A stochastic SIR network epidemic model with preventive dropping of edges

How to correctly fit an SIR model to data from an SEIR model?

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases. This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality. To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments.

Necessary and sufficient conditions for exact closures of epidemic equations on configuration model networks

We prove that it is possible to obtain the exact closure of SIR pairwise epidemic equations on a configuration model network if and only if the degree distribution follows a Poisson, binomial, or negative binomial distribution. The proof relies on establishing the equivalence, for these specific degree distributions, between the closed pairwise model and a dynamical survival analysis (DSA) model that was previously shown to be exact. Specifically, we demonstrate that the DSA model is equivalent to the well-known edge-based Volz model. Using this result, we also provide reductions of the closed pairwise and Volz models to a single equation that involves only susceptibles. This equation has a useful statistical interpretation in terms of times to infection. We provide some numerical examples to illustrate our results.

On regime changes of COVID-19 outbreak

The COVID-19 pandemic has had a very serious impact on societies and caused large-scale economic changes and death toll worldwide. The first cases were detected in China, but soon the virus spread quickly worldwide and the intensity of newly reported infections grew high during this initial period almost everywhere. Later, despite all imposed measures, the intensity shifted abruptly multiple times during the two-year period between 2020 and 2022 causing waves of too high infection rates in almost every part of the world. To target this problem, we assume the data heterogeneity as multiple consecutive regime changes. The research study includes the development of a model based on automatic regime change detection and their combination with the linear birth-death process for long-run data fits. The results are empirically verified on data for 38 countries and US states for the period from February 2020 to April 2022. Finally, the initial phase (conditions) properties of infection development are studied.

Moment closure approximations of susceptible-infected-susceptible epidemics on adaptive networks

The influence of people's individual responses to the spread of contagious phenomena, like the COVID-19 pandemic, is still not well understood. We investigate the Markovian Generalized Adaptive Susceptible-Infected-Susceptible (G-ASIS) epidemic model. The G-ASIS model comprises many contagious phenomena on networks, ranging from epidemics and information diffusion to innovation spread and human brain interactions. The connections between nodes in the G-ASIS model change adaptively over time, because nodes make decisions to create or break links based on the health state of their neighbors. Our contribution is fourfold. First, we rigorously derive the first-order and second-order mean-field approximations from the continuous-time Markov chain. Second, we illustrate that the first-order mean-field approximation fails to approximate the epidemic threshold of the Markovian G-ASIS model accurately. Third, we show that the second-order mean-field approximation is a qualitative good approximation of the Markovian G-ASIS model. Finally, we discuss the Adaptive Information Diffusion (AID) model in detail, which is contained in the G-ASIS model. We show that, similar to most other instances of the G-ASIS model, the AID model possesses a unique steady state, but that in the AID model, the convergence time toward the steady state is very large. Our theoretical results are supported by numerical simulations.

Balancing Quarantine and Self-Distancing Measures in Adaptive Epidemic Networks

We study the relative importance of two key control measures for epidemic spreading: endogenous social self-distancing and exogenous imposed quarantine. We use the framework of adaptive networks, moment-closure, and ordinary differential equations to introduce new model types of susceptible-infected-recovered (SIR) dynamics. First, we compare computationally expensive, adaptive network simulations with their corresponding computationally efficient ODE equivalents and find excellent agreement. Second, we discover that there exists a critical curve in parameter space for the epidemic threshold, which suggests a mutual compensation effect between the two mitigation strategies: as long as social distancing and quarantine measures are both sufficiently strong, large outbreaks are prevented. Third, we study the total number of infected and the maximum peak during large outbreaks using a combination of analytical estimates and numerical simulations. Also for large outbreaks we find a similar compensation mechanism as for the epidemic threshold. This means that if there is little incentive for social distancing in a population, drastic quarantining is required, and vice versa. Both pure scenarios are unrealistic in practice. The new models show that only a combination of measures is likely to succeed to control epidemic spreading. Fourth, we analytically compute an upper bound for the total number of infected on adaptive networks, using integral estimates in combination with a moment-closure approximation on the level of an observable. Our method allows us to elegantly and quickly check and cross-validate various conjectures about the relevance of different network control measures. In this sense it becomes possible to adapt also other models rapidly to new epidemic challenges.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Stochastic dynamics of an SIS epidemic on networks

We derive a stochastic SIS pairwise model by considering the change of the variables of this system caused by an event. Based on approximations, we construct a low-dimensional deterministic system that can be used to describe the epidemic spread on a regular network. The mathematical treatment of the model yields explicit expressions for the variances of each variable at equilibrium. Then a comparison between the stochastic pairwise model and the stochastic mean-field SIS model is performed to indicate the effect of network structure. We find that the variances of the prevalence of infection for these two models are almost equal when the number of neighbors of every individual is large. Furthermore, approximations for the quasi-stationary distribution of the number of infected individuals and the expected time to extinction starting in quasi-stationary are derived. We analyze the approximations for the critical number of neighbors and the persistence threshold based on the stochastic model. The approximate performance is then examined by numerical and stochastic simulations. Moreover, during the early development phase, the temporal variance of the infection is also obtained. The simulations show that our analytical results are asymptotically accurate and reasonable.

Susceptible-Infected-Removed Mathematical Model under Deep Learning in Hospital Infection Control of Novel Coronavirus Pneumonia

Objective

This research aimed to explore the application of a mathematical model based on deep learning in hospital infection control of novel coronavirus (COVID-19) pneumonia.

Methods

First, the epidemic data of Beijing, China, were utilized to make a definite susceptible-infected-removed (SIR) model fitting to determine the estimated value of the COVID-19 removal intensity β, which was then used to do a determined SIR model and a stochastic SIR model fitting for the hospital. In addition, the reasonable β and γ estimates of the hospital were determined, and the spread of the epidemic in hospital was simulated, to discuss the impact of basal reproductive number changes, isolation, vaccination, and so forth on COVID-19.

Results

There was a certain gap between the fitting of SIR to the remover and the actual data. The fitting of the number of infections was accurate. The growth rate of the number of infections decreased after measures, such as isolation, were taken. The effect of herd immunity was achieved after the overall immunity reached 70.9%.

Conclusion

The SIR model based on deep learning and the stochastic SIR fitting model were accurate in judging the development trend of the epidemic, which can provide basis and reference for hospital epidemic infection control.

The prevalence of pregnancy among adolescent girls and young women across the Southern African development community economic hub: A systematic review and meta-analysis

Background: Despite the high rate of HIV infections, there is still high rate of early unprotected sex, unintended pregnancy, and unsafe abortions especially among unmarried adolescent girls and young women (AGYW) 10-24 years of age in sub Saharan Africa. AGYW face challenges in accessing health care, contraception needs, and power to negotiate safer sex. This study aimed to estimate the rate of pregnancy among AGYW aged 10-24, 10-19 and 15-19 years in the Southern African Development Community (SADC) economic region. Methods: A systematic review and meta-analysis was used to describe the prevalence of pregnancy among AGYW in 15 SADC member countries between January 2007 and December2017. The articles were extracted from PubMed/MEDLINE, African Index Medicus, and other reports. They were screened and reviewed according to PRISMA methodology to fulfil study eligibility criteria. Results: The overall regional weighted pregnancy prevalence among AGYW 10-24 years of age was 25% (95% CI: 21% to 29%). Furthermore, sub-population 10-19 years was 22% (95% CI:19% to 26%) while 15-19 years was 24% (18% to 30%). There was a significant heterogeneity detected between the studies (I=99.78%, P < 0.001), even within individual countries. Conclusion: The findings revealed a high pregnancy rate among AGYW in the SADC region. This prompts the need to explore innovative research and programs expanding and improving sexual and reproductive health communication to reduce risk and exposure of adolescents to early planned, unplanned and unwanted pregnancies, SRHR challenges, access to care, HIV/STIs, as well as other risk strategies.

COVID-19 Spread in Saudi Arabia: Modeling, Simulation and Analysis

The novel coronavirus Severe Acute Respiratory Syndrome (SARS)-Coronavirus-2 (CoV-2) has resulted in an ongoing pandemic and has affected over 200 countries around the world. Mathematical epidemic models can be used to predict the course of an epidemic and develop methods for controlling it. As social contact is a key factor in disease spreading, modeling epidemics on contact networks has been increasingly used. In this work, we propose a simulation model for the spread of Coronavirus Disease 2019 (COVID-19) in Saudi Arabia using a network-based epidemic model. We generated a contact network that captures realistic social behaviors and dynamics of individuals in Saudi Arabia. The proposed model was used to evaluate the effectiveness of the control measures employed by the Saudi government, to predict the future dynamics of the disease in Saudi Arabia according to different scenarios, and to investigate multiple vaccination strategies. Our results suggest that Saudi Arabia would have faced a nationwide peak of the outbreak on 21 April 2020 with a total of approximately 26 million infections had it not imposed strict control measures. The results also indicate that social distancing plays a crucial role in determining the future local dynamics of the epidemic. Our results also show that the closure of schools and mosques had the maximum impact on delaying the epidemic peak and slowing down the infection rate. If a vaccine does not become available and no social distancing is practiced from 10 June 2020, our predictions suggest that the epidemic will end in Saudi Arabia at the beginning of November with over 13 million infected individuals, and it may take only 15 days to end the epidemic after 70% of the population receive a vaccine.