The SARS-CoV-2 infectious outbreak has rapidly spread across the globe and precipitated varying policies to effectuate physical distancing to ameliorate its impact. In this study, we propose a new hybrid machine learning model, SIRNet, for forecasting the spread of the COVID-19 pandemic that couples with the epidemiological models. We use categorized spatiotemporally explicit cellphone mobility data as surrogate markers for physical distancing, along with population weighted density and other local data points. We demonstrate at varying geographical granularity that the spectrum of physical distancing options currently being discussed among policy leaders have epidemiologically significant differences in consequences, ranging from viral extinction to near complete population prevalence. The current mobility inflection points vary across geographical regions. Experimental results from SIRNet establish preliminary bounds on such localized mobility that asymptotically induce containment. The model can support in studying non-pharmacological interventions and approaches that minimize societal collateral damage and control mechanisms for an extended period of time.
Once an epidemic outbreak has been effectively contained through non-pharmaceutical interventions, a safe protocol is required for the subsequent release of social distancing restrictions to prevent a disastrous resurgence of the infection. We report individual-based numerical simulations of stochastic susceptible-infectious-recovered model variants on four distinct spatially organized lattice and network architectures wherein contact and mobility constraints are implemented. We robustly find that the intensity and spatial spread of the epidemic recurrence wave can be limited to a manageable e…
How does social distancing affect the reach of an epidemic in social networks? We present Monte Carlo simulation results of a capacity constrained Susceptible-Infected-Removed (SIR) model. The key modelling feature is that individuals are limited in the number of acquaintances that they can interact with, thereby constraining disease transmission to an infectious subnetwork of the original social network. While increased social distancing always reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network. Our results also reveal the import…
Non-pharmaceutical measures such as social distancing, can play an important role to control an epidemic in the absence of vaccinations. In this paper, we study the impact of social distancing on epidemics for which it is executable. We use a mathematical model combining human mobility and disease spreading. For the mobility dynamics, we design an agent based model consisting of pedestrian dynamics with a novel type of force to resemble social distancing in crowded sites. For the spreading dynamics, we consider the compartmental SIE dynamics plus an indirect transmission with the footprints of…
The outbreak of an infectious disease in a human population can lead to individuals responding with preventive measures in an attempt to avoid getting infected. This leads to changes in contact patterns. However, as we show in this paper, rational behaviour at the individual level, such as social distancing from infectious contacts, may not always be beneficial for the population as a whole. We use epidemic network models to demonstrate the potential negative consequences at the population level. We take into account the social structure of the population through several network models. As the…
In this study, we present a new epidemiological model, with contamination from confirmed and unreported. We also compute equilibria and study their stability without intervention strategies. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal disease intervention strategies. We investigate the impact of distancing, case finding, and case holding controls while at the same time, we minimize the number of infected and dead individuals. The method consists of minimizing the cost functional related to …
The aim of this paper consists in the application of a recent epidemiological model, namely SEIR with Social Distancing (SEIR--SD), extended here through the definition of a social distancing function varying over time, to assess the situation related to the spreading of the coronavirus Covid--19 in Italy and in two of its most important regions, i.e., Lombardy and Campania. To profitably use this model, the most suitable values of its parameters must be found. The estimation of the SEIR--SD model parameters takes place here through the use of Differential Evolution, a heuristic optimization t…
The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, $i.e$, the network that sustain the functionality of a society. Then, we survey …
The emergence of SARS-CoV-2 and the coronavirus infectious disease (COVID-19) has become a pandemic. Social (physical) distancing is a key non-pharmacologic control measure to reduce the transmission rate of SARS-COV-2, but high-level adherence is needed. Using daily travel distance and stay-at-home time derived from large-scale anonymous mobile phone location data provided by Descartes Labs and SafeGraph, we quantify the degree to which social distancing mandates have been followed in the U.S. and its effect on growth of COVID-19 cases. The correlation between the COVID-19 growth rate and tra…
Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals, schools, and food producing plants, remain focal points of local outbreaks. Here we develop a model for the stochastic outbreak dynamics in such local communities. We derive analytical expressions for the probability of containment of the outbreak, which is complementary to the probability of seeding a deterministically growing epidemic. This probability depends o…
A novel predictive modeling framework for the spread of infectious diseases using high dimensional partial differential equations is developed and implemented. A scalar function representing the infected population is defined on a high-dimensional space and its evolution over all directions is described by a population balance equation (PBE). New infections are introduced among the susceptible population from non-quarantined infected population based on their interaction, adherence to distancing norms, hygiene levels and any other societal interventions. Moreover, recovery, death, immunity and…
The current COVID-19 pandemic has proven that proper control and prevention of infectious disease require creating and enforcing the appropriate public policies. One critical policy imposed by the policymakers is encouraging the population to practice social distancing (i.e. controlling the contact rate among the population). Here we pose a mean-field game model of individuals each choosing a dynamic strategy of making contacts, given the trade-off of gaining utility but also risking infection from additional contacts. We compute and compare the mean-field equilibrium (MFE) strategy, which ass…
The first mitigation response to the Covid-19 pandemic was to limit person-to-person interaction as much as possible. This was implemented by the temporary closing of many workplaces and people were required to follow social distancing. Networks are a great way to represent interactions among people and the temporary severing of these interactions. Here, we present a network model of human-human interactions that could be mediators of disease spread. The nodes of this network are individuals and different types of edges denote family cliques, workplace interactions, interactions arising from e…
Coronavirus outbreak is one of the most challenging pandemics for the entire human population of the planet Earth. Techniques such as the isolation of infected persons and maintaining social distancing are the only preventive measures against the epidemic COVID-19. The actual estimation of the number of infected persons with limited data is an indeterminate problem faced by data scientists. There are a large number of techniques in the existing literature, including reproduction number, the case fatality rate, etc., for predicting the duration of an epidemic and infectious population. This pap…
Contact tracing and quarantine are well established non-pharmaceutical epidemic control tools. The paper aims to clarify the impact of these measures in COVID-19 epidemic. A new deterministic model is introduced (SEIRQ: susceptible, exposed, infectious, removed, quarantined) with Q compartment capturing individuals and releasing them with delay. We obtain a simple rule defining the reproduction number $\mathcal{R}$ in terms of quarantine parameters, ratio of diagnosed cases and transmission parameters. The model is applied to the epidemic in Poland in March - April 2020, when social distancing…
Major advances in public health have resulted from disease prevention. However, prevention of a new infectious disease by vaccination or pharmaceuticals is made difficult by the slow process of vaccine and drug development. We propose an additional intervention that allows rapid control of emerging infectious diseases, and can also be used to eradicate diseases that rely almost exclusively on human-to-human transmission. The intervention is based on (1) testing every individual for the disease, (2) repeatedly, and (3) isolation of infected individuals. We show here that at a sufficient rate of…
The infectious diseases are spreading due to human interactions enabled by various social networks. Therefore, when a new pathogen such as SARS-CoV-2 causes an outbreak, the non-pharmaceutical isolation strategies (e.g., social distancing) are the only possible response to disrupt its spreading. To this end, we introduce the new epidemic model (SICARS) and compare the centralized (C), decentralized (D), and combined (C+D) social distancing strategies, and analyze their efficiency to control the dynamics of COVID-19 on heterogeneous complex networks. Our analysis shows that the centralized soci…
Epidemiological models with constant parameters may not capture satisfactory infection patterns in the presence of pharmaceutical and non-pharmaceutical mitigation measures during a pandemic, since infectiousness is a function of time. In this paper, an Epidemiology-Informed Neural Network algorithm is introduced to learn the time-varying transmission rate for the COVID-19 pandemic in the presence of various mitigation scenarios. There are asymptomatic infectives, mostly unreported, and the proposed algorithm learns the proportion of the total infective individuals that are asymptomatic infect…
COVID-19--a viral infectious disease--has quickly emerged as a global pandemic infecting millions of people with a significant number of deaths across the globe. The symptoms of this disease vary widely. Depending on the symptoms an infected person is broadly classified into two categories namely, asymptomatic and symptomatic. Asymptomatic individuals display mild or no symptoms but continue to transmit the infection to otherwise healthy individuals. This particular aspect of asymptomatic infection poses a major obstacle in managing and controlling the transmission of the infectious disease. I…
Understanding the dynamics of the COVID-19 pandemic is crucial for improved control and social distancing strategies. To that effect, we have employed the susceptible-exposed-infectious-recovered model, refined by contact tracing and hospitalization data from Indian provinces Kerala, Delhi, Maharashtra, and West Bengal, as well as from overall India. We have performed a sensitivity analysis to identify the most crucial input parameters, and we have calibrated the model to describe the data as best as possible. Short-term predictions reveal an increasing and worrying trend of COVID-19 cases for…
Here we propose and implement a generalized mathematical model to find the time evolution of population in infectious diseases and apply the model to study the recent COVID-19 pandemic. Our model at the core is a non-local generalization of the widely used Kermack-McKendrick(KM) model where the susceptible(S) population evolves into two other categories, namely infectives(I) and removed(R). This is the well-known SIR model in which we further divide both S and I into high and low risk categories. We first formulate a set of non-local dynamical equations for the time evolution of distinct popul…
A number of models in mathematical epidemiology have been developed to account for control measures such as vaccination or quarantine. However, COVID-19 has brought unprecedented social distancing measures, with a challenge on how to include these in a manner that can explain the data but avoid overfitting in parameter inference. We here develop a simple time-dependent model, where social distancing effects are introduced analogous to coarse-grained models of gene expression control in systems biology. We apply our approach to understand drastic differences in COVID-19 infection and fatality c…
In this study, we propose a time-dependent Susceptible-Exposed-Infected-Recovered (SEIR) model for the analysis of the SARS-CoV-2 epidemic outbreak in three different countries, the United States of America, Italy and Iceland using public data inherent the numbers of the epidemic wave. Since several types and grades of actions were adopted by the governments, including travel restrictions, social distancing, or limitation of movement, we want to investigate how these measures can affect the epidemic curve of the infectious population. The parameters of interest for the SEIR model were estimate…
The dense social contact networks and high mobility in congested urban areas facilitate the rapid transmission of infectious diseases. Typical mechanistic epidemiological models are either based on uniform mixing with ad-hoc contact processes or need real-time or archived population mobility data to simulate the social networks. However, the rapid and global transmission of the novel coronavirus (SARS-CoV-2) has led to unprecedented lockdowns at global and regional scales, leaving the archived datasets to limited use. While it is often hypothesized that population density is a significant driv…
Infectious diseases that incorporate pre-symptomatic transmission are challenging to monitor, model, predict and contain. We address this scenario by studying a variant of a stochastic susceptible-exposed-infected-recovered model on arbitrary network instances using an analytical framework based on the method of dynamic message-passing. This framework provides a good estimate of the probabilistic evolution of the spread on both static and contact networks, offering a significantly improved accuracy with respect to individual-based mean-field approaches while requiring a much lower computationa…
We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control regimes and demonstrate that this is sufficient to capture the salient dynamical characteristics and to inform decisions. Contact between individuals in the community is characterised by a contact graph, the structure of that contact graph is selected to mimic community control measures. Our model of city-level transmission of an infectious agent (SEIR model) c…
A pandemic caused by a new coronavirus (COVID-19) has spread worldwide, inducing an epidemic still active in Argentina. In this chapter, we present a case study using an SEIR (Susceptible-Exposed-Infected-Recovered) diffusion model of fractional order in time to analyze the evolution of the epidemic in Buenos Aires and neighboring areas (Región Metropolitana de Buenos Aires, (RMBA)) comprising about 15 million inhabitants. In the SEIR model, individuals are divided into four classes, namely, susceptible (S), exposed (E), infected (I) and recovered (R). The SEIR model of fractional order allows…
We demonstrate the ability of statistical data assimilation to identify the measurements required for accurate state and parameter estimation in an epidemiological model for the novel coronavirus disease COVID-19. Our context is an effort to inform policy regarding social behavior, to mitigate strain on hospital capacity. The model unknowns are taken to be: the time-varying transmission rate, the fraction of exposed cases that require hospitalization, and the time-varying detection probabilities of new asymptomatic and symptomatic cases. In simulations, we obtain accurate estimates of undetect…
Infectious diseases often spread faster near their peak than would be predicted given early data on transmission. Despite the commonality of this phenomena, there are no known general mechanisms able to cause an exponentially spreading dis- ease to begin spreading faster. Indeed most features of real world social networks, e.g. clustering1,2 and community structure3, and of human behaviour, e.g. social distancing4 and increased hygiene5, will slow disease spread. Here, we consider a model where individuals with essential societal roles-e.g. teachers, first responders, health-care workers, etc.…
Coronavirus disease (COVID-19) which is caused by SARS-COV2 has become a pandemic. This disease is highly infectious and potentially fatal, causing a global public health concern. To contain the spread of COVID-19, governments are adopting nationwide interventions, like lockdown, containment and quarantine, restrictions on travel, cancelling social events and extensive testing. To understand the effects of these measures on the control of the epidemic in a data-driven manner, we propose a probabilistic cellular automata (PCA) based modified SEIQR model. The transitions associated with the mode…
We develop an agent-based model to assess the cumulative number of deaths during hypothetical Covid-19-like epidemics for various non-pharmaceutical intervention strategies. We consider local and non-local modes of disease transmission. The first simulates transmission through social contacts in the vicinity of the place of residence while the second through social contacts in public places: schools, hospitals, airports, etc., where many people meet, who live in remote geographic locations. Epidemic spreading is modeled as a discrete-time stochastic process on random geometric networks. We use…
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…
