Increased urbanization reduced the effectiveness of school closures on seasonal influenza epidemics in China

Background School closure is a common mitigation strategy during severe influenza epidemics and pandemics. However, the effectiveness of this strategy remains controversial. In this study, we aimed to explore the effectiveness of school closure on seasonal influenza epidemics in provincial-level administrative divisions (PLADs) with varying urbanization rates in China. Methods This study analyzed influenza surveillance data between 2010 and 2019 provided by the Chinese National Influenza Center. Taking into consideration the climate, this study included a region with 3 adjacent PLADs in Northern China and another region with 4 adjacent PLADs in Southern China. The effect of school closure on influenza transmission was evaluated by the reduction of the effective reproductive number of seasonal influenza during school winter breaks compared with that before school winter breaks. An age-structured Susceptible-Infected-Recovered-Susceptible (SIRS) model was built to model influenza transmission in different levels of urbanization. Parameters were determined using the surveillance data via robust Bayesian method. Results Between 2010 and 2019, in the less urbanized provinces: Hebei, Zhejiang, Jiangsu and Anhui, during school winter breaks, the effective reproductive number of seasonal influenza epidemics reduced 14.6% [95% confidential interval (CI): 6.2–22.9%], 9.6% (95% CI: 2.5–16.6%), 7.3% (95% CI: 0.1–14.4%) and 8.2% (95% CI: 1.1–15.3%) respectively. However, in the highly urbanized cities: Beijing, Tianjin and Shanghai, it reduced only 5.2% (95% CI: -0.7–11.2%), 4.1% (95% CI: -0.9–9.1%) and 3.9% (95% CI: -1.6–9.4%) respectively. In China, urbanization is associated with decreased proportion of children and increased social contact. According to the SIRS model, both factors could reduce the impact of school closure on seasonal influenza epidemics, and the proportion of children in the population is thought to be the dominant influencing factor. Conclusions Effectiveness of school closure on the epidemics varies with the age structure in the population and social contact patterns. School closure should be recommended in the low urbanized regions in China in the influenza seasons. Graphical abstract

Lockdown: a non-pharmaceutical policy to prevent the spread of COVID-19. Mathematical modeling and computation

In this paper, we derive and analyze an extended SIRS-model which includes lockdown policies at the early stages of the pandemic. The latter play a salient role for flattening the curve of infectious diseases such as COVID-19, and is introduced as a model compartment. An error function is reported, which serves as a bridge between the outcomes of the model and available databases; we estimate the values of the model parameters by minimizing the error function. The intervention function, obtained from the equivalent system of the proposed model, and effective reproduction function are also derived to understand the underline scenario of the coronavirus outbreak. We then estimate the epidemiological variables such as susceptible, recovered, lockdown etc. for Canada and three of its provinces, Ontario, Qu\’ebec and British Columbia, significantly affected by the coronavirus. Some improvements, such as spatial dependence or “at risk’‘ vs “healthy” population, will finally be proposed in order to increase the accuracy of the modeling.

Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models

In this paper, we present a new result that allows for studying the global stability of the disease-free equilibrium point when the basic reproduction number is less than 1, in the fractional calculus context. The method only involves basic linear algebra and can be easily applied to study global asymptotic stability. After proving some auxiliary lemmas involving the Mittag–Leffler function, we present the main result of the paper. Under some assumptions, we prove that the disease-free equilibrium point of a fractional differential system is globally asymptotically stable. We then exemplify the procedure with some epidemiological models: a fractional-order SEIR model with classical incidence function, a fractional-order SIRS model with a general incidence function, and a fractional-order model for HIV/AIDS.

Functional Coupled Systems with Generalized Impulsive Conditions and Application to a SIRS-Type Model

In this paper, we consider a first-order coupled impulsive system of equations with functional boundary conditions, subject to the generalized impulsive effects. It is pointed out that this problem generalizes the classical boundary assumptions, allowing two-point or multipoint conditions, nonlocal and integrodifferential ones, or global arguments, as maxima or minima, among others. Our method is based on lower and upper solution technique together with the fixed point theory. The main theorem is applied to a SIRS model where to the best of our knowledge, for the first time, it includes impulsive effects combined with global, local, and the asymptotic behavior of the unknown functions.

The Influence of Investor Emotion on the Stock Market: Evidence from an Infectious Disease Model

In March 2020, four consecutive circuit breakers in the US stock market underscored the impact of investor sentiment on the stock market. With the development of technology, public opinion and other information now spread easily through social media and other channels, indirectly affecting investor sentiment. This makes it important to understand the underlying dynamics of such situations to help manage the market impact of such events going forward. To that end, we analyze investor sentiment, investor structures, and the capital market fuse mechanism using infectious disease dynamics. We use an extension of the SIR (susceptible, infectious, and recovered) model, called the dynamic SIRS model (where individuals return to a susceptible state), to simulate the impact of investor sentiment on the stock market. Accordingly, we study the circuit breakers in the US stock market and the simulation results of the model to analyze the fuse mechanism process in China that triggers a pause in the market based on volatile trading. The results of our study show that when the influence rate of investor mutual communication increases or when the emotional calm rate decreases, investor emotions will start to diffuse, leading to an increase in the probability of either a serious stampede or zealous overbuying in the stock market. At the same time, the trading frequency of investors and the ratio of investors in both buying and selling directions will have a certain formal impact on the direction of the stock market, with the final impact determined by the ratio of normal investors to emotional investors. When emotional investors dominate the market, their emotions are diffused throughout. Our study provides the reference for relevant agencies to monitor and improve the stock market fuse mechanism in the future.

Estimation of the probability of epidemic fade-out from multiple outbreak data

Deterministic epidemic models, such as the SIRS model or an SIR model with demography, that allow for replenishment of susceptibles typically display damped oscillatory behaviour. If the population is initially fully susceptible, once an epidemic takes off a distinct trough will exist between the first and second waves of infection where the number of infectious individuals falls to a low level. Epidemic dynamics are, however, influenced by stochastic effects, particularly when the number of infectives is low. At the beginning of an epidemic, stochastic die-out is possible and well characterised through use of a branching process approximation to the full non-linear stochastic dynamics. Conditional on an epidemic taking off, stochastic extinction is highly unlikely during the first epidemic wave, but the probability of extinction increases again as the wave declines. Extinction during this period, prior to a potential second wave of infection, is defined as "epidemic fade-out". We consider a set of observed epidemics, each distinct and having evolved independently, in which some display fade-out and some do not. While fade-out is necessarily a stochastic phenomenon, in general the probability of fade-out will depend on the model parameters associated with each epidemic. Accordingly, we ask whether time-series data for the epidemics contain sufficient information to identify the key driver(s) of different outcomes\textemdash fade-out or otherwise\textemdash across the sub-populations supporting each epidemic. We apply a Bayesian hierarchical modelling framework to synthetic data from an SIRS model of epidemic dynamics and demonstrate that we can 1) identify when the sub-population specific model parameters supporting each epidemic have significant variability and 2) estimate the probability of epidemic fade-out for each sub-population. We demonstrate that a hierarchical analysis can provide more accurate and precise estimates of the probability of fade-out than is possible if considering each epidemic in isolation. Our methods may be applied more generally, to both epidemiological and other biological data to identify where differences in outcome—fade-out or recurrent infection/waves —across are purely due to chance or driven by underlying changes in the parameters driving the dynamics.