General Model for COVID-19 Spreading With Consideration of Intercity Migration, Insufficient Testing, and Active Intervention: Modeling Study of Pandemic Progression in Japan and the United States.

BACKGROUND: The coronavirus disease (COVID-19) began to spread in mid-December 2019 from Wuhan, China, to most provinces in China and over 200 other countries through an active travel network. Limited by the ability of the country or city to perform tests, the officially reported number of confirmed cases is expected to be much smaller than the true number of infected cases. OBJECTIVE: This study aims to develop a new susceptible-exposed-infected-confirmed-removed (SEICR) model for predicting the spreading progression of COVID-19 with consideration of intercity travel and the difference between the number of confirmed cases and actual infected cases, and to apply the model to provide a realistic prediction for the United States and Japan under different scenarios of active intervention. METHODS: The model introduces a new state variable corresponding to the actual number of infected cases, integrates intercity travel data to track the movement of exposed and infected individuals among cities, and allows different levels of active intervention to be considered so that a realistic prediction of the number of infected individuals can be performed. Moreover, the model generates future progression profiles for different levels of intervention by setting the parameters relative to the values found from the data fitting. RESULTS: By fitting the model with the data of the COVID-19 infection cases and the intercity travel data for Japan (January 15 to March 20, 2020) and the United States (February 20 to March 20, 2020), model parameters were found and then used to predict the pandemic progression in 47 regions of Japan and 50 states (plus a federal district) in the United States. The model revealed that, as of March 19, 2020, the number of infected individuals in Japan and the United States could be 20-fold and 5-fold as many as the number of confirmed cases, respectively. The results showed that, without tightening the implementation of active intervention, Japan and the United States will see about 6.55% and 18.2% of the population eventually infected, respectively, and with a drastic 10-fold elevated active intervention, the number of people eventually infected can be reduced by up to 95% in Japan and 70% in the United States. CONCLUSIONS: The new SEICR model has revealed the effectiveness of active intervention for controlling the spread of COVID-19. Stepping up active intervention would be more effective for Japan, and raising the level of public vigilance in maintaining personal hygiene and social distancing is comparatively more important for the United States.

Extortion provides alternative routes to the evolution of cooperation in structured populations.

In this paper, we study the evolution of cooperation in structured populations (individuals are located on either a regular lattice or a scale-free network) in the context of repeated games by involving three types of strategies, namely, unconditional cooperation, unconditional defection, and extortion. The strategy updating of the players is ruled by the replicator-like dynamics. We find that extortion strategies can act as catalysts to promote the emergence of cooperation in structured populations via different mechanisms. Specifically, on regular lattice, extortioners behave as both a shield, which can enwrap cooperators inside and keep them away from defectors, and a spear, which can defeat those surrounding defectors with the help of the neighboring cooperators. Particularly, the enhancement of cooperation displays a resonance-like behavior, suggesting the existence of optimal extortion strength mostly favoring the evolution of cooperation, which is in good agreement with the predictions from the generalized mean-field approximation theory. On scale-free network, the hubs, who are likely occupied by extortioners or defectors at the very beginning, are then prone to be conquered by cooperators on small-degree nodes as time elapses, thus establishing a bottom-up mechanism for the emergence and maintenance of cooperation.

Global Spatio-temporal Patterns of Influenza in the Post-pandemic Era.

We study the global spatio-temporal patterns of influenza dynamics. This is achieved by analysing and modelling weekly laboratory confirmed cases of influenza A and B from 138 countries between January 2006 and January 2015. The data were obtained from FluNet, the surveillance network compiled by the the World Health Organization. We report a pattern of skip-and-resurgence behavior between the years 2011 and 2013 for influenza H1N1pdm, the strain responsible for the 2009 pandemic, in Europe and Eastern Asia. In particular, the expected H1N1pdm epidemic outbreak in 2011/12 failed to occur (or "skipped") in many countries across the globe, although an outbreak occurred in the following year. We also report a pattern of well-synchronized wave of H1N1pdm in early 2011 in the Northern Hemisphere countries, and a pattern of replacement of strain H1N1pre by H1N1pdm between the 2009 and 2012 influenza seasons. Using both a statistical and a mechanistic mathematical model, and through fitting the data of 108 countries, we discuss the mechanisms that are likely to generate these events taking into account the role of multi-strain dynamics. A basic understanding of these patterns has important public health implications and scientific significance.

Predicting the outcome of roulette.

There have been several popular reports of various groups exploiting the deterministic nature of the game of roulette for profit. Moreover, through its history, the inherent determinism in the game of roulette has attracted the attention of many luminaries of chaos theory. In this paper, we provide a short review of that history and then set out to determine to what extent that determinism can really be exploited for profit. To do this, we provide a very simple model for the motion of a roulette wheel and ball and demonstrate that knowledge of initial position, velocity, and acceleration is sufficient to predict the outcome with adequate certainty to achieve a positive expected return. We describe two physically realizable systems to obtain this knowledge both incognito and in situ. The first system relies only on a mechanical count of rotation of the ball and the wheel to measure the relevant parameters. By applying these techniques to a standard casino-grade European roulette wheel, we demonstrate an expected return of at least 18%, well above the -2.7% expected of a random bet. With a more sophisticated, albeit more intrusive, system (mounting a digital camera above the wheel), we demonstrate a range of systematic and statistically significant biases which can be exploited to provide an improved guess of the outcome. Finally, our analysis demonstrates that even a very slight slant in the roulette table leads to a very pronounced bias which could be further exploited to substantially enhance returns.

Uncovering bifurcation patterns in cortical synapses.

Individual cortical synapses are known to exhibit a very complex short-time dynamic behaviour in response to simple "naturalistic" stimulation. We describe a computational study of the experimentally obtained excitatory post-synaptic potential trains of individual cortical synapses. By adopting a new nonlinear modelling scheme we construct robust and repeatable models of the underlying dynamics. These models suggest that cortical synapses exhibit a wide range of either periodic or chaotic dynamics. For stimulus at a fixed rate our models predict that the response of the individual synapse will vary from a fixed point to periodic and chaotic, depending on the frequency of stimulus. Dynamics for individual synapses vary widely, suggesting that the individual behaviour of synapses is highly tuned and that the dynamic behaviour of even a small network of synapse-coupled neurons could be extremely varied.

Scale-free distribution of avian influenza outbreaks.

Using global case data for the period from 25 November 2003 to 10 March 2007, we construct a network of plausible transmission pathways for the spread of avian influenza among domestic and wild birds. The network structure we obtain is complex and exhibits scale-free (although not necessarily small-world) properties. Communities within this network are connected with a distribution of links with infinite variance. Hence, the disease transmission model does not exhibit a threshold and so the infection will continue to propagate even with very low transmissibility. Consequentially, eradication with methods applicable to locally homogeneous populations is not possible. Any control measure needs to focus explicitly on the hubs within this network structure.