Susceptible-infected-recovered Research Articles

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Many challenges are still faced in bridging the gap between mathematical modeling and biological sciences. Measuring population immunity to assess the epidemiology of health and disease is a challenging task and is currently an active area of research. However, to meet these challenges, mathematical modeling is an effective technique in shaping the population dynamics that can help disease control. In this paper, we introduce a susceptible–infected–recovered (SIR) model and a susceptible–exposed–infected–recovered–deceased (SEIRD) model based on conformable space‐time partial differential equations (PDEs) for the coronavirus disease 2019 (COVID‐19) pandemic. As efficient analytical tools, we present new modifications based on the fractional exponential rational function method (ERFM) and an analytical technique based on the Adomian decomposition method for obtaining the solutions for the proposed models. These analytical approaches are more efficacious for obtaining analytical solutions for nonlinear systems of PDEs with conformable derivatives. The interesting result of this paper is that it yields new exact and approximate solutions to the proposed COVID‐19 pandemic models with conformable space‐time partial derivatives.

Large-deviation properties of SIR model incorporating protective measures

We simulate spreads of diseases for the susceptible–infected–recovered (SIR) model on contact networks with a particular focus on incorporated protective measures such as face masks. We consider the small-world network model. By using a large-deviation approach, in particular the Wang–Landau algorithm, we obtained the full probability density function (pdf) of the cumulative number C of infected people over the full range of its support. In this way we are able to reach probabilities as small as 10−50. We obtain distinct characteristics in the pdf such as non-analyticities induced by the onset of the protective measures. Still, the results indicate that the mathematical large-deviation principle also holds for this extended SIR model, meaning that the size-dependence enters in P(C) in a simple fashion and the distribution is determined by the so-called rate function. We observe different phases in the pdf, which we investigate by analyzing the corresponding infection courses, i.e. time series, and and their correlations to the observed values of C.

The impact of multiple non-pharmaceutical interventions for China-bound travel on domestic COVID-19 outbreaks.

Non-pharmaceutical interventions (NPIs) implemented on China-bound travel have successfully mitigated cross-regional transmission of COVID-19 but made the country face ripple effects. Thus, adjusting these interventions to reduce interruptions to individuals' daily life while minimizing transmission risk was urgent. An improved Susceptible-Infected-Recovered (SIR) model was built to evaluate the Delta variant's epidemiological characteristics and the impact of NPIs. To explore the risk associated with inbound travelers and the occurrence of domestic traceable outbreaks, we developed an association parameter that combined inbound traveler counts with a time-varying initial value. In addition, multiple time-varying functions were used to model changes in the implementation of NPIs. Related parameters of functions were run by the MCSS method with 1,000 iterations to derive the probability distribution. Initial values, estimated parameters, and corresponding 95% CI were obtained. Reported existing symptomatic, suspected, and asymptomatic case counts were used as the training datasets. Reported cumulative recovered individual data were used to verify the reliability of relevant parameters. Lastly, we used the value of the ratio (Bias2/Variance) to verify the stability of the mathematical model, and the effects of the NPIs on the infected cases to analyze the sensitivity of input parameters. The quantitative findings indicated that this improved model was highly compatible with publicly reported data collected from July 21 to August 30, 2021. The number of inbound travelers was associated with the occurrence of domestic outbreaks. A proportional relationship between the Delta variant incubation period and PCR test validity period was found. The model also predicted that restoration of pre-pandemic travel schedules while adhering to NPIs requirements would cause shortages in health resources. The maximum demand for hospital beds would reach 25,000/day, the volume of PCR tests would be 8,000/day, and the number of isolation rooms would reach 800,000/day within 30 days. With the pandemic approaching the end, reexamining it carefully helps better address future outbreaks. This predictive model has provided scientific evidence for NPIs' effectiveness and quantifiable evidence of health resource allocation. It could guide the design of future epidemic prevention and control policies, and provide strategic recommendations on scarce health resource allocation.

Large-deviations of disease spreading dynamics with vaccination.

We numerically simulated the spread of disease for a Susceptible-Infected-Recovered (SIR) model on contact networks drawn from a small-world ensemble. We investigated the impact of two types of vaccination strategies, namely random vaccination and high-degree heuristics, on the probability density function (pdf) of the cumulative number C of infected people over a large range of its support. To obtain the pdf even in the range of probabilities as small as 10-80, we applied a large-deviation approach, in particular the 1/t Wang-Landau algorithm. To study the size-dependence of the pdfs within the framework of large-deviation theory, we analyzed the empirical rate function. To find out how typical as well as extreme mild or extreme severe infection courses arise, we investigated the structures of the time series conditioned to the observed values of C.

Network-augmented compartmental models to track asymptomatic disease spread.

A major challenge in understanding the spread of certain newly emerging viruses is the presence of asymptomatic cases. Their prevalence is hard to measure in the absence of testing tools, and yet the information is critical for tracking disease spread and shaping public health policies. Here, we introduce a framework that combines classic compartmental models with travel networks and we use it to estimate asymptomatic rates. Our platform, traSIR ("tracer"), is an augmented susceptible-infectious-recovered (SIR) model that incorporates multiple locations and the flow of people between them; it has a compartment model for each location and estimates of commuting traffic between compartments. TraSIR models both asymptomatic and symptomatic infections, as well as the dampening effect symptomatic infections have on traffic between locations. We derive analytical formulae to express the asymptomatic rate as a function of other key model parameters. Next, we use simulations to show that empirical data fitting yields excellent agreement with actual asymptomatic rates using only information about the number of symptomatic infections over time and compartments. Finally, we apply our model to COVID-19 data consisting of reported daily infections in the New York metropolitan area and estimate asymptomatic rates of COVID-19 to be ∼34%, which is within the 30-40% interval derived from widespread testing. Overall, our work demonstrates that traSIR is a powerful approach to express viral propagation dynamics over geographical networks and estimate key parameters relevant to virus transmission. No public repository.

Multi-Strain Epidemic Models of Mutating Viruses with Airborne Transmission Based on Cellular Automata and Ordinary Differential Equations

The emergence of SARS-CoV-2 virus mutations is a pressing concern in the context of the COVID-19 pandemic. In this paper, a Susceptible–Infected–Recovered (SIR) compartmental model has been formulated in terms of cellular automata and ordinary differential equations to simulate the transmission dynamics of a virus. This model accounts for the potential of new virus mutations to create additional infections of a multi-strain disease while also considering the impact of vaccination on disease control within a population. The basic reproduction number of the disease is derived, and the effect of virus mutations and vaccination rates is evaluated on a population over five years. The results of numerical simulations demonstrate the significant role of maintaining high vaccination rates in controlling the spread of the virus, even when assuming that all variants have similar illness characteristics and that a single shot of vaccine provides complete and lifelong protection against all strains. The findings underscore the necessity for countries to implement a consistent and high-level vaccination plan as soon as vaccines become available in order to mitigate the impact of a pandemic effectively. In conclusion, this study highlights the importance of taking into account the potential impact of virus mutations for controlling the COVID-19 pandemic. Furthermore, it emphasizes the critical role of vaccination in limiting the spread of the virus, and emphasizes the need to implement and maintain high vaccination rates as part of a comprehensive approach to managing the ongoing pandemic.

Optimality of Maximal-Effort Vaccination

It is widely acknowledged that vaccinating at maximal effort in the face of an ongoing epidemic is the best strategy to minimise infections and deaths from the disease. Despite this, no one has proved that this is guaranteed to be true if the disease follows multi-group SIR (Susceptible–Infected–Recovered) dynamics. This paper provides a novel proof of this principle for the existing SIR framework, showing that the total number of deaths or infections from an epidemic is decreasing in vaccination effort. Furthermore, it presents a novel model for vaccination which assumes that vaccines assigned to a subgroup are distributed randomly to the unvaccinated population of that subgroup. It suggests, using COVID-19 data, that this more accurately captures vaccination dynamics than the model commonly found in the literature. However, as the novel model provides a strictly larger set of possible vaccination policies, the results presented in this paper hold for both models.

Agent Based Modeling of the Spread of Social Unrest Using Infectious Disease Models

Prior research suggests that the timing and location of social unrest may be influenced by similar unrest activities in another nearby region, potentially causing a spread of unrest activities across space and time. In this paper, we model the spread of social unrest across time and space using a novel approach, grounded in agent-based modeling (ABM) . In it, regions (geographic polygons) are represented as agents that transition from one state to another based on changes in their environment. Our approach involves (1) creating a vector for each region/agent based on socio-demographic, infrastructural, economic, geographic, and environmental (SIEGE) factors, (2) formulating a neighborhood distance function to identify an agent's neighbors based on geospatial distance and SIEGE proximity, (3) designing transition probability equations based on two distinct compartmental models—i.e., the Susceptible-Infected-Recovered (SIR) and the Susceptible-Infected-Susceptible (SIS) models, and (4) building a ground truth for evaluating the simulations. We use ABM to determine the individualized probabilities of each region/agent to transition from one state to another. The models are tested using the districts of three states in India as agents at a monthly scale for 2016-2019. For ground truth of unrest events, we use the Armed Conflict Location and Event Data (ACLED) dataset. Our findings include that (1) the transition probability equations are viable, (2) the agent-based modeling of the spread of social unrest is feasible while treating regions as agents (Brier's score < 0.25 for two out of three regions), and (3) the SIS model performs comparatively better than the SIR model.

A neuro Meyer wavelet neural network procedure for solving the nonlinear Leptospirosis model

The aim of such work is to design a Meyer wavelet neural network (WNN) for solving the mathematical form of the Leptospirosis disease model (LDM). The global and local search optimization schemes based on the genetic algorithm (GA) and active-set algorithm (ASA) are used in this study. Leptospirosis is an infection spread by rodents, which is found in the world and causes fatalities in humans. The mathematical LDM model form consists of susceptible-infected-recovered (SIR), which is based on the disease spread processes. A fitness function is designed by using the mathematical LMD and then optimized by the hybridization of the GAASA. For the correctness, and capability of the Meyer WNN along with the procedures of GAASA, the comparison of the obtained and reference results is provided. Moreover, the reducible absolute error provides the efficiency of the proposed Meyer WNN along with the procedures of GAASA. The statistical observations are also provided to authenticate the convergence of the stochastic Meyer WNN along with the procedures of GAASA.

A Proposed Analytical and Numerical Treatment for the Nonlinear SIR Model via a Hybrid Approach

This paper re-analyzes the nonlinear Susceptible–Infected–Recovered (SIR) model using a hybrid approach based on the Laplace–Padé technique. The proposed approach is successfully applied to extract several analytic approximations for the infected and recovered individuals. The domains of applicability of such analytic approximations are addressed. In addition, the present results are validated through various comparisons with the Runge–Kutta numerical method. The obtained analytical results agree with the numerical ones for a wide range of numbers of contacts featured in the studied model. The efficiency of the present analysis reveals that it can be implemented to deal with other systems describing real-life phenomena.

Optimal vaccination strategies for COVID-19 in population migration between two regions scenario

ABSTRACT Population movements had a significant impact on the spread of COVID-19, and vaccination is considered the most effective means for humans to face viral infections. This study identifies the optimal control strategy for COVID-19 prevention and control, and explores the impact of short-term and long-term migration on the optimal proportion of vaccine allocation between two regions. We proposed to establish the SIR (Susceptible-Infectious-Recovered) model and determine the stability by calculating the disease free equilibrium and Jacobi matrix of the model. We then established the vaccine optimization model, solved the optimal vaccine distribution strategy by gradient descent method and explored the impact of short-term and long-term migration on the optimal vaccine allocation ratio. The stability analysis revealed that the virus could not be eliminated only by reducing the migration rates and infection rates. we introduced the vaccine methods and obtained the optimal vaccine allocation ratio in Shenzhen and Hong Kong as p 1 : p 2 = 0.000341 : 0.001739 , and the daily vaccination rate we need to impose in each region as p 1 : p 2 = 0.00068 : 0.001901 . The presence or absence of short-term migration had no greater impact on the distribution of the vaccine, whereas R v with long-term migration had a greater effect than no migration. We found that migration rates could not eliminate the outbreak in both regions and that adopting an effective vaccine distribution strategy could be more effective in eliminating the outbreak. And for different allocation scenarios with limited vaccine supply, we obtained the optimal allocation most favorable to control the epidemic.

Ranking nodes in complex networks based on TsRank

It is theoretically and practically meaningful to rank and identify nodes in complex networks in various fields, however, many existing methods consider single feature of graph. To utilize multiple attributes of graph, a novel ranking method based on Tsallis entropy is proposed in this paper, which considers information transfer efficiency as global information of nodes and takes extended mixed degree and core neighborhood centrality as local information of nodes. We utilize the monotonicity function index, cumulative distribution (CDF), Kendall’s tau coefficient, Jaccard similarity coefficient, and the total number of infected nodes based on susceptible–infected–recovered (SIR) model as evaluation metrics to measure the performance of the proposed method. The simulation results demonstrate that the proposed method has great superiority in terms of monotonicity, resolution, the accuracy of both the whole ranking results and top-c ranked nodes, and spreading ability of the top-10 nodes.

A real-world data validation of the value of early-stage SIR modelling to public health

Performance of Susceptible-Infected-Recovered (SIR) model in the early stage of a novel epidemic may be hindered by data availability. Additionally, the traditional SIR model may oversimplify the disease progress, and knowledge about the virus and transmission is limited early in the epidemic, resulting in a greater uncertainty of such modelling. We aimed to investigate the impact of model inputs on the early-stage SIR projection using COVID-19 as an illustration to evaluate the application of early infection models. We constructed a modified SIR model using discrete-time Markov chain to simulate daily epidemic dynamics and estimate the number of beds needed in Wuhan in the early stage of COVID-19 epidemic. We compared eight scenarios of SIR projection to the real-world data (RWD) and used root mean square error (RMSE) to assess model performance. According to the National Health Commission, the number of beds occupied in isolation wards and ICUs due to COVID-19 in Wuhan peaked at 37,746. In our model, as the epidemic developed, we observed an increasing daily new case rate, and decreasing daily removal rate and ICU rate. This change in rates contributed to the growth in the needs of bed in both isolation wards and ICUs. Assuming a 50% diagnosis rate and 70% public health efficacy, the model based on parameters estimated using data from the day reaching 3200 to the day reaching 6400 cases returned a lowest RMSE. This model predicted 22,613 beds needed in isolation ward and ICU as on the day of RWD peak. Very early SIR model predictions based on early cumulative case data initially underestimated the number of beds needed, but the RMSEs tended to decline as more updated data were used. Very-early-stage SIR model, although simple but convenient and relatively accurate, is a useful tool to provide decisive information for the public health system and predict the trend of an epidemic of novel infectious disease in the very early stage, thus, avoiding the issue of delay-decision and extra deaths.

Long-term prediction of the COVID-19 epidemics induced by Omicron-virus in China based on a novel non-autonomous delayed SIR model

Since the outbreak of COVID-19, the severe acute respiratory syndrome coronavirus 2 genome is still mutating. Omicron, a recently emerging virus with a shorter incubation period, faster transmission speed, and stronger immune escape ability, is soaring worldwide and becoming the mainstream virus in the COVID-19 pandemic. It is especially critical for the governments, healthcare systems, and economic sectors to have an accurate estimate of the trend of this disaster. By using different mathematical approaches, including the classical susceptible-infected-recovered (SIR) model and its extensions, many investigators have tried to predict the outbreaks of COVID-19. In this study, we employed a novel model which is based upon the well-known susceptible-infected-removed (SIR) model with the time-delay and time-varying coefficients in our previous works. We aim to predict the evolution of the epidemics effectively in nine cities and provinces of China, including A City, B City, C City, D City, E City, F City, G City, H City and I Province. The results show it is effective to model the spread of the large-scale and sporadic COVID-19 induced by Omicron virus by the novel non-autonomous delayed SIR compartment model. The significance of this study is that it can provide the management department of epidemic control with theoretical references and subsequent evaluation of the prevention, control measures, and effects.

A deterministic Susceptible–Infected–Recovered model for studying the impact of media on epidemic dynamics

It is important to understand how the provision of information influences individuals’ behavior and its impact on disease transmission dynamics. We formulate a simple deterministic Susceptible–Infected–Recovered (SIR) model with vital dynamics and incorporate, one at a time, four media functions used in previous studies to mimic media reporting of a disease outbreak to investigate their impact on the dynamics of an epidemic. The most sensitive model parameter for the epidemic outcome at initial disease transmission and disease prevalence are obtained through normalized forward-sensitivity analyses. Media reporting does not impact initial disease transmission but affects the effective reproduction number as the media coverage begins. Numerical results show that the epidemic will affect a large proportion of the population with no media functions. Still, the epidemic time line may be short. In contrast, the key epidemiological quantities (such as age at infection, peak magnitude, peak time, end of the epidemic, and final epidemic size) vary depending on the media function used. The choice of the media function in a pandemic is critical. The media reporting on the spread of disease during pandemics should be done with care since it could counter-intuitively lead to under or overestimating the disease outbreak.

COVID‐19: A multiwave SIR‐based model for learning waves

One of the greatest challenges of the COVID‐19 pandemic has been the way evolving regulation, information, and sentiment have driven waves of the disease. Traditional epidemiology models, such as the SIR model, are not equipped to handle these behavioral‐based changes. We propose a novel multiwave susceptible–infected–recovered (SIR) model, which can detect and model the waves of the disease. We bring together the SIR model's compartmental structure with a change‐point detection martingale process to identify new waves. We create a dynamic process where new waves can be flagged and learned in real time. We use this approach to extend the traditional susceptible–exposed–infected–recovered–dead (SEIRD) model into a multiwave SEIRD model and test it on forecasting COVID‐19 cases from the John Hopkins University data set for states in the United States. We find that compared to the traditional SEIRD model, the multiwave SEIRD model improves mean absolute percentage error (MAPE) by 15%–25% for the United States. We benchmark the multiwave SEIRD model against top performing Center for Disease Control (CDC) models for COVID‐19 and find that the multiwave SERID model is able to outperform the majority of CDC models in long‐term predictions.

The Use of Triangular Norms in Epidemiological Models: A Comparative Study Using COVID-19 Data

In this manuscript we use triangular norms to model contact between susceptible and infected individuals in the susceptible-infected-recovered (SIR) epidemiological model. In the classical SIR model, the encounter between susceptible and infected individuals is traditionally modelled by the product of their densities ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SI$</tex-math></inline-formula> ). That is, the encounter is modelled by the product t-norm. We use the COVID-19 data and extended versions of the SIR model whose encounters are modelled by four triangular norms, namely, product, minimum, Frank and Hamacher t-norms, to analyze the scenario in three countries: Germany, Italy, and Switzerland. We compare all versions of the SIR model based on these triangular norms, and we analyze their effectiveness in fitting data and determining important parameters for the pandemic, such as the basic and effective reproduction number. In addition, Frank and Hamacher triangular norms present an auxiliary parameter that can be interpreted as an indicator of control measure, which we show to be important in the current pandemic scenario.

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.

Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: The case study of COVID-19

The emergence of the SARS-CoV-2 virus and new viral variations with higher transmission and mortality rates have highlighted the urgency to accelerate vaccination to mitigate the morbidity and mortality of the COVID-19 pandemic. For this purpose, this paper formulates a new multi-vaccine, multi-depot location-inventory-routing problem for vaccine distribution. The proposed model addresses a wide variety of vaccination concerns: prioritizing age groups, fair distribution, multi-dose injection, dynamic demand, etc. To solve large-size instances of the model, we employ a Benders decomposition algorithm with a number of acceleration techniques. To monitor the dynamic demand of vaccines, we propose a new adjusted susceptible-infectious-recovered (SIR) epidemiological model, where infected individuals are tested and quarantined. The solution to the optimal control problem dynamically allocates the vaccine demand to reach the endemic equilibrium point. Finally, to illustrate the applicability and performance of the proposed model and solution approach, the paper reports extensive numerical experiments on a real case study of the vaccination campaign in France. The computational results show that the proposed Benders decomposition algorithm is 12 times faster, and its solutions are, on average, 16% better in terms of quality than the Gurobi solver under a limited CPU time. In terms of vaccination strategies, our results suggest that delaying the recommended time interval between doses of injection by a factor of 1.5 reduces the unmet demand up to 50%. Furthermore, we observed that the mortality is a convex function of fairness and an appropriate level of fairness should be adapted through the vaccination.

The effect of medical innovation on the cost-effectiveness of Covid 19-related policies in the United States using a SIR model

BackgroundDuring 2020–21, the United States used a multifaceted approach to control SARS-CoV-2 (Covid-19) and reduce mortality and morbidity. This included non-medical interventions (NMIs), aggressive vaccine development and deployment, and research into more effective approaches to medically treat Covid-19. Each approach had both costs and benefits. The objective of this study was to calculate the Incremental Cost Effectiveness Ratio (ICER) for three major Covid-19 policies: NMIs, vaccine development and deployment (Vaccines), and therapeutics and care improvements within the hospital setting (HTCI).MethodsTo simulate the number of QALYs lost per scenario, we developed a multi-risk Susceptible-Infected-Recovered (SIR) model where infection and fatality rates vary between regions. We use a two equation SIR model. The first equation represents changes in the number of infections and is a function of the susceptible population, the infection rate and the recovery rate. The second equation shows the changes in the susceptible population as people recover. Key costs included loss of economic productivity, reduced future earnings due to educational closures, inpatient spending and the cost of vaccine development. Benefits included reductions in Covid-19 related deaths, which were offset in some models by additional cancer deaths due to care delays.ResultsThe largest cost is the reduction in economic output associated with NMI ($1.7 trillion); the second most significant cost is the educational shutdowns, with estimated reduced lifetime earnings of $523B. The total estimated cost of vaccine development is $55B. HTCI had the lowest cost per QALY gained vs “do nothing” with a cost of $2,089 per QALY gained. Vaccines cost $34,777 per QALY gained in isolation, while NMIs alone were dominated by other options. HTCI alone dominated most alternatives, except the combination of HTCI and Vaccines ($58,528 per QALY gained) and HTCI, Vaccines and NMIs ($3.4 m per QALY gained).ConclusionsHTCI was the most cost effective and was well justified under any standard cost effectiveness threshold. The cost per QALY gained for vaccine development, either alone or in concert with other approaches, is well within the standard for cost effectiveness. NMIs reduced deaths and saved QALYs, but the cost per QALY gained is well outside the usual accepted limits.