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SUMMARY:Deterministic models: twenty years on. I. Spatially homogeneous mo
 dels - Roberts\, M (Massey University)
DTSTART:20130819T103000Z
DTEND:20130819T110000Z
UID:TALK46688@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk I will review deterministic epidemic models that 
 do not have an explicit spatial structure. The most ubiquitous of these is
  the 	extit{SIR} model\, which is a special case of the 	extit{Kermack-McK
 endrick} model. Many properties of these models can be deduced from the we
 ll-known basic reproduction number\, $mathcal{R}_0$. Following the introdu
 ction of a typical primary infectious case in an otherwise susceptible pop
 ulation\, $mathcal{R}_0$ measures the expected change in prevalence from o
 ne infection generation to the next. There is a one-to-one correspondence 
 between $mathcal{R}_0$ and $r$\, the Malthusian parameter or initial rate 
 of increase in infection incidence\, directly linking generation time and 
 chronological time. The value of $mathcal{R}_0$ determines the final size 
 of the epidemic\, which is independent of temporal dynamics. It also provi
 des a measure of the control effort required to prevent an epidemic\, or t
 o eliminate an existing infection from a population. Where the modeled pop
 ulations are structured\, for example by sex\, species\, or groups at high
  risk of infection\, $mathcal{R}_0$ can be determined from the 	extit{Next
  Generation Matrix}. However\, it is not always sensible to average over d
 ifferent host types or states at infection\, so an alternative threshold q
 uantity the 	extit{Type Reproduction Number} $mathcal{T}$ has been defined
 . The value of $mathcal{T}$ provides a measure of the effort required when
  control is targeted. For macroparasite life cycles there is only one stat
 e at infection\, as pathogen development proceeds through prescribed stage
 s. Here\, $mathcal{R}_0$ measures the change in parasite population densit
 y from one infection generation to the next. Finally\, in periodic environ
 ments the number of secondary cases depends on the timing of the primary c
 ase. Careful averaging is then necessary\, and the value of $mathcal{R}_0$
  can be determined as the spectral radius of the 	extit{Next Generation Op
 erator}.\n
LOCATION:Seminar Room 1\, Newton Institute
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