New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

Abstract

We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equations (DDEs) with five parameters. One parameter is set to unity by scaling time. The subcase of perfect quarantining and zero self-recovery before quarantine, with two free parameters, is examined first. The method of multiple scales yields a hyperbolic tangent solution; and a long-wave approximation yields a first order ordinary differential equation (ODE). With imperfect quarantining and nonzero self-recovery, the long-wave approximation is a second order ODE. These three approximations each capture the full outbreak, from infinitesimal initiation to final saturation. Low-dimensional dynamics in the DDEs is demonstrated using a six state non-delayed reduced order model obtained by Galerkin projection. Numerical solutions from the reduced order model match the DDE over a range of parameter choices and initial conditions. Finally, stability analysis and numerics show how correctly executed time-varying social distancing, within the present model, can cut the number of affected people by almost half. Alternatively, faster detection followed by near-certain quarantining can potentially be even more effective. : medRxiv preprint SIR model [4] has been modified to study infections where the recovered population can be reinfected (as with the common cold) and is known as the two-state SIS model. In the classic endemic model [5], for diseases that are active over 10-20 years, information of new births and deaths are included. In another variant of the SIR model known as the four-state MSIR [6] model, passive immunity inherited by newborns from their mothers is included: for example, newborn babies can be immune to measles for some time after their birth, but become susceptible later on. Other modifications have considered the effect of a carrier population [6], which never recovers from the disease but is asymptomatic (relevant to, e.g., tuberculosis). Such people can again suffer from the disease later, or continue to infect others while remaining asymptomatic. In SEIR [7], a four-state model, one of the states (E) represents the exposed population, infected but non-infectious. In the SEIQR model [8], yet another state, representing a quarantined population, is added to the SEIR model. All the models discussed above, including SIR, SIS, MSIR, SEIR, and SEIQR are governed by nonlinear differential equations. More complicated partial differential equation models that include the effect of the age structure [4] of the population and vaccination history are also available [7].The models mentioned so far need not include time delays. However, the incubation, asymptomatic, and symptomatic phases of a disease can be incorporated as time delays in mathematical models. Including such delays in the differentia...

An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis

“…As a result, it has been surmised that the actual infection situation is reflected on the daily confirmed PCR test positive number by a delay of about 2 weeks in Japan [19]. Young et al [20] developed a delayed SEIQR model including this delay effect, which was applied to the COVID-19 context by Vyasarayani and Chatterjee [21]. All patients detected by PCR testing should be quarantined but their model does not always guarantee this due to its probabilistic approach.…”

Multi-criteria performance analysis based on Physics of Decision — Application to COVID-19 and future pandemics

“…In the SEIR model, population transmission through dynamic flows has been established using various ODEs. Various pandemics are represented by different input values for the equations, as mentioned in [20].…”

“…Understanding the possible effects of potential on the system trajectory in the Performance Space is the first step in the experiment analysis. Various viruses may have different parameters as inputs in vector u [2], [20]. According to column "Variation" in Table . 1, considering that 1% of the total population is infected at first (α = 0.01 in equation 15), the Fig.…”

A delayed SEIQR epidemic model of COVID-19 in Tokyo

“…If we assume the incubation period to be 5 days [14] and that the patient is infectious before development of symptom by 2 days [3], the two week delay means that infectious patients might not be quarantined for about 11 (=14-5+2) days, if the test reporting delay is not counted in. Young et al developed a delayed SEIQR model [15] including this delay effect, which was applied to COVID-19 by Vysarayani and Chatterjee [16]. However, in their model, the patient that has passed an assumed period is quarantined once with an assumed probability, but if not quarantined, a chance of being quarantined is not left any longer.…”

“…Moreover when a check system is not well coordinated, they have to stand by for several days. Young et al developed a delayed SEIQR model [15] including this delay effect, which was applied to COVID-19 by Vysarayani and Chatterjee [16]. In their model, the patient that has passed an assumed period is quarantined with an assumed probability, but if not quarantined, a chance of being quarantined is not left any longer.…”