10.6. Host-Pathogen Model (Anderson & May)

   Host-pathogen models are similar to predator-prey and host-parasite models. Below
   is the model of Anderson and May (1980, 1981) which describes insect diseases.
   The host population consist of two portions: susceptibles which are healthy
   organisms, and infected individuals. The model describes changes in density of
   susceptibles (S), infected individuals (I) and pathogens (P):

                                      [eq28.gif]

   This model is capable to generate epidemic cycles. It was used to study
   evolutionary strategies of pathogens.

   Models of epidemics in mammalian hosts (including humans) consider immune
   organisms as a separate category.

   Host-pathogen systems may include vectors. For example, malaria is transmitted by
   mosquitoes. In these systems, hosts become infected only when they have contact
   with the vector. Thus, the number of pathogens is not that important as the
   numbers of vectors carrying the patogens. The host-vector-pathogen system can be
   described as the change in numbers of 4 kinds of individuals: healthy hosts,
   infected hosts, uninfected vectors, and infected vectors. An example of such a
   model is given in the following Excel spreadsheet:

   [1][icoexcel.gif] Excel spreadsheet "vector.xls"

References:

   Andreson, R. M. and R. M. May. 1980. Infection diseases and population cycles of
   forest insects. Science 210: 658-661.
   Andreson, R. M. and R. M. May. 1981. The population dynamics of microparasites
   and their vertebrate hosts. Phil. Trans. of the Royal Soc. of London 210:
   658-661.

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   [5]Alexei Sharov 1/12/96

References

   1. http://alexei.nfshost.com/PopEcol/xls/vector.xls
   2. http://alexei.nfshost.com/PopEcol/lec10/paras.html
   3. http://alexei.nfshost.com/PopEcol/lec10/predat.html
   4. http://alexei.nfshost.com/PopEcol/lec10/quest10.html
   5. http://alexei.nfshost.com/~sharov/alexei.html