Frontiers in Physics

For Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-COV-2) the investigation of the heterogeneity of individual infectiousness becomes important due to the cross reactive immunity of general population. Using a sample of infected population with SARS-COV-2 in close geographical proximity to the initial Severe Advanced Respiratory Syndrome-1 (SARS-1) outbreak, we explored the association between infectors age and dispersion (or heterogeneity) of individual infectiousness (k) in order to investigate the relatedness with the age of an individuals capability to disperse SARS-COV-2. Interestingly, we find a negative association between k and increase of infectors age. Significantly this becomes more evident for the age group of 20-60 years comparing with the infectors with younger age. This raises important immuno-epidemiology concerns for effectiveness of public health measures to contain the disease. One Sentence SummaryDispersion of Coronavirus Disease-19 in China differed with age.

The simplest approximation for the first stages of the infection spread is considered. The specific feature of the COVID-19 characterized by its long latent period is taken into account. Exponential increase of numbers of infected people is determined by the half period of the maximal latent time for the COVID-19. The averaging over latent period leads to additional increase of the infected numbers. PACS number(s)02.50.-r, 05.60.-k, 82.39.-k, 87.19.Xx

As of 21st May 2020, there have been 4.89M confirmed cases worldwide and over 323,000 deaths of people who have tested positive for SARS-CoV-2. The outbreak of COVID-19, has not only caused widespread morbidity and mortality, but has also led to a catastrophic breakdown in the global economy and unprecedented social disruption. To lessen the global health consequences of COVID-19, sweeping COVID-19 lockdown and quarantine measures have been imposed within many nations. These measures have significantly impacted the worlds economy and in many cases has led to the loss of livelihood. Mathematical modeling of pandemics is of critical importance to understand the unfolding of transmission events and to formulate control measures. In this research letter, we have introduced a novel approach to forecasting epidemics like COVID-19. The proposed mathematical model stems from the fundamental principles of fluid dynamics, and can be utilized to make projections of the number of infected people. This unique mathematical model can be beneficial for predicting and designing potential strategies to mitigate the spread and impact of pandemics.

The birth and death of a pandemic can be region specific. Pandemic seems to make repeated appearance in some places which is often attributed to human neglect and seasonal change. However, difference could arise from different distributions of inherent susceptibility ({sigma}inh) and external infectivity ({iota}ext) from one population to another. These are often ignored in the theoretical treatments of an infectious disease progression. While the former is determined by the immunity of an individual towards a disease, the latter depends on the duration of exposure to the infection. Here we model the spatio-temporal propagation of a pandemic using a generalized SIR (Susceptible-Infected-Removed) model by introducing the susceptibility and infectivity distributions to comprehend their combined effects. These aspects have remained inadequately addressed till date. We consider the coupling between{sigma} inh and{iota} ext through a new critical infection parameter ({gamma}c). We find that the neglect of these distributions, as in the naive SIR model, results in an overestimation in the estimate of the herd immunity threshold. That is, the presence of the distributions could dramatically reduce the rate of spread. Additionally, we include the effects of long-range migration by seeding new infections in a region. We solve the resulting master equations by performing Kinetic Monte Carlo Cellular Automata (KMC-CA) simulations. Importantly, our simulations can reproduce the multiple infection peak scenario of a pandemic. The latent interactions between disease migration and the distributions of susceptibility and infectivity can render the progression a character vastly different from the naive SIR model. In particular, inclusion of these additional features renders the problem a character of a living percolating system where the disease cluster can survive by spatial migration.

In the last two decades, the impact of human health-related behavior on the spread of the disease has increased in prominence due to the proliferation of sentiment against public health-promoting behaviors such as vaccination and mask-wearing. The recent SARS-COV-2 pandemic brought these effects into sharp focus. Recently, coupled-contagion epidemiological models have been used to study the joint impact of human behavior and disease. These models treat sentiment towards a particular public health intervention as a contagion spreading in parallel to the disease itself. In this paper, we use a coupled-contagion model to study the interaction of two different health behaviors--vaccination and mask-wearing. In particular, we study how a positive or negative association between these behaviors--e.g. a pro-vaccine person may be more likely to be pro-mask-wearing--affects disease dynamics. We find that the strength of such an association alone can determine the outcome of disease spread in the short term and the long term. In addition to studying human health-related behaviors separately, it is vitally important to understand how these behaviors are associated with each other and how these associations affect the outcomes of epidemics.

Identifying the drivers underlying the spatial occurrence and spreading rate of COVID-19 can provide valuable information for their preventions and controls. Here, we examine how socio-economic and climate drivers affect the early growth rates of COVID-19 in China and the other countries, the former of which have consistently stricter quarantine during early epidemic and thus are used to enquire the influences of human interventions on trainsimissions. We find that the early growth rates of COVID-19 are higher in China than the other countries, which is consistent with previous reports. The global spread is mainly driven by the socio-economic factors such as GDP per capita, human movement and population density rather than climate. Among socio-economic factors, GDP per capita is most important showing negative relationships in China, while positive in the other countries. However, the predicability of early growth rates by socio-economic and climate variables is at least 1.6 times higher in Chinas provinces than the other countries, which is further supported by metapopulation network model. These findings collectively indicate that the stochasticity of transimission processes decrease upon strict quarantine measures such as travel restrictions. Key findingsO_LIGDP per capita is most important in driving the spread of COVID-19, which shows negative relationships within China, while positive in the other countries. C_LIO_LISocio-economic and climate factors are key in driving the early growth rate of COVID-19, while the former is more important. C_LIO_LISocio-economic and climate features explain more variations of early growth rates in China due to the decreased stochasticity of transimission processes upon strict quarantine measures. C_LI

Herd immunity refers to the collective resistance of a population against the spreading of an infection as an epidemic. Understanding the dependencies of herd immunity on various epidemiological parameters is of immense importance for strategizing control measures against an infection in a population. Using an age-dependent branching process model of infection propagation, we obtain interesting functional dependencies of herd immunity on the incubation period of the contagion, contact rate, and the probability of disease transmission from an infected to a susceptible individual. We show that herd immunity is difficult to achieve in case of a high incubation period of the contagion. We derive a method to quantify the success probabilities of quarantine measures to mitigate infection from a population, before achieving herd immunity. We provide a mechanistic derivation of the distribution of generation time from basic principles, which is of central importance to estimate the reproduction number R0, but has been assumed in an ad hoc manner in epidemiological studies, by far. This derivation of the generation time distribution has the generality to be applied in the study of many other age-dependent branching processes, such as the growth of bacterial colonies, various problems in evolutionary and population biology etc.

One of the central tools to control the COVID-19 pandemics is the knowledge of its spreading dynamics. Here we develop a fractal model capable of describe this dynamics, in term of daily new cases, and provide quantitative criteria for some predictions. We propose a fractal dynamical model using conformed derivative and fractal time scale. A Burr-XII shaped solution of the fractal-like equation is obtained. The model is tested using data from several countries, showing that a single function is able to describe very different shapes of the outbreak. The diverse behavior of the outbreak on those countries is presented and discussed. Moreover, a criterion to determine the existence of the pandemic peak and a expression to find the time to reach herd immunity are also obtained.

The coronavirus disease 2019 (COVID-19) pandemic is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which can be transmitted via respiratory secretions. Since there are currently no specific therapeutics or vaccines available against the SARS-CoV-2, the commen non-pharmaceutical interventions (NPIs) are still the main measures to curb the COVID-19 epidemic. Face mask wearing is one important measure to suppress the pandemic. In order to know how efficient is face mask wearing in reducing the pandemic even with low efficiency non-professional face masks, we exploit physical abstraction to model the non-professional face masks made from cotton woven fabrics and characterize them by a parameter virus penetration rate (VPR){gamma} . Monte Carlo simulations exhibit that the effective reproduction number R of COVID-19 or similar pandemics can be approximately reduced by factor{gamma} 4 with respect to the basic reproduction number R0, if the face masks with 70% < {gamma} < 90% are universally applied for the entire network. Furthermore, thought experiments and practical exploitation examples in country-level and city-level are enumerated and discussed to support our discovery in this study and indicate that the outbreak of a COVID-19 like pandemic can be even suppressed by the low efficiency non-professional face masks.

An ordinary differential dynamical model is developed to describe the transmission of infectious diseases, considering heterogeneities of region, age, vaccination, and immigration and real-time vaccination simultaneously using a tenderized formulation. Numerical experiments are performed in Xiamen city, China, with the whole population partitioned into 6 regions x 4 age groups x 4 vaccination status groups, showing the numerical stability of the developed model. The heterogeneity consideration makes our model adequate to evaluate specific interventions accurately within specific sub-populations and carry them out. Author summaryNot applicable.

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.

A recently proposed temporal correlation-based- network framework applied on financial markets called Struc- tural Entropy has prompted us to utilize it as a means of analysis for COVID-19 fatalities across countries. Our observation on the resemblance of volatility of fluctuations of daily novel coronavirus related number of deaths to the daily stock exchange returns suggests the applicability of this approach.

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.

Most countries are suffering severely from the ongoing covid-19 pandemic despite various levels of preventive measures. A common question is if and when a country or region will reach herd immunity h. The classical herd immunity level hC is defined as hC =1-1/R0, where R0 is the basic reproduction number, for covid-19 estimated to lie somewhere in the range 2.2-3.5 depending on country and region. It is shown here that the disease-induced herd immunity level hD, after an outbreak has taken place in a country/region with a set of preventive measures put in place, is actually substantially smaller than hC. As an illustration we show that if R0 =2.5 in an age-structured community with mixing rates fitted to social activity studies, and also categorizing individuals into three categories: low active, average active and high active, and where preventive measures affect all mixing rates proportionally, then the disease-induced herd immunity level is hD = 43% rather than hC =1-1/2.5 = 60%. Consequently, a lower fraction infected is required for herd immunity to appear. The underlying reason is that when immunity is induced by disease spreading, the proportion infected in groups with high contact rates is greater than that in groups with low contact rates. Consequently, disease-induced immunity is stronger than when immunity is uniformly distributed in the community as in the classical herd immunity level.

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.

In natural biological systems, cells organize into tissues through interactions of several processes, including cellular signaling, collective migration, contractile activity of cytoskeletal elements and interactions with their surroundings. In recent decades, advancements in microscopy, genetic engineering, biochemistry, and computational modeling have enabled a more quantitative understanding of these processes. In this article, we present an integrated computational framework that couples various physical mechanisms such as: cell-cell adhesion, strength and persistence of cellular motility, and the background stiffness, to study how they collectively interact to determine the selforganization starting from a pseudo-random structure as well as the migration behavior. Notably, our simulations predict that motility has a two-way effect on cellular self-assembly: it promotes aggregation at moderate levels but disrupts clusters when excessively strong, yielding an optimal motility for formation of multicellular clusters. On the other hand, adhesion shows a two-stage effect: At lower value it self-assembles the structure, at higher value it compacts it. Furthermore, We experimentally demonstrate the motility-assisted self-aggregation of cells using cancer cells in a granular mechanical milieu. Finally we show that cell-cell adhesion and background medium tune the strength and persistence of cellular migration. Altogether, this work presents a computational framework that allows us to design phase behavior of collective of cells tuning their interaction, motility, and the background mechanics.

We analyze the temporal evolution of accumulated hospitalization cases due to COVID-19 in Belgium. The increase of hospitalization cases is consistent with an initial exponential phase, and a subsequent power law growth. For the latter, we estimate a power law exponent of {approx} 2.2, which is consistent with growth kinetics of COVID-19 in China and indicative of the underlying small world network structure of the epidemic. Finally, we fit an SIR-X model to the experimental data and estimate the effect of containment policies in comparison to their effect in China. This model suggests that the base reproduction rate has been significantly reduced, but that the number of susceptible individuals that is isolated from infection is very small. Based on the SIR-X model fit, we analyze the COVID-19 mortality and the number of patients requiring ICU treatment over time.

The growth rates of COVID-19 across different geographical regions (e.g., states in a nation, countries in a continent) follow different shapes and patterns. The overall summaries at coarser spatial scales that are obtained by simply averaging individual curves (across regions) obscure nuanced variability and blurs the spatial heterogeneity at finer spatial scales. We employ statistical methods to analyze shapes of local COVID-19 growth rate curves and statistically group them into distinct clusters, according to their shapes. Using this information, we derive the so-called elastic averages of curves within these clusters, which correspond to the dominant incidence patterns. We apply this methodology to the analysis of the daily incidence trajectory of the COVID-pandemic at two spatial scales: A state-level analysis within the USA and a country-level analysis within Europe during mid-February to mid-May, 2020. Our analyses reveal a few dominant incidence trajectories that characterize transmission dynamics across states in the USA and across countries in Europe. This approach results in broad classifications of spatial areas into different trajectories and adds to the methodological toolkit for guiding public health decision making at different spatial scales. HighlightsO_LICoarsely summarizing epidemic data collected at finer spatial scales can result in a loss of heterogenous spatial patterns that exist at finer scales. For instance, the average curves may give the impression that the epidemics trajectory is declining when, in fact, the trajectory of the epidemic is increasing in certain areas. C_LIO_LIShape analysis of COVID-19 growth rate curves discovers significant heterogeneity in epidemic spread patterns across spatial areas which can be statistically clustered into distinct groups. C_LIO_LIAt a higher level, clustering spatial patterns into distinct groups helps discern broad trends, such as rapid growth, leveling off, and slow decline in epidemic growth curves resulting from local transmission dynamics. At a finer level, it helps identify temporal patterns of multiple waves that characterize rate curves for different clusters. C_LIO_LIQuantitative methods for characterizing the spatial-temporal dynamics of evolving epidemic emergencies provide an objective framework to understand transmission dynamics for public health decision making. C_LI

Four months into the ongoing novel coronavirus disease 2019 (COVID-19) pandemic, this work provides a simple and direct projection of the outbreak spreading potential and the pandemic cessation dates in China, Iran, the Philippines and Taiwan, using the generalized logistic model (GLM). The short-term predicted number of cumulative COVID-19 cases matched the confirmed reports of those who were infected across the four countries, suggesting GLM as a valuable tool for characterizing the transmission dynamics process and the trajectory of COVID-19 pandemic along with the impact of interventions.

Although COVID-19 has spread almost all over the world, social isolation is still a controversial public health policy and governments of many countries still doubt its level of effectiveness. This situation can create deadlocks in places where there is a discrepancy among municipal, state and federal policies. The exponential increase of the number of infectious people and deaths in the last days shows that the COVID-19 epidemics is still at its early stage in Brazil and such political disarray can lead to very serious results. In this work, we study the COVID-19 epidemics in Brazilian cities using early-time approximations of the SIR model in networks. Different from other works, the underlying network is constructed by feeding real-world data on local COVID-19 cases reported by Brazilian cities to a regularized vector autoregressive model, which estimates directional COVID-19 transmission channels (links) of every pair of cities (vertices) using spectral network analysis. Our results reveal that social isolation and, especially, the use of masks can effectively reduce the transmission rate of COVID-19 in Brazil. We also build counterfactual scenarios to measure the human impact of these public health measures in terms of reducing the number of COVID-19 cases at the epidemics peak. We find that the efficiency of social isolation and of using of masks differs significantly across cities. For instance, we find that they would potentially decrease the COVID-19 epidemics peak in Sao Paulo (SP) and Brasilia (DF) by 15% and 25%, respectively. We hope our study can support the design of further public health measures.