Abstract
We have seen that, under suitable assumptions such as homogeneous mixing, the basic reproduction number R 0, defined at the start of the epidemic and given by (4.2) in Chap. 4, transcends to the asymptotic equilibrium (t →∞) outcomes such as the final size (5.32) in a closed population or the endemic equilibrium \(x(\infty )=\lim _{t\rightarrow \infty }S_{d}(t)/m\rightarrow R_{0}^{-1}\) in a constant population. Meanwhile, we have also seen that, in compartment transmission models of the SEIRS type (in Chap. 5) with exponentially distributed durations, R 0 is expressed as a function of parameters representing rates in these models, such as R 0 = β∕γ in SEIRS models without mortality or other in-flow and out-flow of the population, or (5.70) in SEIRS models with mortality or other in-flow and out-flow of the population.
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Yan, P., Chowell, G. (2019). More Complex Models and Control Measures. In: Quantitative Methods for Investigating Infectious Disease Outbreaks. Texts in Applied Mathematics, vol 70. Springer, Cham. https://doi.org/10.1007/978-3-030-21923-9_6
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