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A mathematical model is presented for the transmission of a microparasite where the hosts occupy one of two states, uninfected or infected. In each state, the hosts are distributed over a continuous range of immunity. The immune levels vary within hosts due to the processes of waning of immunity (when uninfected), and increasing immunity (when infected), eventually resulting in recovery. Immunity level also influences the host's ability to infect or be infected. Thus the proposed model incorporates both inter- and intra-host dynamics. It is shown from equilibrium results that this model is a general form of the susceptible-infected-resistant (SIR) and susceptible-infected-susceptible (SIS) family of models, a development that is useful for exploring multistrain pathogen transmission and use of vaccines which confer temporary protection.

Original publication

DOI

10.1098/rspb.1998.0528

Type

Journal article

Journal

Proc Biol Sci

Publication Date

22/10/1998

Volume

265

Pages

1977 - 1983

Keywords

Animals, Host-Parasite Interactions, Humans, Models, Biological, Parasitic Diseases, Vaccines