Susceptible-exposed-infectious-recovered Model Research Articles

COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies.

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 time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, to a target value but in distinct ways, which we implement in our model equations. We find that for the same TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

479. Mobility Restrictions and COVID-19 Pandemic Outbreak Control

BackgroundIn December 2009, a cluster of patients with pneumonia was reported in the city of Wuhan, capital of Hubei province in China, caused by a novel coronavirus: SARS-CoV-2.The epidemiological compartmental susceptible-exposed-infected-recovered (SEIR) model has been previously used during the initial wave of the H1N1 influenza pandemic in 2009. This study investigates whether the SEIR model, associated to mobility changes parameters, can determine the likelihood of establishing control over an epidemic in a city, state or country.MethodsThe critical step in the prediction of COVID-19 by a SEIR model are the values of the basic reproduction number (R0) and the infectious period, in days. R0 and the infectious periods were calculated by mathematical constrained optimization, and used to determine the numerically minimum SEIR model errors in a country, based on COVID-19 data until april 11th. The Community Mobility Reports from Google Maps (https://www.google.com/covid19/mobility/) provided mobility changes on april 5th compared to the baseline (Jan 3th to Feb 6th). The data was used to measure the non-pharmacological intervention adherence. The impact of each mobility component was made by logistic regression models. COVID-19 control was defined by R0 of the SEIR model in a country less than 1.0.Algorithm for the SEIR model applied to COVID-19 (initialization) Table 01: Algorithm for the SEIR model applied to COVID-19 (calculation of new COVID-19 cases day-by-day) ResultsResidential mobility restriction presented the higher logistic coefficient (17.7), meaning higher impact on outbreak control. Workplace mobility restriction was the second most effective measure, considering a restriction minimum of 56% for a 53% chance of outbreak control. Retail and recreation mobility presented 53%, and 86% respectively. Transit stations (96% and 54%) were also assessed. Park mobility restriction demonstrated the lowest effectiveness in outbreak control, considering that absolute (100%) restriction provided the lowest chance of outbreak control (46%).Table 2: The Community Mobility Reports from Google Maps: Mobility changes on April 5 compared to the baseline (5- week period; Jan 3–Feb 6, 2020): T_infectious and R0 obtained by using COVID-19 new cases day-by-day in each country, adjusted to the SEIR model by mathematical constrained optimization Logistic regression models to evaluate the chance of an epidemic control based on the non-pharmacological interventions adherence Simulation of the impact of the mobility component in the chance of outbreak control: analysis by using the logistic regression model summarized in Table 2 ConclusionResidential mobility restriction is the most effective measure. The degree to which mobility restrictions increase or decrease the overall epidemic size depends on the level of risk in each community and the characteristics of the disease. More research is required in order to estimate the optimal balance between mobility restriction, outbreak control, economy and freedom of movement.Disclosures All Authors: No reported disclosures

Analytical and cellular automaton approach to a generalized SEIR model for infection spread in an open crowded space

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.

On a Controlled Se(Is)(Ih)(Iicu)AR Epidemic Model with Output Controllability Issues to Satisfy Hospital Constraints on Hospitalized Patients

An epidemic model, the so-called SE(Is)(Ih)(Iicu)AR epidemic model, is proposed which splits the infectious subpopulation of the classical SEIR (Susceptible-Exposed-Infectious-Recovered) model into four subpopulations, namely asymptomatic infectious and three categories of symptomatic infectious, namely slight infectious, non-intensive care infectious, and intensive care hospitalized infectious. The exposed subpopulation has four different transitions to each one of the four kinds of infectious subpopulations governed under eventually different proportionality parameters. The performed research relies on the problem of satisfying prescribed hospitalization constraints related to the number of patients via control interventions. There are four potential available controls which can be manipulated, namely the vaccination of the susceptible individuals, the treatment of the non-intensive care unit hospitalized patients, the treatment of the hospitalized patients at the intensive care unit, and the transmission rate which can be eventually updated via public interventions such as isolation of the infectious, rules of groups meetings, use of face masks, decrees of partial or total quarantines, and others. The patients staying at the non-intensive care unit and those staying at the intensive care unit are eventually, but not necessarily, managed as two different hospitalized subpopulations. The controls are designed based on output controllability issues in the sense that the levels of hospital admissions are constrained via prescribed maximum levels and the measurable outputs are defined by the hospitalized patients either under a joint consideration of the sum of both subpopulations or separately. In this second case, it is possible to target any of the two hospitalized subpopulations only or both of them considered as two different components of the output. Different algorithms are given to design the controls which guarantee, if possible, that the prescribed hospitalization constraints hold. If this were not possible, because the levels of serious infection are too high according to the hospital availability means, then the constraints are revised and modified accordingly so that the amended ones could be satisfied by a set of controls. The algorithms are tested through numerically worked examples under disease parameterizations of COVID-19.

A modified SEIR model applied to the data of COVID-19 spread in Saudi Arabia.

The Susceptible-Exposed-Infectious-Recovered (SEIR) model is an established and appropriate approach in many countries to ascertain the spread of the coronavirus disease 2019 (COVID-19) epidemic. We wished to create a new COVID-19 model to be suitable for patients in any country. In this work, a modified SEIR model was constructed. We used the real data of COVID-19 spread in Saudi Arabia for statistical analyses and complex analyses. The reproduction number and detailed review of stability demonstrated the complexities of our proposed SEIR model. The solution and equilibrium condition were explored based on Jacobian’s linearization approach to the proposed SEIR model. The state of equilibrium was demonstrated, and a stability study was conducted in the disease-free environment. The reproduction number was measured sensitively against its internal parameters. Using the Lyapunov principle of equilibrium, the overall consistency of balance of our model was demonstrated. Findings using the SEIR model and observed outcomes due to COVID-19 spread in Saudi Arabia were compared. The modified SEIR model could enable successful analyses of the spread of epidemics such as COVID-19. An “ideal protocol” comprised essential steps to help Saudi Arabia decelerate COVID-19 spread. The most important aspects are to stay at home as much as possible and for infected people to remain in an isolated zone or secure area.

Simulation based study for estimation of COVID-19 spread in India using SEIR model

COVID -19 (Corona Virus Disease of 2019) what is known to be first incidence from Wuhan, China has now discovered its spread & threat to every other country. Protective measurements and better addressing policies seem to be the only way of fighting against COVID-19 progression till the vaccination to be invented. Study aims at finding the estimated progression of COVID -19 spread in India at different rates of transmission (R0) by using Susceptible, Exposed, Infected, Recovered (SEIR) model using online data COVID -19 registered cases in India collected from 30th January 2020 to 28th April 2020 for earlier phase of the research & then till June 30th 2020 for later part of the study. Also the data of around 206 countries for BCG vaccine coverage & 155 countries for temperature effect were assessed for finding correlation with COVID-19 morbidity. Reproduction number for COVID -19 for India was found at R0 =2.51 with transmission rate (β) = 0.24560 per day, latent period α = 0.19231 & recovery rate γ = 0.09785 for earlier date 28 th April 2020, then found to be decreased at R0 = 2.03 & β = 0.19865 per day later for June 30 th 2020 while recovery and latency time assumed to be constant. Weak negative correlation found for BCG & temperature rise with COVID -19 morbidity.

Condition for Global Stability for a SEIR Model Incorporating Exogenous Reinfection and Primary Infection Mechanisms.

A mathematical model incorporating exogenous reinfection and primary progression infection processes is proposed. Global stability is examined using the geometric approach which involves the generalization of Poincare-Bendixson criterion for systems of n-ordinary differential equations. Analytical results show that for a Susceptible-Exposed-Infective-Recovered (SEIR) model incorporating exogenous reinfection and primary progression infection mechanisms, an additional condition is required to fulfill the Bendixson criterion for global stability. That is, the model is globally asymptotically stable whenever a parameter accounting for exogenous reinfection is less than the ratio of background mortality to effective contact rate. Numerical simulations are also presented to support theoretical findings.

The approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (Appl. Math. Comput. 236:184–194, 2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding implies an approximate characteristic timescale, scaled by this stretch factor, that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.

Modeling the second wave of COVID-19 infections in France and Italy via a stochastic SEIR model.

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 and the economical and social textures, France and Italy governments have partially released lockdown measures. Here, we extrapolate the long-term behavior of the epidemic in both countries using a susceptible-exposed-infected-recovered model, where parameters are stochastically perturbed with a lognormal distribution to handle the uncertainty in the estimates of COVID-19 prevalence and to simulate the presence of super-spreaders. Our results suggest that uncertainties in both parameters and initial conditions rapidly propagate in the model and can result in different outcomes of the epidemic leading or not to a second wave of infections. Furthermore, the presence of super-spreaders adds instability to the dynamics, making the control of the epidemic more difficult. Using actual knowledge, asymptotic estimates of COVID-19 prevalence can fluctuate of the order of 10×106 units in both countries.

TEST SEIRCRT |ˈsəːkrɪt |: For the Health of Our Communities

The 2019 coronavirus disease (COVID-19) cases that are being confirmed in Canada provide an opportunity to expand the epidemic model for the simulation of disease infection spread: Susceptible- Exposed-Infectious-Recovered (SEIR). This paper develops a SEIRCRT |ˈsəːkrɪt | model that integrates the Institute for Disease Modeling’s SEIR model and Critical Race Theory (CRT) to answer the question: What is in a SEIRCRT model? SEIRCRT provides a basic modeling structure from a CRT lens to simulate, predict and forecast COVID-19 cases, comorbidities affecting African Canadians, and deaths through predictive modeling. Knowledge of SEIRCRT is critical to characterize the severity of COVID-19 in this early stage. To this end, the purpose of this paper is to describe SEIRCRT’s model and summarize its key characteristics. SEIRCRT as a public health framework provides insight into the conclusions drawn about race and COVID-19, and expands our thinking about what health disparities mean for African Canadian communities.

A mathematical model of COVID-19 transmission in a tertiary hospital and assessment of the effects of different intervention strategies.

Novel coronavirus (named SARS-CoV-2) can spread widely in confined settings including hospitals, cruise ships, prisons, and places of worship. In particular, a healthcare-associated outbreak could become the epicenter of coronavirus disease (COVID-19). This study aimed to evaluate the effects of different intervention strategies on the hospital outbreak within a tertiary hospital. A mathematical model was developed for the COVID-19 transmission within a 2500-bed tertiary hospital of South Korea. The SEIR (susceptible-exposed-infectious-recovered) model with a compartment of doctor, nurse, patient, and caregiver was constructed. The effects of different intervention strategies such as front door screening, quarantine unit for newly admitted patients, early testing of suspected infected people, and personal protective equipment for both medical staff and visitors were evaluated. The model suggested that the early testing (within eight hours) of infected cases and monitoring the quarantine ward for newly hospitalized patients are effective measures for decreasing the incidence of COVID-19 within a hospital (81.3% and 70% decrease of number of incident cases, respectively, during 60 days). Front door screening for detecting suspected cases had only 42% effectiveness. Screening for prohibiting the admission of COVID-19 patients was more effective than the measures for patients before emergency room or outpatient clinic. This model suggests that under the assumed conditions, some effective measures have a great influence on the incidence of COVID-19 within a hospital. The implementation of the preventive measures could reduce the size of a hospital outbreak.

Evaluation of COVID-19 control strategies in differentcountries and periods based on an adaptive PSO-SEIR model

<p indent="0mm">The COVID-19 pandemic has battered the world in more than 100 countries and regions due to its deadly and high transmission. How to control or limit the first and possible second wave of the infection has become an essential problem based on the control strategies implemented globally. This study presented a model to evaluate the efficiency of strategies based on an improved multi-stage SEIR (susceptible-exposed-infectious-recovered) model considering quarantine factor, treatment delay, transmission risk by the exposed, and time. The particle swarm optimization (PSO) algorithm with an adaptive weight strategy is adopted to find the SEIR model’s critical parameters associated with the control strategies based on the confirmed cases, the cured cases, and the death cases in the Chinese mainland, Italy, Spain, and Germany. The model was verified by the coefficients of correlation (<italic>R</italic>²) between the predicted results using parameters found by PSO and the actual data on the confirmed, the death, and the cured cases. The <italic>R</italic>²s are all greater than 0.93 in the Chinese mainland, Italy, Spain, and Germany, showing a good accuracy of the proposed model. Base on the data of analyzed countries, PSO finds the incubation period of COVID-19 is approximately <sc>5.1 d</sc>, which is consistent with other literatures. Besides, the period from exposure to medical care delivery is the most significant for controlling the transmission, followed by the quarantined rate according to our model. The effective reproduction number reduces from 3.9 to 1.4 while the delivery period shortens from 13 to <sc>1 d, </sc> even without considering the effect of quarantined rate and crowd protection awareness, indicating the importance of acid testing. Moreover, the effective reproduction number is smaller than 1 when the delivery period is 1 d and the quarantined rate is higher than 0.1, which shows the transmission of COVID-19 can be contained in these conditions. Furthermore, the establishment of Fangcang shelter hospitals and the implication of aided diagnosis guideline of COVID-19 gradually reduce the period to the hospital for patients in Hubei Province from 16 to 1–<sc>2 d.</sc> In addition, the efficiency of strategies among Italy, Spain, and Germany shows that Germany reached a better condition in comparison with others, and the number of confirmed cases in each country can drop by nearly 1/3 as the protection awareness of the population rises from 0.25 to 0.69, through reducing social activities, keeping social distance, and wearing masks, indicating the importance of government advertisement, education, etc. This study might help the governments to make strategies to limit the spreading of COVID-19 or potential outbreak of emerging infectious diseases in the future.

The probability of the 6-week lockdown in Victoria (commencing 9 July 2020) achieving elimination of community transmission of SARS-CoV-2.

The probability of the 6-week lockdown in Victoria (commencing 9 July 2020) achieving elimination of community transmission of SARS-CoV-2.

Warmer weather unlikely to reduce the COVID-19 transmission: An ecological study in 202 locations in 8 countries

PurposeTo examine the association between meteorological factors (temperature, relative humidity, wind speed, and UV radiation) and transmission capacity of COVID-19. MethodsWe collected daily numbers of COVID-19 cases in 202 locations in 8 countries. We matched meteorological data from the NOAA National Centers for Environmental Information. We used a time-frequency approach to examine the possible association between meteorological conditions and basic reproductive number (R0) of COVID-19. We determined the correlations between meteorological factors and R0 of COVID-19 using multiple linear regression models and meta-analysis. We further validated our results using a susceptible-exposed-infectious-recovered (SEIR) metapopulation model to simulate the changes of daily cases of COVID-19 in China under different temperatures and relative humidity conditions. Principal resultsTemperature did not exhibit significant association with R0 of COVID-19 (meta p = 0.446). Also, relative humidity (meta p = 0.215), wind speed (meta p = 0.986), and ultraviolet (UV) radiation (meta p = 0.491) were not significantly associated with R0 either. The SEIR model in China showed that with a wide range of meteorological conditions, the number of COVID-19 confirmed cases would not change substantially. ConclusionsMeteorological conditions did not have statistically significant associations with the R0 of COVID-19. Warmer weather alone seems unlikely to reduce the COVID-19 transmission.

Forecasting of COVID-19: spread with dynamic transmission rate

The COVID-19 was firstly reported in Wuhan, Hubei province, and it was brought to all over China by people travelling for Chinese New Year. The pandemic coronavirus with its catastrophic effects is now a global concern. Forecasting of COVID-19 spread has attracted a great attention for public health emergency. However, few researchers look into the relationship between dynamic transmission rate and preventable measures by authorities. In this paper, the SEIR (Susceptible Exposed Infectious Recovered) model is employed to investigate the spread of COVID-19. The epidemic spread is divided into two stages: before and after intervention. Before intervention, the transmission rate is assumed to be a constant since individual, community and government response has not taken into place. After intervention, the transmission rate is reduced dramatically due to the societal actions or measures to reduce and prevent the spread of disease. The transmission rate is assumed to follow an exponential function, and the removal rate is assumed to follow a power exponent function. The removal rate is increased with the evolution of the time. Using the real data, the model and parameters are optimized. The transmission rate without measure is calculated to be 0.033 and 0.030 for Hubei and outside Hubei province, respectively. After the model is established, the spread of COVID-19 in Hubei province, France and USA is predicted. From results, USA performs the worst according to the dynamic ratio. The model has provided a mathematical method to evaluate the effectiveness of the government response and can be used to forecast the spread of COVID-19 with better performance.

Beyond just \u201cflattening the curve\u201d: Optimal control of epidemics with purely non-pharmaceutical interventions

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 competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple “flattening of the curve”. Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.

Feasibility study of mitigation and suppression strategies for controlling COVID-19 outbreaks in London and Wuhan.

Recent outbreaks of coronavirus disease 2019 (COVID-19) has led a global pandemic cross the world. Most countries took two main interventions: suppression like immediate lockdown cities at epicenter or mitigation that slows down but not stopping epidemic for reducing peak healthcare demand. Both strategies have their apparent merits and limitations; it becomes extremely hard to conduct one intervention as the most feasible way to all countries. Targeting at this problem, this paper conducted a feasibility study by defining a mathematical model named SEMCR, it extended traditional SEIR (Susceptible-Exposed-Infectious-Recovered) model by adding two key features: a direct connection between Exposed and Recovered populations, and separating infections into mild and critical cases. It defined parameters to classify two stages of COVID-19 control: active contain by isolation of cases and contacts, passive contain by suppression or mitigation. The model was fitted and evaluated with public dataset containing daily number of confirmed active cases including Wuhan and London during January 2020 and March 2020. The simulated results showed that 1) Immediate suppression taken in Wuhan significantly reduced the total exposed and infectious populations, but it has to be consistently maintained at least 90 days (by the middle of April 2020). Without taking this intervention, we predict the number of infections would have been 73 folders higher by the middle of April 2020. Its success requires efficient government initiatives and effective collaborative governance for mobilizing of corporate resources to provide essential goods. This mode may be not suitable to other countries without efficient collaborative governance and sufficient health resources. 2) In London, it is possible to take a hybrid intervention of suppression and mitigation for every 2 or 3 weeks over a longer period to balance the total infections and economic loss. While the total infectious populations in this scenario would be possibly 2 times than the one taking suppression, economic loss and recovery of London would be less affected. 3) Both in Wuhan and London cases, one important issue of fitting practical data was that there were a portion (probably 62.9% in Wuhan) of self-recovered populations that were asymptomatic or mild symptomatic. This finding has been recently confirmed by other studies that the seroprevalence in Wuhan varied between 3.2% and 3.8% in different sub-regions. It highlights that the epidemic is far from coming to an end by means of herd immunity. Early release of intervention intensity potentially increased a risk of the second outbreak.

The introduction of population migration to SEIAR for COVID-19 epidemic modeling with an efficient intervention strategy

In this paper, we present a mathematical model of an infectious disease according to the characteristics of the COVID-19 pandemic. The proposed enhanced model, which will be referred to as the SEIR (Susceptible–Exposed–Infectious–Recovered) model with population migration, is inspired by the role that asymptomatic infected individuals, as well as population movements can play a crucial role in spreading the virus. In the model, the infected and the basic reproduction numbers are compared under the influence of intervention policies. The experimental simulation results show the impact of social distancing and migration-in rates on reducing the total number of infections and the basic reproductions. And then, the importance of controlling the number of migration-in people and the policy of restricting residents’ movements in preventing the spread of COVID-19 pandemic are verified.

The end of social confinement and COVID-19 re-emergence risk.

The lack of effective pharmaceutical interventions for SARS-CoV-2 raises the possibility of COVID-19 recurrence. We explore different post-confinement scenarios by using a stochastic modified SEIR (susceptible-exposed-infectious-recovered) model that accounts for the spread of infection during the latent period and also incorporates time-decaying effects due to potential loss of acquired immunity, people's increasing awareness of social distancing and the use of non-pharmaceutical interventions. Our results suggest that lockdowns should remain in place for at least 60 days to prevent epidemic growth, as well as a potentially larger second wave of SARS-CoV-2 cases occurring within months. The best-case scenario should also gradually incorporate workers in a daily proportion at most 50% higher than during the confinement period. We show that decaying immunity and particularly awareness and behaviour have 99% significant effects on both the current wave of infection and on preventing COVID-19 re-emergence. Social distancing and individual non-pharmaceutical interventions could potentially remove the need for lockdowns.

The resumption of sports competitions after COVID-19 lockdown: The case of the Spanish football league.

In this work, we present a stochastic discrete-time SEIR Susceptible-Exposed-Infectious-Recoveredmodel adapted to describe the propagation of COVID-19 during a football tournament. Specifically, we are concerned about the re-start of the Spanish national football league, La Liga, which is currently -May 2020- stopped with 11 fixtures remaining. Our model includes two additional states of an individual, confined and quarantined, which are reached when an individual presents COVID-19 symptoms or has undergone a virus test with a positive result. The model also accounts for the interaction dynamics of players, considering three different sources of infection: the player social circle, the contact with his/her team colleagues during training sessions, and the interaction with rivals during a match. Our results highlight the influence of the days between matches, the frequency of virus tests and their sensitivity on the number of players infected at the end of the season. Following our findings, we finally propose a variety of strategies to minimise the probability that COVID-19 propagates in case the season of La Liga was re-started after the current lockdown.