An SEIR Infectious Disease Model with Testing and Conditional Quarantine

Abstract

We extend the baseline Susceptible-Exposed-Infectious-Recovered (SEIR) infectious disease epidemiology model to understand the role of testing and case-dependent quarantine. Our model nests the SEIR model. During a period of asymptomatic infection, testing can reveal infection that otherwise would only be revealed later when symptoms develop. Along with those displaying symptoms, such individuals are deemed known positive cases. Quarantine policy is case-dependent in that it can depend on whether a case is unknown, known positive, known negative, or recovered. Testing therefore makes possible the identification and quarantine of infected individuals and release of non-infected individuals. We fix a quarantine technology-a parameter determining the differential rate of transmission in quarantine-and compare simple testing and quarantine policies. We start with a baseline quarantine-only policy that replicates the rate at which individuals are entering quarantine in the US in March, 2020. We show that the total deaths that occur under this policy can occur under looser quarantine measures and a substantial increase in random testing of asymptomatic individuals. Testing at a higher rate in conjunction with targeted quarantine policies can (i) dampen the economic impact of the coronavirus and (ii) reduce peak symptomatic infections-relevant for hospital capacity constraints. Our model can be plugged into richer quantitative extensions of the SEIR model of the kind currently being used to forecast the effects of public health and economic policies.

Population-scale testing can suppress the spread of COVID-19

“…26), and the other by a team consisting of David Berger, Kyle Hirkenhoff and Simon Mongey that report similar conclusions (Ref. 27).…”

Extensions of the SEIR Model for the Analysis of Tailored Social Distancing and Tracing Approaches to Cope with COVID-19

“…We assume that the free beds are rationed proportionally across groups. 2 Then, σ k is endogenously determined from the lethality rateσ k of patients with a severe infection who have access to ICU care as follows,…”

“…All individuals from E tr k enter compartments Q when they become infectious while all individuals from E nt k enter compartments I. 2 A different rationing mechanism might be interesting to look at if one is interested in the age structure of the dead or if one wants to analyze the effect of different triage mechanisms that imply preferential treatment, e.g., for young people. Those extensions are easily possible by modifying of Equation (3).…”

Simplified model of Covid-19 epidemic prognosis under quarantine and estimation of quarantine effectiveness

“…Consequently, on the basis of eq. ( 3 ), the parameter of SIR model can be estimated as the number of new registered cases of infection to number of active cases ratio: ( 4 ) where is the rate of new infected cases ( 5 ) which can be estimated by counting new cases of infection, and usually is measured by number of registered new cases per time period ( 6 ) The number of daily new infected cases is defined as ( 7 ) So, expected number of new cases in next day could be predicted by the today number of active infected individuals multiplied by the infectious rate ( 8 ) In general, the infectious rate is time dependent and usually can be described by a complex function with additional parameters that must be daily calibrated according to last epidemiological data. Behaviour of the infectious rate during quarantine may differ in different countries, which reduces possibilities to build correct model of the infectious rate on the basis of epidemiological data from other countries.…”

“…Most popular epidemic dynamics models of Covid-19 are based on transmission model for a directly transmitted infectious disease, such as standard compartment models of disease SIR [5,6], or more advances derivates, such as SEIR and similar models [7][8][9][10]. Many of the models, which are used to forecast the COVID-19 epidemic, do not accurately capture the transient dynamics of epidemics; therefore, they give poor predictions of both the epidemic's peak and its duration [11], because calibration of parameters are based on dynamics of such non-reliable epidemiological data as number of active infectious cases.…”