Shapes of Hazard Functions and Lifetime Distributions

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


The main focus of this book is to address phenomenological questions regarding the spread of infectious diseases at the population level. Examples of such questions include:
  1. 1.
    If one or a few infected individuals are “seeded” in a large and completely susceptible population, will it only lead to a handful of infected individuals and the (small) outbreak burns out; or will it lead to an “explosive” (large) outbreak that results in a significant proportion of the population infected?
    1. (a)

      If the outcome is the former, what is the expected total number of infected individuals and what is the expected time to extinction?

    2. (b)

      If the outcome is the latter, how fast will it grow?

  2. 2.

    In a large outbreak, can we predict the peak burden of the disease and the timing of the peak? How about the long-term outcomes? Will it simply go away after a single wave or a few repeated waves, or will it settle down at some equilibrium state and the epidemic becomes endemic?

  3. 3.

    What about the effects of control measures, such as public health interventions including quarantine, isolation, or pharmaceutical treatments and vaccination?



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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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