfiguration and ripple effect analysis integrated with an epidemic dynamics model. We provide supply chain managers with the optimal choice over a planning horizon among subsets of interchangeable suppliers and corresponding orders; this will maximize demand satisfaction given their prices, lead times, exposure to infection, and upstream suppliers’ risk exposure. Numerical illustrations show that our prescriptive forward-looking model can help reconfigure a supply chain and mitigate the ripple effect due to reduced production because of suppliers’ infected workers. A risk aversion factor incorporates a measure of supplier risk exposure at the upstream echelons. We examine three scenarios: (a) infection limits the capacity of suppliers, (b) the pandemic recedes but not at the same pace for all suppliers, and (c) infection waves affect the capacity of some suppliers, while others are in a recovery phase. We illustrate through a case study how our model can be immediately deployed in manufacturing or retail supply chains since the data are readily accessible from suppliers and health authorities. This work opens new avenues for prescriptive models in operations management and the study of viable supply chains by combining optimal control and epidemiological models.

Traffic-driven SIR epidemic spread dynamics on scale-free networks

Traffic flow affects the transmission and distribution of pathogens. The large-scale traffic flow that emerges with the rapid development of global economic integration plays a significant role in the epidemic spread. In order to more accurately indicate the time characteristics of the traffic-driven epidemic spread, new parameters are added to represent the change of the infection rate parameter over time on the traffic-driven Susceptible–Infected–Recovered (SIR) epidemic spread model. Based on the collected epidemic data in Hebei Province, a linear regression method is performed to estimate the infection rate parameter and an improved traffic-driven SIR epidemic spread dynamics model is established. The impact of different link-closure rules, traffic flow and average degree on the epidemic spread is studied. The maximum instantaneous number of infected nodes and the maximum number of ever infected nodes are obtained through simulation. Compared to the simulation results of the links being closed between large-degree nodes, closing the links between small-degree nodes can effectively inhibit the epidemic spread. In addition, reducing traffic flow and increasing the average degree of the network can also slow the epidemic outbreak. The study provides the practical scientific basis for epidemic prevention departments to conduct traffic control during epidemic outbreaks.

Estimation of COVID-19 incidence in Shanghai under optimized epidemic prevention and control strategies

Objective: To quantitatively estimate the incidence of COVID-19 in different backgrounds, including vaccination coverage, non-pharmacological interventions (NPIs) measures, home quarantine willingness and international arrivals, and the demands of healthcare resource in Shanghai in the context of optimized epidemic prevention and control strategies. Methods: Based on the natural history of 2019-nCoV, local vaccination coverage and NPI performance, an age-structured Susceptible-Exposed-Infections-Removed (SEIR) epidemic dynamic model was established for the estimation of the incidence of COVID-19 and demand of hospital beds in Shanghai by using the data on December 1, 2022 as the basis. Results: Based on current vaccination coverage, it is estimated that 180 184 COVID-19 cases would need treatment in hospitals in Shanghai within 100 days. When the booster vaccination coverage reaches an ideal level, the number of the cases needing hospitalization would decrease by 73.20%. School closure or school closure plus workplace closure could reduce the peak demand of regular beds by 24.04% or 37.73%, respectively, compared with the situation without NPI. Increased willingness of home quarantine could reduce the number of daily new cases and delay incidence peak of COVID-19. The number of international arrivals has little impact on the development of the epidemic. Conclusions: According to the epidemiological characteristics of COVID-19 and the actual situation of vaccination in Shanghai, the incidence of COVID-19 and health resource demand might be reduced by increasing vaccination coverage and early implementation of NPI.

The impact of social media marketing on the dissemination of mini program in social network with different community structure

Mini program has become an important infrastructure for the Internetisation of traditional brands. Previous studies have mostly explored the design and development of mini program, but little research has been conducted on the mini program dissemination process. Studying the impact of social media marketing on the mini program dissemination process has important theoretical and applicable value for the in-depth discovery of the mini program dissemination mechanism and the marketing strategies improvement for mini program operators. Based on the classical Susceptible–Infected–Recovered (SIR) epidemic dissemination dynamic model and combined with the Sense, Interest and Interactive, Connect and Diffusion, Action and Share user behaviour consumption model, we propose a mini program propagation model considering social media marketing and community structure, and establish a set of differential equations reflecting the mini program propagation rules. The validity of the model and experimental results are verified through the comparison among the simulation, actual data and numerical experimental results. The experimental results show that the improvement of social media marketing can considerably promote the dissemination of mini program. Surprisingly, with the same social media marketing investment, the dissemination effect of mini program in a weak community is better than that in a strong community. The reason for this is that the higher clustering coefficient fails to offset the negative impact of high modularity on marketing information dissemination. Consequently, compared with the marketing needs of the weak community structure, more social media marketing efforts need to be invested in the strong community structure. Improving social media marketing in the early stages of dissemination can maximise the marketing effect. Moreover, the effect of combining of advertising marketing and interactive marketing in social media marketing is better than that of a single marketing strategy.