The stage-structured epidemic : linking disease and demography with a multi-state matrix approach model

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Theoretical Ecology 4 (2011): 301-319, doi:10.1007/s12080-010-0079-8.Stage-structured epidemic models provide a way to connect the interacting processes of infection and demography. Reproduction and development can replenish the pool of susceptible hosts, and demographic structure leads to heterogeneous transmission and disease risk. Epidemics, in turn, can increase mortality or reduce fertility of the host population. Here we present a framework that integrates both demography and epidemiology in models for stage-structured epidemics. We use the vec-permutation matrix approach to classify individuals jointly by their demographic stage and infection status. We describe demographic and epidemic processes as alternating in time with a periodic matrix models. The application of matrix calculus to this framework allows for the calculation of R0 and sensitivity analysis.P.K. acknowledges support of UNESCO-L’Or´eal Fellowship ”For Women in Science”, Bill and Melinda Gates Foundation, National Institute of Health Grant R01-GM083983-01, National Science Foundation Grant 0742373. H.C. acknowledges support from National Science Foundation Grant DEB-0816514 and the Ocean Life Institute