Klepac Petra

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  • Preprint
    The stage-structured epidemic : linking disease and demography with a multi-state matrix approach model
    ( 2010-05) Klepac, Petra ; Caswell, Hal
    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.
  • Thesis
    Interacting populations : hosts and pathogens, prey and predators
    (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 2007-06) Klepac, Petra
    The interactions between populations can be positive, neutral or negative. Predation and parasitism are both relationships where one species benefits from the interaction at the expense of the other. Predators kill their prey instantly and use it only for food, whereas parasites use their hosts both as their habitat and their food. I am particularly interested in microbial parasites (including bacteria, fungi, viri, and some protozoans) since they cause many infectious diseases. This thesis considers two different points in the population-interaction spectrum and focuses on modeling host-pathogen and predator-prey interactions. The first part focuses on epidemiology, i. e., the dynamics of infectious diseases, and the estimation of parameters using the epidemiological data from two different diseases, phocine distemper virus that affects harbor seals in Europe, and the outbreak of HIV/AIDS in Cuba. The second part analyzes the stability of the predator-prey populations that are spatially organized into discrete units or patches. Patches are connected by dispersing individuals that may, or may not differ in the duration of their trip. This travel time is incorporated via a dispersal delay in the interpatch migration term, and has a stabilizing effect on predator-prey dynamics.
  • Preprint
    Dispersal delays, predator–prey stability, and the paradox of enrichment
    ( 2007-03-26) Klepac, Petra ; Neubert, Michael G. ; van den Driessche, P.
    It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator{prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator{prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment.