Modeling accurately the evolution and intervention strategies for the Covid-19 pandemic is a challenging problem. We present here an analysis of an extended Susceptible-Exposed-Infected-Recovered (SEIR ) model that accounts for asymptomatic carriers, and 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 R_0 to a target value R _0^{\rm target < 1, but in distinct ways, which we implement in our model equations. We find that for the same target R_0^{\rm target < 1, TQ is more efficient in controlling the pandemic than lockdowns that only implement SD. However, for TQ to be effective, it has to be based on contact tracing and the ratio of tests/day to the number of new cases/day has to be scaled with the mean number of contacts of an infectious person, which would be high in densely populated regions with low levels of SD. We point out that , apart from R_0, an important quantity is the largest eigenvalue of the linearised dynamics which provides a more complete understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. Weak intervention strategies (that reduce R_0 but not to a value less than 1) can reduce the peak values of infections and the asymptotic affected population. We provide simple analytic expressions for these in terms of the disease parameters and apply them in the Indian context to obtain heuristic projections for the course of the pandemic . We find that the predictions strongly depend on the assumed fraction of asymptomatic carriers.
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 , R_0, to a target value R ^{\rm target < 1, but in distinct ways, which we implement in our model equations. We find that for the same R^{\rm target < 1, 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.
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Modeling accurately the evolution and intervention strategies for the Covid-19 pandemic is a challenging problem. We present here an analysis of an extended
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(SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR
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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
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Weak intervention strategies (that reduce R_0 but not to a value less than 1) can reduce the peak values of infections and the asymptotic affected population. We provide simple analytic expressions for these in terms of the disease parameters and apply them in the Indian context
We apply our results to the COVID data for India
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