The 2019 Novel Corona virus infection (COVID 19) is an ongoing public health emergency of international focus. Significant gaps persist in our knowledge of COVID 19 epidemiology, transmission dynamics, investigation tools and management, despite (or possibly because of) the fact that the outbreak is an unprecedented global threat. On the positive side, enough is currently known about the epidemic process to permit the construction of mathematical predictive models. In our work, we adapt a traditional SEIR epidemic model to the specific dynamic compartments and epidemic parameters of COVID 19, as it spreads in an age-heterogeneous community. We analyze management strategies of the epidemic course (as they were implemented through lockdown and reopening procedures in many of the US states and countries worldwide); however, to more clearly illustrate ideas, we focus on the example of a small scale college town community, with the timeline of control measures introduced in the state of New York. We generate predictions, and assess the efficiency of these control measures (closures, mobility restrictions, social distancing), in a sustainability context.
We analytically study the SEIR (Susceptible Exposed Infectious Removed) epidemic model. The aim is to provide simple analytical expressions for the peak and asymptotic values and their characteristic times of the populations affected by the COVID-19 pandemic.
COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in significantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health as well as the economical and social textures, France and Italy governments have partially released lockdown measures. Here we extrapolate the long-term behavior of the epidemics in both countries using a Susceptible-Exposed-Infected-Recovered (SEIR) model where parameters are stochastically perturbed to handle the un…
In this paper we analyze the effects of commuting and social inequalities for the epidemic development of the novel coronavirus (COVID-19). With this aim we consider a SEIRD (susceptible, exposed, infected, recovered and dead by disease) model without vital dynamics in a population divided into patches that have different economic resources and in which the individuals can commute from one patch to another (bilaterally). In the modeling we choose the social and commuting parameters arbitrarily. We calculate the basic reproductive number $R_0$ with the next generation approach and analyze the s…
We shall apply a generalized SEIR model to study the outbreak of COVID-19 in Brazil. In particular, we would like to explain the projections of the increase in the level of infection over a long period of time, overlapping large local outbreaks in the most populous states in the country. A time-dependent dynamic SEIR model inspired in a model previously used during the outbreak in China was used to analyses the time trajectories of infected, recovered, and deaths. The model has parameters that vary with time and are fitted considering a nonlinear least-squares method. The simulations starting …
Measures to reduce the impact of the COVID-19 pandemic require a mix of logistic, political and social capacity. Depending on the country, different approaches to increase hospitalization capacity or to properly apply lock-downs are observed. In order to better understand the impact of these measures we have developed a compartmental model which, on the one hand allows to calibrate the reduction of movement of people within and among different areas, and on the other hand it incorporates a hospitalization dynamics that differentiates the available kinds of treatment that infected people can re…
We consider the $SEIRS$ epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. Within a compartmental realization of this model, we found the disease-free and the endemic stationary states. They exist in their respective restricted regions of the le via linear stability analysis. The expression for the basic reproductive number is obtained as well. The positions and heights of a first peak for the fractions of infected individuals are obtained numerically and are fitted to sim…
We study variants of the SEIR model for interpreting some qualitative features of the statistics of the Covid-19 epidemic in France. Standard SEIR models distinguish essentially two regimes: either the disease is controlled and the number of infected people rapidly decreases, or the disease spreads and contaminates a significant fraction of the population until herd immunity is achieved. After lockdown, at first sight it seems that social distancing is not enough to control the outbreak. We discuss here a possible explanation, namely that the lockdown is creating social heterogeneity: even if …
In this paper, I study epidemic diffusion in a generalized spatial SEIRD model, where individuals are initially connected in a social or geographical network. As the virus spreads in the network, the structure of interactions between people may endogenously change over time, due to quarantining measures and/or spatial-distancing policies. I explore via simulations the dynamic properties of the co-evolutionary process dynamically linking disease diffusion and network properties. Results suggest that, in order to predict how epidemic phenomena evolve in networked populations, it is not enough to…
A pandemic caused by a new coronavirus has spread worldwide, affecting Argentina. We implement an SEIR model to analyze the disease evolution in Buenos Aires and neighbouring cities. The model parameters are calibrated using the number of casualties officially reported. Since infinite solutions honour the data, we show different cases. In all of them the reproduction ratio $R_0$ decreases after early lockdown, but then raises, probably due to an increase in contagion in highly populated slums. Therefore it is mandatory to reverse this growing trend in $R_0$ by applying control strategies to av…
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…
We study the dynamic evolution of COVID-19 cased by the Omicron variant via a fractional susceptible-exposedinfected-removed (SEIR) model. Preliminary data suggest that the symptoms of Omicron infection are not prominent and the transmission is therefore more concealed, which causes a relatively slow increase in the detected cases of the new infected at the beginning of the pandemic. To characterize the specific dynamics, the Caputo-Hadamard fractional derivative is adopted to refined the classical SEIR model. Based on the reported data, we infer the fractional order, timedependent parameters,…
This manuscript proposes a model of $n$ distinct populations interaction structured SEIR to describe the spread of COVID-19 pandemic diseases. The proposed model has the flexibility to include geographically separated communities as well as taking into account aging population groups and their interactions. We show that distinct assumptions on the dynamics of the proposed model lead to a plateau-like curve of the infected population, reflecting collected data from large countries like Brazil. Such observations aim to the following conjecture: " Covid-19 diseased diffusion from the capitals to …
We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases, both analytically, and numerically, by means of a cellular automata simulation of the individual dynamics in the system. As a result, we provide the infection ratio in the system as a function of controllable parameters, which allows for quantifying how acting on the human behavior may effectively lower the disease spread throughout the system.
This paper is an exploratory study of two epidemiological questions on a worldwide basis. How fast is the disease spreading? Are the restrictions (especially mobility restrictions) for people bring the expected effect? To answer the first question, we propose a tool for estimating the reproduction number of epidemic (the number of secondary infections $R_t$) based on the SEIR model and compare it with an non-model $R_t$ estimation. To measure the $R_t$ of COVID-19 for different countries, real-time data on coronavirus daily cases of infections, recoveries, deaths are retrieved from the Center …
The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early …
We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are time-varying and learned from the data. This approach serves to forecast the evolution of the outbreak over a relatively short time period and provide scheduled controls of the epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effectiv…
OBJECTIVES: to describe the first wave of the COVID-19 pandemic with a focus on undetected cases and to evaluate different post-lockdown scenarios. DESIGN: the study introduces a SEIR compartmental model, taking into account the region-specific fraction of undetected cases, the effects of mobility restrictions, and the personal protective measures adopted, such as wearing a mask and washing hands frequently. SETTING AND PARTICIPANTS: the model is experimentally validated with data of all the Italian regions, some European countries, and the US. MAIN OUTCOME MEASURES: the accuracy of the model …
The last leg of the year 2019 gave rise to a virus named COVID-19 (Corona Virus Disease 2019). Since the beginning of this infection in India, the government implemented several policies and restrictions to curtail its spread among the population. As the time passed, these restrictions were relaxed and people were advised to follow precautionary measures by themselves. These timely decisions taken by the Indian government helped in decelerating the spread of COVID-19 to a large extent. Despite these decisions, the pandemic continues to spread and hence, there is an urgent need to plan and cont…
In this paper we explore a time-depended SEIR model, in which the dynamics of the infection in four groups from a selected target group (population), divided according to the infection, are modeled by a system of nonlinear ordinary differential equations. Several basic parameters are involved in the model: coefficients of infection rate, incubation rate, recovery rate. The coefficients are adaptable to each specific infection, for each individual country, and depend on the measures to limit the spread of the infection and the effectiveness of the methods of treatment of the infected people in …
India was under a grave threat from the second wave of the COVID-19 pandemic particularly in the beginning of May 2021. The situation appeared rather gloomy as the number of infected individuals/active cases had increased alarmingly during the months of May and June 2021 compared to the first wave peak. Indian government/state governments have been implementing various control measures such as lock-downs, setting up new hospitals, and putting travel restrictions at various stages to lighten the virus spread from the initial outbreak of the pandemic. Recently, we have studied the susceptible-ex…
We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitati…
Following the spread of the COVID-19 pandemic and pending the establishment of vaccination campaigns, several non pharmaceutical interventions such as partial and full lockdown, quarantine and measures of physical distancing have been imposed in order to reduce the spread of the disease and to lift the pressure on healthcare system. Mathematical models are important tools for estimating the impact of these interventions, for monitoring the current evolution of the epidemic at a national level and for estimating the potential long-term consequences of relaxation of measures. In this paper, we m…
The present article studies the extension of two deterministic models for describing the novel coronavirus pandemic crisis, the SIR model and the SEIR model. The models were studied and compared to real data in order to support the validity of each description and extract important information regarding the pandemic, such as the basic reproductive number R0, which might provide useful information concerning the rate of increase of the pandemic predicted by each model. We next proceed to making predictions and comparing more complex models derived from the SEIR model with the SIRD model, in ord…
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…
An epidemic disease caused by a new coronavirus has spread in Northern Italy with a strong contagion rate. We implement an SEIR model to compute the infected population and number of casualties of this epidemic. The example may ideally regard the situation in the Italian Region of Lombardy, where the epidemic started on February 25. We calibrate the model with the number of dead individuals to date (May 5, 2020) and constraint the parameters on the basis of values reported in the literature. The peak occurs at day 37 (March 31) approximately, when there is a rapid decrease, with a reproduction…
An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in $\ln S$ and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptotic approximant (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48) in the form of a modified symmetric Padé approximant that incorporates this damping. The utility of the analytical form is demonstrated through its application to the COVID…
Strategies adopted globally to mitigate the threat of COVID-19 have primarily involved lockdown measures with substantial economic and social costs with varying degrees of success. Morbidity patterns of COVID-19 variants have a strong association with age, while restrictive lockdown measures have association with negative mental health outcomes in some age groups. Reduced economic prospects may also afflict some age cohorts more than others. Motivated by this, we propose a model to describe COVID-19 community spread incorporating the role of age-specific social interactions. Through a flexible…
In this study, we develop the mathematical model to understand the coupling between the spreading dynamics of infectious diseases and the mobility dynamics through urban transportation systems. We first describe the mobility dynamics of the urban population as the process of leaving from home, traveling to and from the activity locations, and engaging in activities. We then embed the susceptible-exposed-infectious-recovered (SEIR) process over the mobility dynamics and develops the spatial SEIR model with travel contagion (Trans-SEIR), which explicitly accounts for contagions both during trave…
HKUST (University of Science & Technology)（香港科技大学）；International Computer Science Institute（国际计算机科学研究所）；Ecole de Guerre Economique（经济战争学院）；University of Cambridge（剑桥大学）；Manifold Research；University College London（伦敦大学学院）；ELU AI Ltd（ELU AI有限公司）；Royal Free Hospital（皇家自由医院）；Population Research Institute, The Family Federation of Finland（芬兰家庭联合会人口研究所）
We present two models for the COVID-19 pandemic predicting the impact of universal face mask wearing upon the spread of the SARS-CoV-2 virus--one employing a stochastic dynamic network based compartmental SEIR (susceptible-exposed-infectious-recovered) approach, and the other employing individual ABM (agent-based modelling) Monte Carlo simulation--indicating (1) significant impact under (near) universal masking when at least 80% of a population is wearing masks, versus minimal impact when only 50% or less of the population is wearing masks, and (2) significant impact when universal masking is …
The outbreak of the coronavirus disease 2019 (COVID-19) has now spread throughout the globe infecting over 150 million people and causing the death of over 3.2 million people. Thus, there is an urgent need to study the dynamics of epidemiological models to gain a better understanding of how such diseases spread. While epidemiological models can be computationally expensive, recent advances in machine learning techniques have given rise to neural networks with the ability to learn and predict complex dynamics at reduced computational costs. Here we introduce two digital twins of a SEIRS model a…
We introduce a Python package for modeling and studying the spread of infectious diseases using an agent-based SEIR style epidemiological model with a focus on university campuses. This document explains the epidemiological model used in the package and gives examples highlighting the ways that the package can be used.
The goal of this work is to study the optimal controls for the COVID-19 epidemic in Brazil. We consider an age-structured SEIRQ model with quarantine compartment, where the controls are the quarantine entrance parameters. We then compare the optimal controls for different quarantine lengths and distribution of the total control cost by assessing their respective reductions in deaths in comparison to the same period without quarantine. The best strategy provides a calendar of when to relax the isolation measures for each age group. Finally, we analyse how a delay in the beginning of the quarant…
This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic currently ravaging the planet. There are two objectives: to arrive at an appropriate model that captures the collected data faithfully, and to use that as a basis to explore the nonlinear behavior. We use a nonlinear SEIR (Susceptible, Exposed, Infectious & Removed) transmission model with added behavioral and government policy dynamics. We develop a genetic algorithm technique to identify key model parameters employing COVID19 data from South Korea. Stability, bifurcations and dynamic behavior are analyzed. …
Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model uses a compartmental approach including dynamic and nonlinear behavior of transmission through three factors: susceptible, infected, and removed (recovered and deceased) individuals. Using the Lambert W Function, we propose a framework to study solutions of the SIR model. This demonstrates the applications of COVID-19 transmission data to model the spread of a…
The COVID-19 pandemic constitutes one of the largest threats in recent decades to the health and economic welfare of populations globally. In this paper, we analyze different types of policy measures designed to fight the spread of the virus and minimize economic losses. Our analysis builds on a multi-group SEIR model, which extends the multi-group SIR model introduced by Acemoglu et al.~(2020). We adjust the underlying social interaction patterns and consider an extended set of policy measures. The model is calibrated for Germany. Despite the trade-off between COVID-19 prevention and economic…
The SEIRS model, an extension of the SEIR model for analyzing and predicting the spread of virus infection, was further extended to consider the movement of people across regions. In contrast to previous models that con-sider the risk of travelers from/to other regions, we consider two factors. First, we consider the movements of susceptible (S), exposed (E), and recovered (R) individuals who may get infected and infect others in the destination region, as well as infected (I) individuals. Second, people living in a region and moving from other regions are dealt as separate but interacting gro…
Current efforts of modelling COVID-19 are often based on the standard compartmental models such as SEIR and their variations. As pre-symptomatic and asymptomatic cases can spread the disease between populations through travel, it is important to incorporate mobility between populations into the epidemiological modelling. In this work, we propose to modify the commonly-used SEIR model to account for the dynamic flight network, by estimating the imported cases based on the air traffic volume as well as the test positive rate at the source. This modification, called Flight-SEIR, can potentially e…
We propose an SEIR-type meta-population model to simulate and monitor the Covid-19 epidemic evolution. The basic model consists of seven compartments, namely susceptible (S), exposed (E), three infective classes, recovered (R), and deceased (D). We define these compartments for n age and gender groups in m different spatial locations. So, the resulting model has, for each age group, gender, and place, all epidemiological classes. The mixing between them is accomplished by means of time-dependent infection rate matrices. The model is calibrated with the curve of daily new infections in New York…
We study the epidemic spreading on spatial networks where the probability that two nodes are connected decays with their distance as a power law. As the exponent of the distance dependence grows, model networks smoothly transition from the random network limit to the regular lattice limit. We show that despite keeping the average number of contacts constant, the increasing exponent hampers the epidemic spreading by making long-distance connections less frequent. The spreading dynamics is influenced by the distance-dependence exponent as well and changes from exponential growth to power-law gro…
To model the spread of COVID-19 coronavirus in Russian regions and in Moscow, a discrete logistic equation describing the increase in the number of cases is used. To check the adequacy of the mathematical model, the simulation results were compared with the spread of coronavirus in China, in a number of European and Asian countries, and the United States. The parameters of the logistics equation for Russia, Moscow and other large regions were determined in the interval (01.03 - 08.04). A comparative analysis of growth rates of COVID-19 infected population for different countries and regions is…
To curb the spread of COVID-19, many governments around the world have implemented tiered lockdowns with varying degrees of stringency. Lockdown levels are typically increased when the disease spreads and reduced when the disease abates. A predictive control approach is used to develop optimized lockdown strategies for curbing the spread of COVID-19. The strategies are then applied to South African data. The South African case is of interest as the South African government has defined five distinct levels of lockdown, which serves as a discrete control input. An epidemiological model for the s…
We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all thr…
We propose a mathematical model to analyze the time evolution of the total number of infected population with Covid-19 disease at a region in the ongoing pandemic. Using the available data of Covid-19 infected population on various countries we formulate a model which can successfully track the time evolution from early days to the saturation period in a given wave of this infectious disease. It involves a set of effective parameters which can be extracted from the available data. Using those parameters the future trajectories of the disease spread can also be projected. A set of differential …
In December 2019, COVID-19 were detected in Wuhan City, Hubei Province of China. SARS-CoV-2 rapidly spread to the whole Chinese mainland with the people during the Chinese Spring Festival Travel Rush. As of 19 February 2020, 74576 confirmed cases of COVID-19 had been reported in Chinese Mainland. What kind of cities have more confirmed cases, and is there any relationship between GDP and confirmed cases? In this study, we explored the relationship between the confirmed cases of COVID-19 and GDP at the prefectural-level, found a positive correlation between them. This finding warns high GDP are…
We develop an agent-based model on a network meant to capture features unique to COVID-19 spread through a small residential college. We find that a safe reopening requires strong policy from administrators combined with cautious behavior from students. Strong policy includes weekly screening tests with quick turnaround and halving the campus population. Cautious behavior from students means wearing facemasks, socializing less, and showing up for COVID-19 testing. We also find that comprehensive testing and facemasks are the most effective single interventions, building closures can lead to in…
This study aims to determine an optimal control strategy for vaccine scheduling in COVID-19 pandemic treatment by converting widely acknowledged infectious disease model named SEIR into an optimal control problem. The problem is augmented by adding medication and vaccine limitations to match real-world situations. Two version of the problem is formulated to minimize the number of infected individuals at the same provide the optimal vaccine possible to reduce the susceptible population to a considerably lower state. Optimal control problems are solved using RBF-Galerkin method. These problems a…
We introduce an epidemic spreading model on a network using concepts from percolation theory. The model is motivated by discussing the standard SIR model, with extensions to describe effects of lockdowns within a population. The underlying ideas and behavior of the lattice model, implemented using the same lockdown scheme as for the SIR scheme, are discussed in detail and illustrated with extensive simulations. A comparison between both models is presented for the case of COVID-19 data from the USA. Both fits to the empirical data are very good, but some differences emerge between the two appr…
In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community. Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically. To the contrary, as we show herein, it can be increased in surge periods! In partic…
Large-scale events like the UEFA Euro~2020 football (soccer) championship offer a unique opportunity to quantify the impact of gatherings on the spread of COVID-19, as the number and dates of matches played by participating countries resembles a randomized study. Using Bayesian modeling and the gender imbalance in COVID-19 data, we attribute 840,000 (95% CI: [0.39M, 1.26M]) COVID-19 cases across 12 countries to the championship. The impact depends non-linearly on the initial incidence, the reproduction number $R$, and the number of matches played. The strongest effects are seen in Scotland and…
A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can interchange during the epidemic. We apply the model to the COVID-19 case and demonstrate the predictive features of our model.
The COVID-19 pandemic has rapidly spread around the world and burdened public health in almost all countries involving France. After the spread of SARS-CoV-2, France harvested many deaths in total. In this paper, we develop models with integer and fractional orders to investigate the dynamics of COVID-19 transmission in French hospitals and intensive care units (ICUs). Moreover, this paper aims to explore the impact of precautionary measures on the total infected cases in hospitals and ICUs of COVID-19 for the entire France by using available actual data.
In this paper, we introduce a novel modeling framework for incorporating fear of infection and frustration with social distancing into disease dynamics. We show that the resulting SEIR behavior-perception model has three principal modes of qualitative behavior---no outbreak, controlled outbreak, and uncontrolled outbreak. We also demonstrate that the model can produce transient and sustained waves of infection consistent with secondary outbreaks. We fit the model to cumulative COVID-19 case and mortality data from several regions. Our analysis suggests that regions which experience a significa…
We use aggregated data from Facebook to show that COVID-19 is more likely to spread between regions with stronger social network connections. Areas with more social ties to two early COVID-19 "hotspots" (Westchester County, NY, in the U.S. and Lodi province in Italy) generally had more confirmed COVID-19 cases by the end of March. These relationships hold after controlling for geographic distance to the hotspots as well as the population density and demographics of the regions. As the pandemic progressed in the U.S., a county's social proximity to recent COVID-19 cases and deaths predicts futu…
