More Complex Models and Control Measures

  • Ping Yan
  • Gerardo Chowell
Part of the Texts in Applied Mathematics book series (TAM, volume 70)


We have seen that, under suitable assumptions such as homogeneous mixing, the basic reproduction number R0, 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, R0 is expressed as a function of parameters representing rates in these models, such as R0 = βγ 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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Copyright information

© Crown 2019

Authors and Affiliations

  • Ping Yan
    • 1
    • 2
  • Gerardo Chowell
    • 3
  1. 1.Infectious Diseases Prevention and Control BranchPublic Health Agency of CanadaOttawaCanada
  2. 2.Department of Statistics and Actuarial Science, Faculty of MathematicsUniversity of WaterlooWaterlooCanada
  3. 3.School of Public HealthGeorgia State UniversityAtlantaUSA

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