I employ a simple mathematical model of an epidemic process to evaluate how four basic quantities: the reproduction number (R), the numbers of sensitive (S) and infectious individuals(I), and total community size (N) affect strategies to control COVID-19. Numerical simulations show that strict suppression measures at the beginning of an epidemic can create low infectious numbers, which thereafter can be managed by mitigation measures over longer periods to flatten the epidemic curve. The stronger the suppression measure, the faster it achieves the low numbers of infections that are conducive to subsequent management. We discuss the predictions of this analysis and how it fits into longer-term sequences of measures, including using the herd immunity concept to leverage acquired immunity.
We are currently facing a highly critical case of a world-wide pandemic. The novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely contagious and the original outbreak from Asia has now spread to all continents. This situation will fruitfully profit from the study in regards of the spread of the virus, assessing effective countermeasures to weight the impact of the adopted strategies. The standard Susceptible-Infectious-Recovered (SIR) model is a very successful and widely used mathematical model for predicting the spread of an epidemic. We adopt the SIR model on a random …
Though pandemic preparedness has been a focus of public health planning for centuries, during which our understanding of infectious disease dynamics has grown, our methodologies for managing outbreaks have remained relatively unchanged. We propose leveraging this history to identify opportunities for actual progress. We contrast current plans with historical outbreak control measures and isolate how the complexities of a modern era yield additional challenges in how best to anticipate and mitigate outbreaks. We analyze a diversity of publicly available modern preparedness plans against the con…
The COVID-19 pandemic poses challenges for continuing economic activity while reducing health risks. While these challenges can be mitigated through testing, testing budget is often limited. Here we study how institutions, such as nursing homes, should utilize a fixed test budget for early detection of an outbreak. Using an extended network-SEIR model, we show that given a certain budget of tests, it is generally better to test smaller subgroups of the population frequently than to test larger groups but less frequently. The numerical results are consistent with an analytical expression we der…
A central feature of an emerging infectious disease in a pandemic scenario is the spread through geographical scales and the impacts on different locations according to the adopted mitigation protocols. We investigated a stochastic epidemic model with the metapopulation approach in which patches represent municipalities. Contagion follows a stochastic compartmental model for municipalities; the latter, in turn, interact with each other through recurrent mobility. As a case of study, we consider the epidemic of COVID-19 in Brazil performing data-driven simulations. Properties of the simulated e…
Background: Early detection and isolation of COVID-19 patients are essential for successful implementation of mitigation strategies and eventually curbing the disease spread. With a limited number of daily COVID-19 tests performed in every country, simulating the COVID-19 spread along with the potential effect of each mitigation strategy currently remains one of the most effective ways in managing the healthcare system and guiding policy-makers. Methods: We introduce COVIDHunter, a flexible and accurate COVID-19 outbreak simulation model that evaluates the current mitigation measures that are …
Returning universities to full on-campus operations while the COVID-19 pandemic is ongoing has been a controversial discussion in many countries. The risk of large outbreaks in dense course settings is contrasted by the benefits of in-person teaching. Transmission risk depends on a range of parameters, such as vaccination coverage and efficacy, number of contacts and adoption of non-pharmaceutical intervention measures (NPIs). Due to the generalised academic freedom in Europe, many universities are asked to autonomously decide on and implement intervention measures and regulate on-campus opera…
Assessing and managing the impact of large-scale epidemics considering only the individual risk and severity of the disease is exceedingly difficult and could be extremely expensive. Economic consequences, infrastructure and service disruption, as well as the recovery speed, are just a few of the many dimensions along which to quantify the effect of an epidemic on society's fabric. Here, we extend the concept of resilience to characterize epidemics in structured populations, by defining the system-wide critical functionality that combines an individual's risk of getting the disease (disease at…
School environments are thought to play an important role in the community spread of airborne infections (e.g., influenza) because of the high mixing rates of school children. The closure of schools has therefore been proposed as efficient mitigation strategy, with however high social and economic costs: alternative, less disruptive interventions are highly desirable. The recent availability of high-resolution contact networks in school environments provides an opportunity to design micro-interventions and compare the outcomes of alternative mitigation measures. We consider mitigation measures…
The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, sub-exponential increase of confirmed cases during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak with sufficiently large reproduction rate. Although case counts vary significantly between affected provinces in Mainland China, the scaling law $t^μ$ is surprisingly universal, with a range of exponents $μ=2.1\pm0.3$. The universality of this behavior indicates that despite social, regional, demographical, geographical, and socio-economi…
We present Coronavirus disease 2019 (COVID-19) statistics in China dataset: daily statistics of the COVID-19 outbreak in China at the city/county level. For each city/country, we include the six most important numbers for epidemic research: daily new infections, accumulated infections, daily new recoveries, accumulated recoveries, daily new deaths, and accumulated deaths. We cross validate the dataset and the estimate error rate is about 0.04%. We then give several examples to show how to trace the spreading in particular cities or provinces, and also contrast the development of COVID-19 in al…
A method for detecting a trend change in cross-border epidemic transmission is developed for a standard epidemiological SIR compartment model and a meta-population network model. The method is applicable to investigating the efficacy of the implemented public health intervention in managing infectious travelers across borders from a time series of the number of new cases reported in multiple geographical regions. It is found that the change point of the probability of travel movements was one week after the WHO worldwide alert on the SARS outbreak in 2003. The alert was effective in managing i…
In May 2022, a cluster of mpox cases were detected in the UK that could not be traced to recent travel history from an endemic region. Over the coming months, the outbreak grew, with over 3000 total cases reported in the UK, and similar outbreaks occurring worldwide. These outbreaks appeared linked to sexual contact networks between gay, bisexual and other men who have sex with men. Following the COVID-19 pandemic, local health systems were strained, and therefore effective surveillance for mpox was essential for managing public health policy. However, the mpox outbreak in the UK was character…
A significant proportion of the infections driving the current {SARS-CoV-2} pandemic are transmitted asymptomatically. Here we introduce and study a simple epidemic model with separate compartments comprising asymptomatic and symptomatic infected individuals. The linear dynamics determining the outbreak condition of the model is equivalent to a renewal theory approach with exponential waiting time distributions. Exploiting a nontrivial conservation law of the full nonlinear dynamics, we derive analytic bounds on the peak number of infections in the absence and presence of mitigation through is…
The novel coronavirus SARS-CoV-2 and resulting COVID-19 disease have had an unprecedented spread and continue to cause an increasing number of fatalities worldwide. While vaccines are still under development, social distancing, extensive testing, and quarantining of confirmed infected subjects remain the most effective measures to contain the pandemic. These measures carry a significant socioeconomic cost. In this work, we introduce a novel optimization-based decision-making framework for managing the COVID-19 outbreak in the US. This includes modeling the dynamics of affected populations, est…
Novel coronavirus-19 (2019-nCoV or COVID-19) is by far the most dangerous coronavirus ever identified for the third time in the three decades capable of infecting not only the animals but also the humans across the globe. Nearly 6000 deaths have been recorded due mainly to COVID-19 outbreak worldwide and more than 50% of these deaths appeared to have evolved from China where the virus was thought to originate. The endemicity of COVID-19 dramatically surpassed severe acute respiratory syndrome coronavirus (SARS-CoV) and Middle East respiratory syndrome coronavirus (MERS-CoV) that were so far di…
The use of model experimental systems and mathematical models is important to further understanding of infectious disease dynamics and strategize disease mitigation. Gyrodactylids are helminth ectoparasites of teleost fish which have many dynamical characteristics of microparasites but offer the advantage that they can be quantified and tracked over time, allowing further insight into within-host and epidemic dynamics. In this paper, we design a model to describe host-parasite dynamics of the well-studied guppy-Gyrodactylus turnbulli system, using experimental data to estimate parameters and v…
Various non pharmaceutical interventions have been settled to minimise the burden of the COVID-19 outbreak. We build a framework to analyse the dynamics of non pharmaceutical interventions, to distinguish between mitigations measures leading to objective scientific improvements and mitigations based on both political and scientific considerations. We analyse two possible strategies within this framework. Namely, we consider mitigations driven by the limited resources of the health system and mitigations where a constant set of measures is applied at different moments. We describe the optimal i…
Background: The analysis of the Sars-CoV-2 epidemic is of paramount importance to understand the dynamics of the coronavirus spread. This can help health and government authorities take the appropriate measures and implement suitable politics aimed at fighting and preventing it. Methods: A time-dependent dynamic SEIR model inspired in a model previously used during the MERS outbreak in South Korea was used to analyse the time trajectories of active and hospitalized cases in Portugal. Results: The time evolution of the virus spread in the country was adequately modelled. The model has changeabl…
Transmission rates in epidemic outbreaks may vary over time depending on the societal response. Non-pharmacological mitigation strategies such as social distancing and the adoption of protective equipment aim precisely at reducing transmission rates by reducing infectious contacts. To investigate the effects of mitigation strategies on the evolution of epidemics, nonlinear transmission rates that are influenced by the levels of infections, deaths or recoveries have been included in many variants of the classical SIR model. This class of models is particularly relevant to the COVID-19 epidemic,…
Absent a drug or vaccine, containing epidemic outbreaks is achieved by means of social distancing, specifically mobility restrictions and lock-downs. Such measures impose a hurtful toll on the economy, and are difficult to sustain for extended periods. As an alternative, we propose here an alternating quarantine strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and quarantine. This regime affords a dual partition:\ half of the population interacts for only…
As South and Central American countries prepare for increased birth defects from Zika virus outbreaks and plan for mitigation strategies to minimize ongoing and future outbreaks, understanding important characteristics of Zika outbreaks and how they vary across regions is a challenging and important problem. We developed a mathematical model for the 2015 Zika virus outbreak dynamics in Colombia, El Salvador, and Suriname. We fit the model to publicly available data provided by the Pan American Health Organization, using Approximate Bayesian Computation to estimate parameter distributions and p…
With the unfolding of the COVID-19 pandemic, mathematical modeling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long term predictions were extremely challenging to address. Moreover, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modeling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitiga…
The sudden outbreak of the Coronavirus disease (COVID-19) swept across the world in early 2020, triggering the lockdowns of several billion people across many countries, including China, Spain, India, the U.K., Italy, France, Germany, and most states of the U.S. The transmission of the virus accelerated rapidly with the most confirmed cases in the U.S., and New York City became an epicenter of the pandemic by the end of March. In response to this national and global emergency, the NSF Spatiotemporal Innovation Center brought together a taskforce of international researchers and assembled imple…
We develop a minimalist compartmental model to study the impact of mobility restrictions in Italy during the Covid-19 outbreak. We show that an early lockdown shifts the epidemic in time, while that beyond a critical value of the lockdown strength, the epidemic tend to restart after lifting the restrictions. As a consequence, specific mitigation strategies must be introduced. We characterize the relative importance of different broad strategies by accounting for two fundamental sources of heterogeneity, i.e. geography and demography. First, we consider Italian regions as separate administrativ…
The COVID-19 pandemic began over two years ago, yet schools, businesses, and other organizations are still struggling to keep the risk of disease outbreak low while returning to (near) normal functionality. Observations from these past years suggest that this goal can be achieved through the right balance of mitigation strategies, which may include some combination of mask use, vaccinations, viral testing, and contact tracing. The choice of mitigation measures will be uniquely based on the needs and available resources of each organization. This article presents practical guidance for creating…
Mathematical models of SARS-CoV-2 spread are used for guiding the design of mitigation steps aimed at containing and decelerating the contagion, and at identifying impending breaches of health care system surge capacity. The challenges of having only lacunary information about daily new infections are compounded by the geographic heterogeneity of the population. To address this problem, we propose to account for the differences between rural and urban settings using network-based, distributed models where the spread of the pandemic is described in distinct local cohorts with nested SEIR models…
Vrije Universiteit Brussel（布鲁塞尔自由大学）；National University of Ireland Galway（爱尔兰国立大学戈尔韦分校）；University of Antwerp（安特卫普大学）；Hasselt University（哈瑟尔特大学）；HU University of Applied Sciences Utrecht（乌得勒支应用科学大学）
Infectious disease outbreaks can have a disruptive impact on public health and societal processes. As decision making in the context of epidemic mitigation is hard, reinforcement learning provides a methodology to automatically learn prevention strategies in combination with complex epidemic models. Current research focuses on optimizing policies w.r.t. a single objective, such as the pathogen's attack rate. However, as the mitigation of epidemics involves distinct, and possibly conflicting criteria (i.a., prevalence, mortality, morbidity, cost), a multi-objective approach is warranted to lear…
The COVID-19 pandemic is the most significant global crisis since World War II that affected almost all the countries of our planet. To control the COVID-19 pandemic outbreak, it is necessary to understand how the virus is transmitted to a susceptible individual and eventually spread in the community. The primary transmission pathway of COVID-19 is human-to-human transmission through infectious droplets. However, a recent study by Greenhalgh et al. (Lancet: 397:1603-1605, 2021) demonstrates 10 scientific reasons behind the airborne transmission of SARS-COV-2. In the present study, we introduce…
Background: While many infectious disease epidemics are initially characterized by an exponential growth in time, we show that district-level Ebola virus disease (EVD) outbreaks in West Africa follow slower polynomial-based growth kinetics over several generations of the disease. Methods: We analyzed epidemic growth patterns at three different spatial scales (regional, national, and subnational) of the Ebola virus disease epidemic in Guinea, Sierra Leone and Liberia by compiling publicly available weekly time series of reported EVD case numbers from the patient database available from the Worl…
Strong social distancing restrictions have been crucial to controlling the COVID-19 outbreak thus far, and the next question is when and how to relax these restrictions. A sequential timing of relaxing restrictions across groups is explored in order to identify policies that simultaneously reduce health risks and economic stagnation relative to current policies. The goal will be to mitigate health risks, particularly among the most fragile sub-populations, while also managing the deleterious effect of restrictions on economic activity. The results of this paper show that a properly constructed…
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 (ODEs) to introduce several novel models based upon susceptible-infected-recovered (SIR) dynamics. First, we compare computationally expensive, adaptive network simulations with their corresponding computationally highly efficient ODE equivalents and find excellent agreement. Second, we discover that there exists a relatively simple critical curve in…
In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like COVID-19 and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number $R_{0}$ is derived. When $R_{0}<1$, the disease-free equilibrium point is unique and locally asymptotically stable. When $R_{0}>1$, the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asympto…
While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enfor…
The impact of mitigation or control measures on an epidemics can be estimated by fitting the parameters of a compartmental model to empirical data, and running the model forward with modified parameters that account for a specific measure. This approach has several drawbacks, stemming from biases or lack of availability of data and instability of parameter estimates. Here we take the opposite approach -- that we call reverse epidemiology. Given the data, we reconstruct backward in time an ensemble of networks of contacts, and we assess the impact of measures on that specific realization of the…
This paper studies if and to which extent COVID-19 epidemics can be controlled by authorities taking decisions on public health measures on the basis of daily reports of swab test results, active cases and total cases. A suitably simplified process model is derived to support the controllability analysis, highlighting the presence of very significant time delay; the model is validated with data from several outbreaks. The analysis shows that suppression strategies can be effective if strong enough and enacted early on. It also shows how mitigation strategies can fail because of the combination…
The rapid spread of the Coronavirus SARS-2 is a major challenge that led almost all governments worldwide to take drastic measures to respond to the tragedy. Chief among those measures is the massive lockdown of entire countries and cities, which beyond its global economic impact has created some deep social and psychological tensions within populations. While the adopted mitigation measures (including the lockdown) have generally proven useful, policymakers are now facing a critical question: how and when to lift the mitigation measures? A carefully-planned exit strategy is indeed necessary t…
It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian Process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea, and Brazil. We assume that the second wave was more accurately monitored and hence that it can be trusted. We then construct a manifold diffeomorphic to that of the implied original dynamical system, usin…
Motivated by the recent outbreak of coronavirus (COVID-19), we propose a stochastic model of epidemic temporal growth and mitigation based on a time-modulated Hawkes process. The model is sufficiently rich to incorporate specific characteristics of the novel coronavirus, to capture the impact of undetected, asymptomatic and super-diffusive individuals, and especially to take into account time-varying counter-measures and detection efforts. Yet, it is simple enough to allow scalable and efficient computation of the temporal evolution of the epidemic, and exploration of what-if scenarios. Compar…
University of Southampton（南安普顿大学）；Number Theory Software Pvt Ltd（数论软件私人有限公司）；Federal University of Rio de Janeiro（里约热内卢联邦大学）；Digital University Kerala（喀拉拉数字大学）
Many countries have experienced at least two waves of the COVID-19 pandemic. The second wave is far more dangerous as distinct strains appear more harmful to human health, but it stems from the complacency about the first wave. This paper introduces a parsimonious yet representative stochastic epidemic model that simulates the uncertain spread of the disease regardless of the latency and recovery time distributions. We also propose a Markov decision process to seek an optimal trade-off between the usage of the healthcare system and the economic costs of an epidemic. We apply the model to COVID…
The outbreak of the novel coronavirus, COVID-19, has been declared a pandemic by the WHO. The structures of social contact critically determine the spread of the infection and, in the absence of vaccines, the control of these structures through large-scale social distancing measures appears to be the most effective means of mitigation. Here we use an age-structured SIR model with social contact matrices obtained from surveys and Bayesian imputation to study the progress of the COVID-19 epidemic in India. The basic reproductive ratio R0 and its time-dependent generalization are computed based o…
Phenomenological and deterministic models are often used for the estimation of transmission parameters in an epidemic and for the prediction of its growth trajectory. Such analyses are usually based on single peak outbreak dynamics. In light of the present COVID-19 pandemic, there is a pressing need to better understand observed epidemic growth with multiple peak structures, preferably using first-principles methods. Along the lines of our previous work [Physica A 574, 126014 (2021)], here we apply 2D random-walk Monte Carlo calculations to better understand COVID-19 spread through contact int…
