Susceptible-infected-recovered Research Articles

Predicting Optimum Lockdown Pattern of Epidemic Spread Using AI Techniques

Recent COVID-19 has revealed that we are still unable to find a sustainable approach to combat such infections in order to maintain a stable economy and minimize death rates. COVID-19 vaccine is available but when COVID-19 first arrived, restricting movement was the only option to control the spread, yet, one of its consequences is an economic crisis. This paper proposes predicting optimum lockdown patterns of epidemic spread using AI techniques (MESA ABM) which will help to balance economic fall and death rates while conducting vaccine research. We created a computergenerated environment to replicate a pandemic, such as the initial wave of COVID-19. The model was created using the SIR (Susceptible, Infected, Recovered) hypothesis for disease propagation and implemented using the Mesa, which is an agent-based modeling framework. Using this model, we develop an optimum lockdown pattern using agents (entities that act like humans). Our model produces optimal movement restrictions by randomly putting lockdowns ranging from one to a hundred days using given conditions. Additionally, we carry out several assessments and offer the justification for the action.

Using a population-based Kalman estimator to model the COVID-19 epidemic in France: estimating associations between disease transmission and non-pharmaceutical interventions.

In response to the COVID-19 pandemic caused by SARS-CoV-2, governments have adopted a wide range of non-pharmaceutical interventions (NPI). These include stringent measures such as strict lockdowns, closing schools, bars and restaurants, curfews, and barrier gestures such as mask-wearing and social distancing. Deciphering the effectiveness of each NPI is critical to responding to future waves and outbreaks. To this end, we first develop a dynamic model of the French COVID-19 epidemics over a one-year period. We rely on a global extended Susceptible-Infectious-Recovered (SIR) mechanistic model of infection that includes a dynamic transmission rate over time. Multilevel data across French regions are integrated using random effects on the parameters of the mechanistic model, boosting statistical power by multiplying integrated observation series. We estimate the parameters using a new population-based statistical approach based on a Kalman filter, used for the first time in analysing real-world data. We then fit the estimated time-varying transmission rate using a regression model that depends on the NPIs while accounting for vaccination coverage, the occurrence of variants of concern (VoC), and seasonal weather conditions. We show that all NPIs considered have an independent significant association with transmission rates. In addition, we show a strong association between weather conditions that reduces transmission in summer, and we also estimate increased transmissibility of VoC.

Bounding pandemic spread by heat spread

The beginning of a pandemic is a crucial stage for policymakers. Proper management at this stage can reduce overall health and economical damage. However, knowledge about the pandemic is insufficient. Thus, the use of complex and sophisticated models is challenging. In this study, we propose analytical and stochastic heat spread-based boundaries for the pandemic spread as indicated by the Susceptible-Infected-Recovered (SIR) model. We study the spread of a pandemic on an interaction (social) graph as a diffusion and compared it with the stochastic SIR model. The proposed boundaries are not requiring accurate biological knowledge such as the SIR model does.

The Analysis of SIIR Mathematical Model Time Delay as The Solution of Tuberculosis Transmission in South Sulawesi

This study discusses the numerical solution of the Susceptible-Infected-Recovered (SIIR) transmission model for Tuberculosis (TB) transmission in South Sulawesi. The data used is secondary data from the number of Tuberculosis (TB) sufferers in South Sulawesi from the South Sulawesi Provincial Health Office. The discussion begins with a study of the SIIR model, then builds a time delay SIIR model on the spread of tuberculosis. Next, simulate the delay time SIIR model to find out the number of tuberculosis cases in South Sulawesi. Determining the parameters, simulation and analysis of the results in this study obtained a graph of the movement of the SIIR model of time delay of the spread of tuberculosis with real data. After analyzing the numerical simulation, it is seen that there is a tendency for the spread of Tuberculosis (TB) in South Sulawesi. The SIIR model is a four-dimensional non-linear differential equation. The results of the modeling are simulated using MatLab software to predict the number of TB cases so that early prevention measures are the government’s attention to prevent the spread of Tuberculosis (TB) in South Sulawesi.

Estimating Changes in Contact Patterns in China Over the First Year of the COVID-19 Pandemic: Implications for SARS-CoV-2 Spread - Four Cities, China, 2020.

Previous studies have demonstrated significant changes in social contacts during the first-wave coronavirus disease 2019 (COVID-19) in Chinese mainland. The purpose of this study was to quantify the time-varying contact patterns by age in Chinese mainland in 2020 and evaluate their impact on the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Diary-based contact surveys were performed for four periods: baseline (prior to 2020), outbreak (February 2020), post-lockdown (March-May 2020), and post-epidemic (September-November 2020). We built a Susceptible-Infected-Recovered (SIR) model to evaluate the effect of reducing contacts on transmission. During the post-epidemic period, daily contacts resumed to 26.7%, 14.8%, 46.8%, and 44.2% of the pre-COVID levels in Wuhan, Shanghai, Shenzhen, and Changsha, respectively. This suggests a moderate risk of resurgence in Changsha, Shenzhen, and Wuhan, and a low risk in Shanghai. School closure alone was not enough to interrupt transmission of SARS-CoV-2 Omicron BA.5, but with the addition of a 75% reduction of contacts at the workplace, it could lead to a 16.8% reduction of the attack rate. To control an outbreak, concerted strategies that target schools, workplaces, and community contacts are needed. Monitoring contact patterns by age is key to quantifying the risk of COVID-19 outbreaks and evaluating the impact of intervention strategies.

An Intelligent ABM-based Framework for Developing Pandemic-Resilient Urban Spaces in Post-COVID Smart Cities

As of August 2022, the COVID-19 pandemic has accounted for over six million deaths globally. The urban population has been severely affected by this viral pandemic and the ensuing lockdowns, resulting in increased poverty and inequality, slowed economic growth, and a general decline in quality of life. This paper proposes a framework to evaluate the effects of the pandemic by combining agent-based simulations—based on Susceptible-Infectious-Recovered (SIR) model—with a hybrid neural network. A baseline agent-based model (ABM) incorporating various epidemiological parameters of a viral pandemic was developed, followed by an additional functional layer that integrates factors like agent mobility restrictions and isolation. It is inferred from the results that low population densities of agents and high restrictions on agent mobility could inhibit the rapid spread of the pandemic. This framework also envisages a hybrid neural network that combines the layers of convolutional neural network (CNN) and long-short-term memory (LSTM) architecture for predicting the spatiotemporal probability of infection spread using real-world pandemic data for future pandemics. This framework could aid designers, regulators, urban planners, and policymakers develop resilient, healthy, and sustainable urban spaces in post-COVID smart cities.

PHYSICS-INFORMED NEURAL NETWORKS FOR INFORMED VACCINE DISTRIBUTION INMETA-POPULATIONS

Accurate numerical and physical models play an important role in modeling the spread of infectious disease as well as informing policy decisions. Vaccination programs rely on the estimation of disease parameters from limited, error-prone reported data. Using physics-informed neural networks (PINNs) as universal function approximators of the susceptible-infected-recovered (SIR) compartmentalized differential equation model, we create a data-driven framework that uses reported data to estimate disease spread and approximate corresponding disease parameters. We apply this to data from a London boarding school, demonstrating the framework's ability to produce accurate disease and parameter estimations despite noisy data. However, real-world populations contain sub-populations, each exhibiting different levels of risk and activity. Thus, we expand our framework to model meta-populations of preferentially-mixed subgroups with various contact rates, introducing a new substitution to decrease the number of parameters. Optimal parameters are estimated through PINNs which are then used in a negative gradient approach to calculate an optimal vaccine distribution plan for informed policy decisions. We also manipulate a new hyperparameter in the loss function of the PINNs network to expedite training. Together, our work creates a data-driven tool for future infectious disease vaccination efforts in heterogeneously mixed populations.

Passenger flow analysis and emergency response simulation in a metro network using virus transmission model

ObjectivesThe potential virus in transportation facilities poses a serious risk to travelers. This research focus on the commuting by metro on the risk of the coronavirus disease 2019 (COVID-19). The main purpose is to explore the trajectory of virus transmission and the effectiveness of various control measures. MethodsA transmission model was established on the basis of the susceptible-infected-recovered (SIR) model, combined with the spatial and temporal characteristics of the metro passenger flow. The implementation effects of the emergency strategies were analyzed through a series of simulation experiments. The changes in passenger flow affected by the virus transmission were analyzed both under the single intervention condition of the disinfection or off-peak travel policy and their double interventions. ResultsThe results of the experiments show that disinfection and off-peak travel can effectively reduce the number of the infected people. To promote the disinfection is better than the off-peak travel strategy. The optimal solution is the combination of these two strategies, thereby reducing the infection rate in the stations effectively. In particular, it can reduce the number of potential infected people in high-traffic stations by 50%. ConclusionsThis study provides a scientific basis for the prevention of COVID-19 in the urban transportation system and the formulation of public emergency strategies. It can also be applied to other epidemic diseases such as the seasonal flu, for public health prevention.

Generalization of Relative Change in a Centrality Measure to Identify Vital Nodes in Complex Networks

Identifying vital nodes is important in disease research, spreading rumors, viral marketing, and drug development. The vital nodes in any network are used to spread information as widely as possible. Centrality measures such as Degree centrality (D), Betweenness centrality (B), Closeness centrality (C), Katz (K), Cluster coefficient (CC), PR (PageRank), LGC (Local and Global Centrality), ISC (Isolating Centrality) centrality measures can be used to effectively quantify vital nodes. The majority of these centrality measures are defined in the literature and are based on a network’s local and/or global structure. However, these measures are time-consuming and inefficient for large-scale networks. Also, these measures cannot study the effect of removal of vital nodes in resource-constrained networks. To address these concerns, we propose the six new centrality measures namely GRACC, LRACC, GRAD, LRAD, GRAK, and LRAK. We develop these measures based on the relative change of the clustering coefficient, degree, and Katz centralities after the removal of a vertex. Next, we compare the proposed centrality measures with D, B, C, CC, K, PR, LGC, and ISC to demonstrate their efficiency and time complexity. We utilize the SIR (Susceptible-Infected-Recovered) and IC (Independent Cascade) models to study the maximum information spread of proposed measures over conventional ones. We perform extensive simulations on large-scale real-world data sets and prove that local centrality measures perform better in some networks than global measures in terms of time complexity and information spread. Further, we also observe the number of cliques drastically improves the efficiency of global centrality measures.

Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics

The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The Susceptible-Infected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes ‘ℎ’. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease.

Pandemic meltdown and economic recovery – A multi-phase dynamic model, empirics, and policy

In this paper a two-phase pandemic-economic model is proposed, with phase-specific modeling and policy variables – as suggested by the chronicle of pandemic and economic policy developments over the period 2020–2021. In a first phase, the spread of a pandemic disease is the primary concern of authorities, that still also pay attention to economic activity. A dynamic model is introduced, embedding a two-way interaction between an extended epidemic Susceptible-Infected-Recovered (SIR) model and output gap dynamics. In the second phase, posterior to lockdowns when waves fade away, monetary policy becomes the control variable, pursuing again a joint objective, of supporting a non-inflationary recovery without causing significant fatalities. We then use a standard stylized model for the macroeconomy with simplified infection dynamics, that also enter the policy objective. The two phases are thus studied in a regime change model where the control and state variables as well as the objective function are allowed to change across phases. We solve the model over a finite horizon and derive the optimal lockdown or monetary policy path that jointly minimizes pandemic and economic losses. The two-phase finite horizon decision model is empirically calibrated and numerically solved by discretization and optimization methods. In the first phase, albeit with lasting adverse effects on output, lockdown-based control can be effective in reducing infection rates, but less so when starting from a negative output gap. In the second phase, accommodative monetary policy appears to be effective on both fronts, with even an eventual need for a return to tightening as output gap closes and inflation resumes.

On the Duration of an Epidemic.

A stochastic SIR (Susceptible, Infected, Recovered) model for the spread of a non-lethal disease is considered. The size of the population is constant. The problem of computing the moment-generating function of the random time until all members of the population are recovered is solved in special cases. The expected duration of the epidemic is also computed, as well as the probability that the whole population will be either cured or immunized before every member is infected. The method of similarity solutions is used to solve the various Kolmogorov partial differential equations, subject to the appropriate boundary conditions.

A Dynamic Compartmental Model to Explore the Optimal Strategy of Varicella Vaccination: An Epidemiological Study in Jiangsu Province, China.

Varicella (chickenpox) is highly contagious among children and frequently breaks out in schools. In this study, we developed a dynamic compartment model to explore the optimal schedule for varicella vaccination in Jiangsu Province, China. A susceptible-infected-recovered (SIR) model was proposed to simulate the transmission of varicella in different age groups. The basic reproduction number was computed by the kinetic model, and the impact of three prevention factors was assessed through the global sensitivity analysis. Finally, the effect of various vaccination scenarios was qualitatively evaluated by numerical simulation. The estimated basic reproduction number was 1.831 ± 0.078, and the greatest contributor was the 5-10 year-old group (0.747 ± 0.042, 40.80%). Sensitivity analysis indicated that there was a strong negative correlation between the second dose vaccination coverage rate and basic reproduction number. In addition, we qualitatively found that the incidence would significantly decrease as the second dose vaccine coverage expands. The results suggest that two-dose varicella vaccination should be mandatory, and the optimal age of second dose vaccination is the 5-10 year-old group. Optimal vaccination time, wide vaccine coverage along with other measures, could enhance the effectiveness of prevention and control of varicella in China.

Modeling the resumption of work and production of enterprises during COVID-19: An SIR-based quantitative framework.

The ongoing COVID-19 pandemic has evolved beyond being a public health crisis as it has exerted worldwide severe economic impacts, triggering cascading failures in the global industrial network. Although certain powerful enterprises can remain its normal operation during this global shock, what's more likely to happen for the majority, especially those small- and medium-sized firms, is that they are experiencing temporary suspension out of epidemic control requirement, or even permanent closure due to chronic business losses. For those enterprises that sustain the pandemic and only suspend for a relatively short period, they could resume work and production when epidemic control and prevention conditions are satisfied and production and operation are adjusted correspondingly. In this paper, we develop a novel quantitative framework which is based on the classic susceptible-infectious-recovered (SIR) epidemiological model (i.e., the SIR model), containing a set of differential equations to capture such enterprises' reactions in response to COVID-19 over time. We fit our model from the resumption of work and production (RWP) data on industrial enterprises above the designated size (IEDS). By modeling the dynamics of enterprises' reactions, it is feasible to investigate the ratio of enterprises' state of operation at given time. Since enterprises are major economic entities and take responsibility for most output, this study could potentially help policy makers better understand the economic impact caused by the pandemic and could be heuristic for future prevention and resilience-building strategies against suchlike outbreaks of public health crises.

Epidemics from the Eye of the Pathogen

While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic SIR (Susceptible, Infected, Recovered) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona.

Positivity-Preserving Numerical Method for a Stochastic Multi-Group SIR Epidemic Model

Abstract The stochastic multi-group susceptible–infected–recovered (SIR) epidemic model is nonlinear, and so analytical solutions are generally difficult to obtain. Hence, it is often necessary to find numerical solutions, but most existing numerical methods fail to preserve the nonnegativity or positivity of solutions. Therefore, an appropriate numerical method for studying the dynamic behavior of epidemic diseases through SIR models is urgently required. In this paper, based on the Euler–Maruyama scheme and a logarithmic transformation, we propose a novel explicit positivity-preserving numerical scheme for a stochastic multi-group SIR epidemic model whose coefficients violate the global monotonicity condition. This scheme not only results in numerical solutions that preserve the domain of the stochastic multi-group SIR epidemic model, but also achieves the “ order - 1 2 {\mathrm{order}-\frac{1}{2}} ” strong convergence rate. Taking a two-group SIR epidemic model as an example, some numerical simulations are performed to illustrate the performance of the proposed scheme.

Transmission of Tuberculosis and Reproduction Number Using Lyapunov Function of SIR Model

This paper studies the mechanism of transmission of Tuberculosis (TB) caused by the mycobacterium tuberculosis bacteria. TB is an airborne disease that endangering human population globally. Mathematical modelling of tuberculosis was developed using the Susceptible-Infected-Recovered (SIR) model in this analysis. The model generated by the four-dimensional, nonlinear dynamic system is reduced to three dimensions, with some assumptions. Then, the model will be analyzed by creating a mathematical theorem that will prove the existence of a TB event, the disease-free equilibrium phase, and the TB endemic disease stage. By using the Lyapunov function method, the three theorems can be proved. The basic reproduction number R0 also can be obtained from the model. If the basic reproduction number R0 ≤ 1, then the disease-free equilibrium is global asymptotically stable and if R0 > 1, then the endemic equilibrium is asymptotically stable globally. Carrying out a simulation using data in a selected region, the result of the model successfully describes and forecast the number of TB cases and it may also be used for assessing the TB disease status.

Robust observer-based output-feedback control for epidemic models: Positive fuzzy model and separation principle approach

A feedback-type vaccination and treatment policy for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances is designed by considering only the number of infected individuals. Specifically, an observer-based output-feedback (OBOF) controller design methodology in the Takagi–Sugeno fuzzy model framework is established. The designed controller exhibits L∞–L∞ disturbance attenuation performance, is robust against norm-bounded parametric uncertainties, and can preserve the closed-loop positivity. The primary contributions of the proposed design condition can be characterized as follows: (i) a novel structure of a fuzzy OBOF controller to ensure the closed-loop positivity; (ii) separate disturbance attenuation performances for the independent design of the controller and observer; (iii) The independent design conditions formulated as convex optimization problems in the presence of parametric uncertainties; (iv) the demonstration of the separation principle in the positive L∞–L∞ disturbance attenuation problem. Results of the case study pertaining to the SIR model demonstrate the efficacy of the proposed methodology.

A Synthesis of Pulse Influenza Vaccination Policies Using an Efficient Controlled Elitism Non-Dominated Sorting Genetic Algorithm (CENSGA)

Seasonal influenza (also known as flu) is responsible for considerable morbidity and mortality across the globe. The three recognized pathogens that cause epidemics during the winter season are influenza A, B and C. The influenza virus is particularly dangerous due to its mutability. Vaccines are an effective tool in preventing seasonal influenza, and their formulas are updated yearly according to the WHO recommendations. However, in order to facilitate decision-making in the planning of the intervention, policymakers need information on the projected costs and quantities related to introducing the influenza vaccine in order to help governments obtain an optimal allocation of the vaccine each year. In this paper, an approach based on a Controlled Elitism Non-Dominated Sorting Genetic Algorithm (CENSGA) model is introduced to optimize the allocation of the influenza vaccination. A bi-objective model is formulated to control the infection volume, and reduce the unit cost of the vaccination campaign. An SIR (Susceptible–Infected–Recovered) model is employed for representing a potential epidemic. The model constraints are based on the epidemiological model, time management and vaccine quantity. A two-phase optimization process is proposed: guardian control followed by contingent controls. The proposed approach is an evolutionary metaheuristic multi-objective optimization algorithm with a local search procedure based on a hash table. Moreover, in order to optimize the scheduling of a set of policies over a predetermined time to form a complete campaign, an extended CENSGA is introduced with a variable-length chromosome (VLC) along with mutation and crossover operations. To validate the applicability of the proposed CENSGA, it is compared with the classical Non-Dominated Sorting Genetic Algorithm (NSGA-II). The results indicate that optimal vaccination campaigns with compromise tradeoffs between the two conflicting objectives can be designed effectively using CENSGA, providing policymakers with a number of alternatives to accommodate the best strategies. The results are analyzed using graphical and statistical comparisons in terms of cardinality, convergence, distribution and spread quality metrics, illustrating that the proposed CENSGA is effective and useful for determining the optimal vaccination allocation campaigns.

The Stochastic Approach for SIR Epidemic Models: Do They Help to Increase Information from Raw Data?

The recent outbreak of COVID-19 underlined the need for a fast and trustworthy methodology to identify the features of a pandemic, whose early identification is of help for designing non-pharmaceutical interventions (including lockdown and social distancing) to limit the progression of the disease. A common approach in this context is the parameter identification from deterministic epidemic models, which, unfortunately, cannot take into account the inherent randomness of the epidemic phenomenon, especially in the initial stage; on the other hand, the use of raw data within the framework of a stochastic model is not straightforward. This note investigates the stochastic approach applied to a basic SIR (Susceptible, Infected, Recovered) epidemic model to enhance information from raw data generated in silico. The stochastic model consists of a Continuous-Time Markov Model, describing the epidemic outbreak in terms of stochastic discrete infection and recovery events in a given region, and where independent random paths are associated to different provinces of the same region, which are assumed to share the same set of model parameters. The estimation procedure is based on the building of a loss function that symmetrically weighs first-order and second-order moments, differently from the standard approach that considers a highly asymmetrical choice, exploiting only first-order moments. Instead, we opt for an innovative symmetrical identification approach which exploits both moments. The new approach is specifically proposed to enhance the statistical information content of the raw epidemiological data.