We present a compartmental SEIAR model of epidemic spread as a generalization of the SEIR model. We believe that the asymptomatic infectious cohort is an omitted part of the understanding of the epidemic dynamics of disease COVID-19. We introduce and derive the basic reproduction number as the weighted arithmetic mean of the basic reproduction numbers of the symptomatic and asymptomatic cohorts. Since the asymptomatic subjects people are not detected, they can spread the disease much longer, and this increases the COVID-19 $R_0$ up to around 9. We show that European epidemic outbreaks in various European countries correspond to the simulations with commonly used parameters based on clinical characteristics of the disease COVID-19, but $R_0$ is around three times bigger if the asymptomatic cohort is taken into account. Many voices in the academic world are drawing attention to the asymptomatic group of infectious subjects at present. We are convinced that the asymptomatic cohort plays a crucial role in the spread of the COVID-19 disease, and it has to be understood during government measures.
We measure the effect of different public health regulations to the spread of COVID-19, based on a SEIRA model -- a SEIR model including asymptomatic transmissions. The cumulative confirmed cases and death show nonlinear positive relationship with the value of asymptomatic rate. Based on this model, we analyze the inhibit effects to COVID-19 of three types of public health policies, i.e. isolation of laboratory confirmed cases, general personal protection and quarantine (lock-down). The simulations conclude that the isolation display limited effects to the asymptomatic viral carriers. The gene…
Considering the propagation characteristics of COVID-19 in different regions, the dynamics analysis and numerical demonstration of long-term and short-term models of COVID-19 are carried out, respectively. The long-term model is devoted to investigate the global stability of COVID-19 model with asymptomatic infections and quarantine measures. By using the limit system of the model and Lyapunov function method, it is shown that the COVID-19-free equilibrium $V^0$ is globally asymptotically stable if the control reproduction number $\mathcal{R}_{c}<1$ and globally attractive if $\mathcal{R}_{c}=…
In this article, we present a modification to the network-based stochastic SEIR epidemic model which allows for modifications to the underlying contact network to account for the effects of quarantine. We also discuss the changes needed to the model to incorporate situations where some proportion of the individuals who are infected remain asymptomatic throughout the course of the disease. Using a generic network model where every potential contact exists with the same common probability, we conduct a simulation study in which we vary four key model parameters (transmission rate, probability of…
We develop and analyze in this work an epidemiological model for COVID-19 using Tunisian data. Our aims are first to evaluate Tunisian control policies for COVID-19 and secondly to understand the effect of different screening, quarantine and containment strategies and the rule of the asymptomatic patients on the spread of the virus in the Tunisian population. With this work, we show that Tunisian control policies are efficient in screening infected and asymptomatic individuals and that if containment and curfew are maintained the epidemic will be quickly contained.
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases.
The Covid-19 pandemic is ongoing worldwide, and the damage it has caused is unprecedented. For prevention, South Korea has adopted a local quarantine strategy rather than a global lockdown. This approach not only minimizes economic damage, but it also efficiently prevents the spread of the disease. In this work, the spread of COVID-19 under local quarantine measures is modeled using the Susceptible-Exposed-Infected-Recovered model on complex networks. In this network approach, the links connected to isolated people are disconnected and then reinstated when they are released. This link dynamics…
In this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: isolation (or social distancing) of a portion of the population, quarantine for confirmed cases and testing. We model isolation by separating the population in two groups: one composed by key-workers that keep working during the pandemic and have a usual contact rate, and a second group consisting of people that are enforced/recommended to stay at home. …
We introduce a system of differential equations to assess the impact of (self-)quarantine of symptomatic infectious individuals on disease dynamics. To this end we depart from using the classic bilinear infection process, but remain still within the framework of the mass-action assumption. From the mathematical point of view our model is interesting due to the lack of continuous differentiability at disease free steady states, which implies also that the basic reproductive number cannot be computed following established approaches for certain parameter values. However, we parametrise our mathe…
As of December 2020, the COVID-19 pandemic has infected over 75 million people, making it the deadliest pandemic in modern history. This study develops a novel compartmental epidemiological model specific to the SARS-CoV-2 virus and analyzes the effect of common preventative measures such as testing, quarantine, social distancing, and vaccination. By accounting for the most prevalent interventions that have been enacted to minimize the spread of the virus, the model establishes a paramount foundation for future mathematical modeling of COVID-19 and other modern pandemics. Specifically, the mod…
The quarantine of identified close contacts has been vital to reducing transmission rates and averting secondary infection risk before symptom onset and by asymptomatic cases. The effectiveness of this contact tracing strategy to mitigate transmission is sensitive to the adherence to quarantines, which may be lower for longer quarantine periods or in vaccinated populations (where perceptions of risk are reduced). This study develops a simulation model to evaluate contact tracing strategies based on the sequential testing of identified contacts after exposure as an alternative to quarantines, i…
Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic models have a long history of assisting in public health planning and policy making. In this paper, we introduce epidemic models including variable population size, degree-related imperfect vaccination and quarantine on scale-free networks. More specifically, the models are formulated both on the population with and without permanent natural immunity to infectio…
We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a 0D compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations. We emphasize the importance of the viral latent period and the key role of an asymptomatic population. We optimize model parameters for both regions by comparing predictions to the cumulative number of infected and total number of deaths via minimizing the $\ell^2$…
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…
This paper is based on the observation that, during Covid-19 epidemic, the choice of which individuals should be tested has an important impact on the effectiveness of selective confinement measures. This decision problem is closely related to the problem of optimal sensor selection, which is a very active research subject in control engineering. The goal of this paper is to propose a policy to smartly select the individuals to be tested. The main idea is to model the epidemics as a stochastic dynamic system and to select the individual to be tested accordingly to some optimality criteria, e.g…
The COVID-19 infection cases have surged globally, causing devastations to both the society and economy. A key factor contributing to the sustained spreading is the presence of a large number of asymptomatic or hidden spreaders, who mix among the susceptible population without being detected or quarantined. Here we propose an effective non-pharmacological intervention method of detecting the asymptomatic spreaders in contact-tracing networks, and validated it on the empirical COVID-19 spreading network in Singapore. We find that using pure physical spreading equations, the hidden spreaders of …
We propose a tractable epidemic model that includes containment measures. In the absence of containment measures, the epidemics spread exponentially fast whenever the infectivity rate is positive, $λ>0$. The containment measures are modeled by considering a time-dependent modulation of the bare infectivity $λ$ leading to effective infectivity that decays in time for each infected individual, mimicking for instance the combined effect of the asymptomatic onset of the disease, testing policies and quarantine. We consider a wide range of temporal kernels for effective infectivity and we investiga…
To increase situational awareness and support evidence-based policy-making, we formulated two types of mathematical models for COVID-19 transmission within a regional population. One is a fitting function that can be calibrated to reproduce an epidemic curve with two timescales (e.g., fast growth and slow decay). The other is a compartmental model that accounts for quarantine, self-isolation, social distancing, a non-exponentially distributed incubation period, asymptomatic individuals, and mild and severe forms of symptomatic disease. Using Bayesian inference, we have been calibrating our mod…
After the blockade that many nations suffered to stop the growth of the incidence curve of COVID-19 during the first half of 2020, they face the challenge of resuming their social and economic activity. The rapid airborne transmissibility of SARS-CoV-2, and the absence of a vaccine, calls for active containment measures to avoid the propagation of transmission chains. The best strategy up to date, popularly known as Test-Track-Treat (TTT), consist in testing the population for diagnosis, track the contacts of those infected, and treat by quarantine all these cases. The dynamical process that b…
