Objectives. Public health officials need tools to assist with anticipating the healthcare resources required to confront the SARS-COV-2 pandemic. We built a modeling tool to aid practicing public health officials with estimating healthcare demand from the pandemic in their jurisdictions and to evaluate the potential impacts of population-wide social-distancing interventions. Methods. The tool uses a SEIR compartmental model to project the local spread of the pandemic. Users input case counts, healthcare resources, and select intervention strategies to evaluate. Outputs include the number of infections and deaths with and without intervention, and the demand for hospital and critical care beds and ventilators relative to existing capacity. We illustrate the tool using data from three regions of Chile. Results. Our scenarios indicate a surge in COVID-19 patients could overwhelm Chilean hospitals by June, peaking in July or August at 6 to 50 times the current supply of beds and ventilators. A lockdown strategy or combination of case isolation, home quarantine, social distancing of individuals greater than 70 years, and telework interventions may keep treatment demand below capacity. Conclusions. Aggressive interventions can avert substantial morbidity and mortality from COVID-19. Our tool permits rapid evaluation of locally-applicable policy scenarios and updating of results as new data become available.
An Ebola outbreak of unparalleled size is currently affecting several countries in West Africa, and international efforts to control the outbreak are underway. However, the efficacy of these interventions, and their likely impact on an Ebola epidemic of this size, is unknown. Forecasting and simulation of these interventions may inform public health efforts. We use existing data from Liberia and Sierra Leone to parameterize a mathematical model of Ebola and use this model to forecast the progression of the epidemic, as well as the efficacy of several interventions, including increased contact …
In the absence of drugs and vaccines, policymakers use non-pharmaceutical interventions such as social distancing to decrease rates of disease-causing contact, with the aim of reducing or delaying the epidemic peak. These measures carry social and economic costs, so societies may be unable to maintain them for more than a short period of time. Intervention policy design often relies on numerical simulations of epidemic models, but comparing policies and assessing their robustness demands clear principles that apply across strategies. Here we derive the theoretically optimal strategy for using …
I discuss the so-called SuperSpreader epidemic, for which SARS is the canonical examples (and, perhaps, MERS will be another). I use simulation by an agent-based model as well as the mathematics of multi-type branching-processes to illustrate how the SS epidemic differs from the more familiar uniform epidemic (e.g., caused by influenza). The conclusions may surprise the reader: (a) The SS epidemic must be described by at least two numbers, such as the mean reproductive number (of "secondary" cases caused by a "primary case"), R0, and the variance of same, call it V0; (b) Even if R0 > 1, if V0 …
Our paper investigates distributions of exposed and infectious time periods in an epidemic model and how applying a disease control strategy affects the model's accuracy. While ordinary differential equations are widely used for their simplicity, they incorporate an exponential distribution for time spent exposed or infectious. This allows for a high probability of unrealistically short exposed and infectious time periods. We propose that caution must be taken when applying intervention methods to basic models in order to avoid inaccurate predictions. Delay differential equations, which use a …
Many countries are managing COVID-19 epidemic by switching between lighter and heavier restrictions. While an open-close and a close-open cycle have comparable socio-economic costs, the former leads to a much heavier burden in terms of deaths and pressure on the healthcare system. An empirical demonstration of the toll ensuing from procrastination was recently observed in Israel, where both cycles were enforced from late August to mid-December 2020, yielding some 1,600 deaths with open-close compared to 440 with close-open.
Frequent emergence of communicable diseases has been a major concern worldwide. Lack of sufficient resources to mitigate the disease-burden makes the situation even more challenging for lower-income countries. Hence, strategy development towards disease eradication and optimal management of the social and economic burden has garnered a lot of attention in recent years. In this context, we quantify the optimal fraction of resources that can be allocated to two major intervention measures, namely reduction of disease transmission and improvement of healthcare infrastructure. Our results demonstr…
Protecting interventions of many types (both pharmaceutical and non-pharmaceutical) can be deployed against the spreading of a communicable disease, as the worldwide COVID-19 pandemic has dramatically shown. Here we investigate in detail the effects at the population level of interventions that provide an asymmetric protection between the people involved in a single interaction. Masks of different filtration types, either protecting mainly the wearer or the contacts of the wearer, are a prominent example of these interventions. By means of analytical calculations and extensive simulations of s…
National responses to the Covid-19 pandemic varied markedly across countries, from business-as-usual to complete shutdowns. Policies aimed at disrupting the viral transmission cycle and preventing the healthcare system from being overwhelmed, simultaneously exact an economic toll. We developed a intervention policy model that comprised the relative human, economic and healthcare costs of non-pharmaceutical epidemic intervention and arrived at the optimal strategy using the neuroevolution algorithm. The proposed model finds the minimum required reduction in contact rates to maintain the burden …
Epidemic spread in a population is traditionally modeled via compartmentalized models which represent the free evolution of disease in absence of any intervention policies. In addition, these models assume full observability of disease cases and do not account for under-reporting. We present a mathematical model, namely PolSIRD, which accounts for the under-reporting by introducing an observation mechanism. It also captures the effects of intervention policies on the disease spread parameters by leveraging intervention policy data along with the reported disease cases. Furthermore, we allow ou…
Epidemic spreading of infectious diseases is ubiquitous and has often considerable impact on public health and economic wealth. The large variability in spatio-temporal patterns of epidemics prohibits simple interventions and demands for a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, a mathematical framework is introduced which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution both in disease prevalence and transmission network topology …
Non-pharmaceutical interventions have been critical in the fight against the COVID-19 pandemic. However, these sanitary measures have been partially lifted due to socioeconomic factors causing a worrisome rebound of the epidemic in several countries. In this work, we assess the effectiveness of the mitigation implemented to constrain the spread of SARS-CoV-2 in the Mexican territory during 2020. We also investigate to what extent the initial deployment of the vaccine will help to mitigate the pandemic and reduce the need for social distancing and other mobility restrictions. Our modeling appro…
The 2014-2015 Ebola Virus Disease (EVD) epidemic in West Africa was the largest ever recorded, representing a fundamental shift in Ebola epidemiology with unprecedented spatiotemporal complexity. We developed spatial transmission models using a gravity-model framework to explain spatiotemporal dynamics of EVD in West Africa at both the national and district-level scales, and to compare effectiveness of local interventions (e.g. local quarantine) and long-range interventions (e.g. border-closures). Incorporating spatial interactions, the gravity model successfully captures the multiple waves of…
The pandemic caused by the novel Coronavirus SARS-CoV2 has been responsible for life threatening health complications, and extreme pressure on healthcare systems. While preventive and definite curative medical interventions are yet to arrive, Non-Pharmaceutical Interventions (NPIs) like physical isolation, quarantine and drastic social measures imposed by governing agencies are effective in arresting the spread of infections in a population. In densely populated countries like India, lockdown interventions are partially effective due to social and administrative complexities. Using detailed de…
There has been much recent interest in modelling epidemics on networks, particularly in the presence of substantial clustering. Here, we develop pairwise methods to answer questions that are often addressed using epidemic models, in particular: on the basis of potential observations early in an outbreak, what can be predicted about the epidemic outcomes and the levels of intervention necessary to control the epidemic? We find that while some results are independent of the level of clustering (early growth predicts the level of `leaky' vaccine needed for control and peak time, while the basic r…
Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical sol…
When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet compe…
The SARS-CoV-2 pandemic has caused significant mortality and morbidity worldwide, sparing almost no community. As the disease will likely remain a threat for years to come, an understanding of the precise influences of human demographics and settlement, as well as the dynamic factors of climate, susceptible depletion, and intervention, on the spread of localized epidemics will be vital for mounting an effective response. We consider the entire set of local epidemics in the United States; a broad selection of demographic, population density, and climate factors; and local mobility data, trackin…
We highlight the usefulness of city-scale agent-based simulators in studying various non-pharmaceutical interventions to manage an evolving pandemic. We ground our studies in the context of the COVID-19 pandemic and demonstrate the power of the simulator via several exploratory case studies in two metropolises, Bengaluru and Mumbai. Such tools become common-place in any city administration's tool kit in our march towards digital health.
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…
Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic features, such as the different effectiveness of the vaccine against transmission and development of severe symptoms, testing practices, the possible implementation of non-pharmaceutical interventions to reduce the transmission, isolation of detecte…
The Ebola epidemic in West Africa is the largest ever recorded, with over 27,000 cases and 11,000 deaths as of June 2015. The public health response was challenged by difficulties with disease surveillance, which impacted subsequent analysis and decision-making regarding optimal interventions. We developed a stage-structured model of Ebola virus disease (EVD). A key feature of the model is that it includes a generalized correction term accounting for factors such as the fraction of cases reported and fraction of the population at risk (e.g. due to contact patterns, interventions, spatiotempora…
We consider an age-structured epidemic model with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and quarantine of the contacts of identified infectives. The dynamics of the infected population are modeled by a nonlinear infection-age-dependent partial differential equation, which is coupled with an ordinary differential equation that describes the dynamics of the susceptible population. Theoretical results about global existence and uniqueness of positive solutions are proved. We also present two practical applications of our model: (1…
We create a network model to study the spread of an epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for two kinds of agents - poor and non-poor. Under non-intervention, peak caseload is maximised, but no differences are observed in infection rates across poor and non-poor. Introducing interventions to control spread, peak caseloads are reduced, but both cumulative infection rates and current infection rates are systematically higher for the poor than for non-poor, across all scenarios. Larger populations, higher fractions of poor, and …
Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The models do not apply if the initial proportion is large (and fail whenever R_0<1), and cannot measure the impact of an intervention. Methods: In this paper we adapt "edge-based compartmental models" to situations having finite-sized initial conditions. Results: The resulting models remain simple and accurately capture the effect of the initial conditions. It …
The pandemic of COVID-19 has caused severe public health consequences around the world. Many interventions of COVID-19 have been implemented. It is of great public health and societal importance to evaluate the effects of interventions in the pandemic of COVID-19. In this paper, with help of synthetic control method, regression discontinuity and a Susceptible-Infected and infectious without isolation-Hospitalized in isolation-Removed (SIHR) model, we evaluate the horizontal and longitudinal effects of stringent interventions implemented in Wenzhou, a representative urban city of China, where s…
We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing, quarantining and vaccination. We describe the admissible and maximal robust positively invariant (MRPI) sets of these two models via the theory of barriers. We show how the sets may be used in the management of epidemics, for both perfect and imperfect/uncertain models, detailing how intervention strategies may be specified such that the hard infection cap is nev…
Evaluating the Impact of Epidemic Control via State-Dependent Markovian Switching Modeling
National and Kapodistrian University of Athens（雅典国立卡波季斯特里安大学）；Université de Lorraine（洛林大学）；CentraleSupélec, Université Paris-Saclay（巴黎萨克雷大学中央理工-高等师范学院）
We review epidemiological models for the propagation of the COVID-19 pandemic during the early months of the outbreak: from February to May 2020. The aim is to propose a methodological review that highlights the following characteristics: (i) the epidemic propagation models, (ii) the modeling of intervention strategies, (iii) the models and estimation procedures of the epidemic parameters and (iv) the characteristics of the data used. We finally selected 80 articles from open access databases based on criteria such as the theoretical background, the reproducibility, the incorporation of interv…
In this paper, we propose a two-group SIR epidemic model to simulate the outcome of stay-at-home policy and wearing face masks during the first COVID-19 epidemic wave in the United States. Based on our proposed model, we further use the optimal control approach (with the objective of minimizing total deaths) to find the optimal dynamical distribution of face masks between the healthcare workers and the general public. It is not surprising that all the face masks should be solely reserved for the healthcare workers if the supply is short. However, when the supply is indeed sufficient, our numer…
In this paper we conduct a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a scale-free network and that each infected individual in the network gains a temporary immunity after its infectious period is over. After the temporary immunity period is over, the individual becomes susceptible to the virus again. When the underlying contact network is embedded in Euclidean geometry, we model three different intervention strategies that aim to contr…
The paper deals with a modeling of the ongoing epidemic caused by Coronavirus disease 2019 (COVID-19) on the closed territory of the Republic of Croatia. Using the official public information on the number of confirmed infected, recovered and deceased individuals, the modified SEIR compartmental model is developed to describe the underlying dynamics of the epidemic. Fitted modified SEIR model provides the prediction of the disease progression in the near future, considering strict control interventions by means of social distancing and quarantine for infected and at-risk individuals introduced…
Since December 2019, A novel coronavirus (2019-nCoV) has been breaking out in China, which can cause respiratory diseases and severe pneumonia. Mathematical and empirical models relying on the epidemic situation scale for forecasting disease outbreaks have received increasing attention. Given its successful application in the evaluation of infectious diseases scale, we propose a Susceptible-Undiagnosed-Infected-Removed (SUIR) model to offer the effective prediction, prevention, and control of infectious diseases. Our model is a modified susceptible-infected-recovered (SIR) model that injects u…
As infectious disease outbreaks emerge, public health agencies often enact vaccination and social distancing measures to slow transmission. Their success depends on not only strategies and resources, but also public adherence. Individual willingness to take precautions may be influenced by global factors, such as news media, or local factors, such as infected family members or friends. Here, we compare three modes of epidemiological decision-making in the midst of a growing outbreak. Individuals decide whether to adopt a recommended intervention based on overall disease prevalence, the proport…
Voluntary nonpharmaceutical intervention as a feedback-evolving game
CEFE, Univ Montpellier, CNRS, EPHE, IRD（法国国家科学研究中心、高等教育与研究学院、热带研究所）；Institute of Tropical Medicine, Nagasaki University（长崎大学热带医学研究所）；Multidisciplinary Pandemic Research Center, Nagasaki University（长崎大学多学科流行病研究中心）；National Institute of Genetics（国立遗传学研究所）；SOKENDAI（综合研究大学院大学）；The University of Queensland（昆士兰大学）；Yokohama National University（横滨国立大学）；The University of Tokyo（东京大学）
The reproductive number R_0 (and its value after initial disease emergence R) has long been used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic virus SARS-CoV-2, the causative agent of COVID-19. We address some of these misconceptions, namely, how R changes over time, varies over space, and relates to epidemic size by referencing the mathematical definition of R an…
The ongoing COVID-19 pandemic calls for a multi-faceted public health response comprising complementary interventions to control the spread of the disease while vaccines and therapies are developed. Many of these interventions need to be informed by epidemic risk predictions given available data, including symptoms, contact patterns, and environmental factors. Here we propose a novel probabilistic formalism based on Individual-Level Models (ILMs) that offers rigorous formulas for the probability of infection of individuals, which can be parameterised via Maximum Likelihood Estimation (MLE) app…
We propose a targeted intervention protocol where recovery is restricted to individuals that have the least number of infected neighbours. Our recovery strategy is highly efficient on any kind of network, since epidemic outbreaks are minimal when compared to the baseline scenario of spontaneous recovery. In the case of spatially embedded networks, we find that an epidemic stays strongly spatially confined with a characteristic length scale undergoing a random walk. We demonstrate numerically and analytically that this dynamics leads to an epidemic spot with a flat surface structure and a radiu…
We study dynamics of a variant of the SIR the model, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. The degree of heterogeneity of the response is measured by the variance $σ^2$ of the corresponding distribution (the Preisach density function). The proposed model has a continuum of endemic equilibrium states characterized by different proportions of susceptible, infected and recovered populations. We consider how the limit point of the epidemic trajectory and the infection peak along…
We propose a simple model with two infective classes in order to model the cholera epidemic in Haiti. We include the impact of environmental events (rainfall, temperature and tidal range) on the epidemic in the Artibonite and Ouest regions by introducing terms in the transmission rate that vary with environmental conditions. We fit the model on weekly data from the beginning of the epidemic until December 2013, including the vaccination programs that were recently undertaken in the Ouest and Artibonite regions. We then modified these projections excluding vaccination to assess the programs' ef…
A Mathematical Model of Dengue Transmission Incorporating Hospital Capacity and Threshold-Based Fogging Interventions
Universitas Indonesia（印度尼西亚大学）；Escuela Superior Politécnica del Litoral（沿海高等理工学院）；TU Dresden（德累斯顿工业大学）；Ordu University（奥尔杜大学）；University of Koblenz（科布伦茨大学）；Johannes–Gutenberg Universität Mainz（约翰内斯·古腾堡美因茨大学）；Institute for Quantitative and Computational Biosciences (IQCB), Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学定量与计算生物科学研究所）
High impact epidemics constitute one of the largest threats humanity is facing in the 21st century. Testing, contact tracing and quarantining are critical in slowing down epidemic dynamics, but may prove insufficient for highly contagious diseases. In the absence of pharmaceutical interventions, physical distancing measures remain as the last resort to avoid a widespread outbreak. Here we show that such combined countermeasures drastically change the rules of the epidemic transition if testing capacities are limited: Instead of continuous the response to countermeasures becomes discontinuous a…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which typically are fulfilled for the Covid-19 pandemic it can be used to reproduce the development of an epidemic from a small number of parameters closely related to the data. We demonstrate this at the development in Germany and Switzerland. It also allows model predictions assuming nearly constant reproduction numbers. Thus it might be a useful tool for sheddin…
We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov Chain Monte Carlo (MCMC) methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model …
We study SIS epidemic spreading models under population dispersal on multi-layer networks. We consider a patchy environment in which each patch comprises individuals belonging to different classes. Individuals disperse to other patches on a multi-layer network in which each layer corresponds to a class. The dispersal on each layer is modeled by a Continuous Time Markov Chain (CTMC). At each time, individuals disperse according to their CTMC and subsequently interact with the local individuals in the patch according to an SIS model. We establish the existence of various equilibria under differe…
We are currently living in a state of uncertainty due to the pandemic caused by the Sars-CoV-2 virus. There are several factors involved in the epidemic spreading such as the individual characteristics of each city/country. The true shape of the epidemic dynamics is a large, complex system such as most of the social systems. In this context, Complex networks are a great candidate to analyze these systems due to their ability to tackle structural and dynamical properties. Therefore this study presents a new approach to model the COVID-19 epidemic using a multi-layer complex network, where nodes…
The ongoing SARS-CoV-2 pandemic has been holding the world hostage for more than a year now. Mobility is key to viral spreading and its restriction is the main non-pharmaceutical interventions to fight the virus expansion. Previous works have shown a connection between the structural organization of cities and the movement patterns of their residents. This puts urban centers in the focus of epidemic surveillance and interventions. Here we show that the organization of urban flows has a tremendous impact on disease spreading and on the amenability of different mitigation strategies. By studying…
Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model parameters for a disease spreading on a network of communities from limited, noisy observations; the state-of-the-art computational framework compensates for the model complexity by exploiting massively parallel computing architectures. Using noisy, synthetic data, we show the potential of the approach to perform robust model fitting and additionally demonst…
