Frontiers in Physics

We investigate time scale separation in the vector borne disease model SIRUV, as previously described in the literature [1], and recently reanalyzed with the singular perturbation technique [2]. We focus on the analysis with a single small parameter, the birth and death rate {micro}, whereas all other model parameters are much larger and describe fast transitions. The scaling of the endemic stationary state, the Jacobian matrix around it and its eigenvalues with this small parameter {micro} is calculated and the center manifold analysis performed with the method described in [3] which goes back to earlier work [4, 5], namely a transformation of the Jacobian matrix to block structure in zeroth order in the parameter {micro} is used and then a family of center manifolds with {micro} larger than zero is obtained.

Our manuscript was based on surveillance cases of COVID-19 identified before January 26, 2020. As of February 20, 2020, the total number of confirmed cases in mainland China has reached 18 times of the number in our manuscript. While the methods and the main conclusions in our original analyses remain solid, we decided to withdraw this preprint for the time being, and will replace it with a more up-to-date version shortly. Should you have any comments or suggestions, please feel free to contact the corresponding author.

Many countries established strong population lockdowns as a response to the pandemic of COVID-19 in 2020. While these measures proved efficient in stopping the spreading of the virus, they also introduced collateral effects in the economies of these countries. We report in this work that the imprints in mobility of both the lockdown and post-lockdown on the Spanish population are measurable by means of the daily radius of gyration using mobile phone data. We cross mobility with economic data segmented by average salary per person so as to find large inequalities between low- and high-income populations. Indeed, low-income populations typically show a 17% higher radius of gyration than high-income ones during pre-lockdown (8.1 km vs. 6.9 km). However, this relative difference grows to a maximum during lock-down (3.3 km vs. 900 m) since most of the essential workers (carriers, nurses, supermarket cashiers, farmworkers, etc.) belong to the first segment. Post-lockdown shows reversed inequality in the weeks during summer vacations as high-income populations multiplied their pre-lockdown radius by 70% as a rebound effect driven by leisure, while low-income populations recovered their normal pre-lockdown radius. This period is correlated with an extraordinary increase in the number of new Covid cases, which stabilized after the holyday weeks once at the so-called new normal. We find that this new normal emphasizes the pre-lockdown inequalities in mobility between low- and high-income population, increasing the inequality up to a 47%. These results show the relevance of devising measures that could account for potential collateral inequalities.

Within the framework of a two-component model of the COVID-19 epidemic, taking into account the special role of superspreaders, we consider the impact of the recovery factor and quarantine measures on the course of the epidemic, as well as the possibility of a second wave of morbidity. It is assumed that there is no long-term immunity in asymptomatic superspreaders who have undergone the infection, and the emergence of long-term immunity in those who have undergone severe illness. It is shown that, under these assumptions, the relaxation of quarantine measures leads to the resumption of virus circulation among asymptomatic superspreaders. Depending on the characteristics of the quarantine, its removal may or may not lead to a renewed wave of daily morbidity. A criterion for the occurrence of repeated wave of morbidity is proposed based on the analysis of the final phase of the first wave. Based on this criterion, the repeated wave of the epidemic is predicted in New Zealand. A natural explanation is given for the decrease in lethality among the infected against the background of an absolute increase in their number.

Predictions about the further development of the Corona pandemic are of great public interest but many approaches demand a large number of country specific parameters and are not easily transferable. A special interest of simulations on the pandemic is to trace the effect of politics for reducing the virus spread, since these measures have had an enormous impact on economy and daily life. Here a simple yet powerful algorithm is introduced for fitting the infection numbers by simple analytic functions. This way, the increase of the case numbers in periods with different regulations can be distinguished, and by extrapolating the fit functions, a forecast for the maximum numbers and time scales are possible. The effect of the restraints such as lock down are demonstrated by comparing the resulting infection history with the likely unconstrained virus spread, and it is shown that a delay of 1-4 weeks before imposing measures aiming at social distancing could have led to a complete infection of the respective populations. The approach is simply transferable to many different states. Here data from six E.U. countries, the UK, Russia, two Asian countries, the USA and ten states inside the USA with significant case numbers are analyzed, and striking qualitative similarities are found. Keywords: Covid-19, forecast, analytic fit, France, Germany, Italy, Spain South Korea, New York, Washington, Florida, Michigan, Poland, Sweden, USA, Pennsylvania, China, Russia, UK, California, Illinois, Indiana, Maryland, North Carolina.

The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage.

After the major exponential phase, the Covid-19 pandemic is on a milder rate of increase globally, and past the peak in many countries. In this phase a marked systematic weekly periodicity in the Covid-19 attack has become clear, the study of which could be useful for the long term strategy to deal with the virus and the pandemic. The most important aspect of this strong weekly modulation is its global nature, phase-coherent over most of globe, independent of the geographical location. The fact that the same periodicity is now evident even those countries Asia and Africa, where it was absent or not prominent earlier, suggests the possibility that the pattern could be an early indicator for significant community transmission. The global coherent periodicity with a time scale that agrees with the time scales of virus incubation and infection may be important in tracking the long term interaction of the virus with the host.

We present a mathematical model of infection dynamics that might explain slower approaching the herd immunity during the covid-19 epidemy in Sweden than it was predicted by a variety of other models; see graphs Fig. 2. The new model takes into account the hierarchic structure of social clusters in the human society. We apply the well developed theory of random walk on the energy landscapes represented mathematically with ultrametric spaces. This theory was created for applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchys levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider linearly increasing (with respect to hierarchys levels) barriers. This structure of barriers matches with a rather soft regulations imposed in Sweden in March 2020. In this model, the infection spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This models feature matches with the real situation during the covid-19 epidemy, with its cluster spreading structure. Clusters need not be determined solely geographically, they are based on a number of hierarchically ordered social coordinates. The model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. In particular, our model describes such a specialty of spread of covid-19 virus as the presence of "super-spreaders" who by performing a kind of random walk on a hierarchic landscape of social clusters spreads infection. In future, this model will be completed by adding the SIR-type counterpart. But, the latter is not a specialty of covid-19 spreading. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=126 SRC="FIGDIR/small/20146209v1_fig2.gif" ALT="Figure 2"> View larger version (8K): org.highwire.dtl.DTLVardef@1b3b3fcorg.highwire.dtl.DTLVardef@ed8c38org.highwire.dtl.DTLVardef@190b208org.highwire.dtl.DTLVardef@9848be_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 2:C_FLOATNO Asymptotic behavior of probability to become immune; increasing of the herd immunity (for fixed social temperature T, the upper graphs correspond to one-step barrier growth 10 and 100 times, respectively. C_FIG

BackgroundThe COVID-19 pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is straining health systems around the world. Although the Chinese government implemented a number of severe restrictions on peoples movement in an attempt to contain its local and international spread, the virus had already reached many areas of the world in part due to its potent transmissibility and the fact that a substantial fraction of infected individuals develop little or no symptoms at all. Following its emergence, the virus started to generate sustained transmission in neighboring countries in Asia, Western Europe, Australia, Canada and the United States, and finally in South America and Africa. As the virus continues its global spread, a clear and evidence-based understanding of properties and dynamics of the global transmission network of SARS-CoV-2 is essential to design and put in place efficient and globally coordinated interventions. MethodsWe employ molecular surveillance data of SARS-CoV-2 epidemics for inference and comprehensive analysis of its global transmission network before the pandemic declaration. Our goal was to characterize the spatial-temporal transmission pathways that led to the establishment of the pandemic. We exploited a network-based approach specifically tailored to emerging outbreak settings. Specifically, it traces the accumulation of mutations in viral genomic variants via mutation trees, which are then used to infer transmission networks, revealing an up-to-date picture of the spread of SARS-CoV-2 between and within countries and geographic regions. Results and ConclusionsThe analysis suggest multiple introductions of SARS-CoV-2 into the majority of world regions by means of heterogeneous transmission pathways. The transmission network is scale-free, with a few genomic variants responsible for the majority of possible transmissions. The network structure is in line with the available temporal information represented by sample collection times and suggest the expected sampling time difference of few days between potential transmission pairs. The inferred network structural properties, transmission clusters and pathways and virus introduction routes emphasize the extent of the global epidemiological linkage and demonstrate the importance of internationally coordinated public health measures.

An impact of viral mutations on the extent of an epidemic is examined. A mechanism of immunization of the population via spread of weakly mutated strain as a natural factor terminating the epidemic is indicated. An epidemic model which details this mechanism is proposed.

The novel coronavirus pandemic generates extensive attention in political and scholarly domains 1-4. Its potentially lasting prospects, economic and social consequences call for a better understanding of its nature. The widespread expectations of large portions of the population to be infected or vaccinated before containing the COVID-19 epidemics rely on assuming a homogeneous population. In reality, people differ in the propensity to catch the infection and spread it further. Here, we incorporate population heterogeneity into the Kermack-McKendrick SIR compartmental model 5 and show the cost of the pandemic may be much lower than usually assumed. We also indicate the crucial role of correctly planning lockdown interventions. We found that an efficient lockdown strategy may reduce the cost of the epidemic to as low as several percents in a heterogeneous population. That level is comparable to prevalences found in serological surveys 6. We expect that our study will be followed by more extensive data-driven research on epidemiological dynamics in heterogeneous populations.

There has recently emerged a striking consistency to the mortality from SARS-CoV-2, [1,2,3] as a fraction of population, across many nations. We have constructed a model for the spread of the virus that reproduces this phenomenon via inclusion of two (or more) categories of susceptibility to the virus. In the simplest case, the population is given a smaller fraction of 10-20% with higher susceptibility and the balance of 80-90% with lower susceptibility. Susceptibility is taken to include the level of immunity to the virus combined with the societal circumstances of certain smaller groups within a population. This is programmed numerically by considering a realistic random rate of contacts, together with an assumed constant viral genome. The remaining major variable is the societal response of nations to the outbreak, with earlier or later application of various degrees of lockdown, tracing and sanitation. China, South Korea and other nations, including Germany, have stopped or greatly slowed the spread of the disease before it could run its course through a whole population. Using this model the extent of progress toward herd immunity is discussed, with an in-principle estimate of the remaining toll to be experienced.

We study a statistical lattice model of a mitigated epidemic. The level of mitigation, defined by measures to slow down the spread of the infection, is characterized by the infection transmissivity. It is determined by peoples mobility, frequency of contacts, and probability to catch the virus from a contact. In the absence of testing the infected people are isolated for a finite period of time during which they are symptomatic. In the presence of testing, people become isolated a soon as they are tested positive. We compute time dependence of daily new infections as function of transmissivity, initial infection, and testing. The duration of the epidemic increases rapidly with the increased level of mitigation while the number of people falling sick daily decreases. Testing, regardless of the level, has little effect on the duration of the epidemic. The total number of people who contract the disease over the lifetime of the epidemic depends weakly on its duration. It does not change significantly for the homogeneous testing of the population at the level below 10% daily.

The effective reproduction ratio r(t) of an epidemic, defined as the average number of secondary infected cases per infectious case in a population in the current state, including both susceptible and non-susceptible hosts, controls the transition between a subcritical threshold regime (r(t) < 1) and a supercritical threshold regime (r(t) > 1). While in subcritical regimes, an index infected case will cause an outbreak that will die out sooner or later, with large fluctuations observed when approaching the epidemic threshold, the supercritical regimes leads to an exponential growths of infection. The super- or subcritical regime of an outbreak is often not distinguished when close to the epidemic threshold, but its behaviour is of major importance to understand the course of an epidemic and public health management of disease control. In a subcritical parameter regime undetected infection, here called "imported case" or import, i.e. a susceptible individual becoming infected from outside the study area e.g., can either spark recurrent isolated outbreaks or keep the ongoing levels of infection, but cannot cause an exponential growths of infection. However, when the community transmission becomes supercritical, any index case or few "imported cases" will lead the epidemic to an exponential growths of infections, hence being distinguished from the subcritical dynamics by a critical epidemic threshold in which large fluctuations occur in stochastic versions of the considered processes. As a continuation of the COVID-19 Basque Modeling Task Force, we now investigate the role of critical fluctuations and import in basic Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) epidemiological models on disease spreading dynamics. Without loss of generality, these simple models can be treated analytically and, when considering the mean field approximation of more complex underlying stochastic and eventually spatially extended or generalized network processes, results can be applied to more complex models used to describe the COVID-19 epidemics. In this paper, we explore possible features of the course of an epidemic, showing that the subcritical regime can explain the dynamic behaviour of COVID-19 spreading in the Basque Country, with this theory supported by empirical data data.

AO_SCPLOWBSTRACTC_SCPLOWIn an earlier paper we proposed a recursive model for epidemics; in the present paper we generalize this model to include the asymptomatic or unrecorded symptomatic people, which we call dark people (dark sector). We call this the SEPARd-model. A delay differential equation version of the model is added; it allows a better comparison to other models. We carry this out by a comparison with the classical SIR model and indicate why we believe that the SEPARd model may work better for Covid-19 than other approaches. In the second part of the paper we explain how to deal with the data provided by the JHU, in particular we explain how to derive central model parameters from the data. Other parameters, like the size of the dark sector, are less accessible and have to be estimated more roughly, at best by results of representative serological studies which are accessible, however, only for a few countries. We start our country studies with Switzerland where such data are available. Then we apply the model to a collection of other countries, three European ones (Germany, France, Sweden), the three most stricken countries from three other continents (USA, Brazil, India). Finally we show that even the aggregated world data can be well represented by our approach. At the end of the paper we discuss the use of the model. Perhaps the most striking application is that it allows a quantitative analysis of the influence of the time until people are sent to quarantine or hospital. This suggests that imposing means to shorten this time is a powerful tool to flatten the curves.

The Covid-19 pandemic impacted the human life all over the globe, starting in the year of its emergence, 2019, and in the following years. A epidemiological key indicator that gained particular recognition in politics and decision making is the time-dependent reproduction number Rt, which is commonly calculated by institutions responsible for disease control following a method presented by Cori et. al. Here, we propose an improved as well as an alternative method, which make the calculation more stable against oscillations arising from daily variations in testing. Both methods can be used without great statistical knowledge or effort. The methods provides a smoother result without increasing the time-lag, and provides an advantage particular in the timeframe of weeks, which might serve as a better ground for forecasts and the raising of alarms.

We consider the transmission dynamics of COVID-19 which is characterized by two distinct features. One is the existence of asymptomatic carriers which is the hidden variable in the problem. The other is the issue of latency which means that among the symptomatic carriers there could be a fraction whose symptoms develop after a couple of days. We write down a Henon-like map to take these effects into account and find that the map has an unusual fixed point which corresponds to a very high ratio of asymptomatic to symptomatic infected persons. This fixed point has its own stability zone and influences the dynamics overall. Although a rather elementary model, we show that it is not totally devoid of reality.

We show that the standard SIR model is not effective to predict the 2019-20 coronavirus pandemic propagation. We propose a new model where the logarithm of the detected population number follows a linear dynamical system. We estimate the parameters of this system and compare models obtained with data observed from different countries. Based on the given estimator and results obtained with the Pr. Raoults treatment, we affirm with a reasonable degree of confidence that his "test-treat-noconfine" policy was less expensive in human lives than the"confine and wait for a proved treatment" policy adopted by the French government.

Timely information acquisition and stay-at-home measures have been considered as two effective steps that every person could take to help contain the coronavirus (COVID-19) pandemic. From the perspectives of information and mobility, this work aims at evaluating to what degree the massive population has responded to the emergencies of the COVID-19 pandemic in China. Using the real-time and historical data collected from the Baidu Maps and Baidu search engines, we confirm the strong correlation between the local pandemic situation in every major Chinese city and the population inflows from Wuhan between 1 January and 23 January 2020. We further evidence that, in cities under more critical situations, people are likely to engage COVID-19-related searches more frequently, while they are not likely to escape from the cities. Finally, the correlation analysis using search and mobility data shows that well-informed individuals are likely to travel less, even while the overall travel demands are low compared to the historical records. Partial correlation analysis has been conducted to test the significance of these observations with respect to other controlling factors.

This article presents a mathematical infection model that is designed to estimate the course of coronavirus infection in Germany for several days in advance: How many people become ill or die, what is the temporal development? If the contact restriction is perfect, then the model predicts the development of the virus infection after the initial subsidence of the infection. However, since this restriction cannot always be strictly adhered to, the model is dynamically adapted to the development. This makes it possible to estimate the number of infected people, the number of new infections and deaths in Germany about a week in advance.