Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission.

Hantavirus, a zoonotic disease carried by wild rodents, is spread among rodents via direct contact and indirectly via infected rodent excreta in the soil. Spillover to humans is primarily via the indirect route through inhalation of aerosolized viral particles. Rodent-hantavirus models that include direct and indirect transmission and periodically varying demographic and epidemiological parameters are studied in this investigation. Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients and an autonomous system, where the coefficients are taken to be the time-average. In the nonautonomous system, births, deaths, transmission rates and viral decay rates are assumed to be periodic. For both models, the basic reproduction numbers are calculated. The models are applied to two rodent populations, reservoirs for a New World and for an Old World hantavirus. The numerical examples show that periodically varying demographic and epidemiological parameters may substantially increase the basic reproduction number. Also, large variations in the viral decay rate in the environment coupled with an outbreak in rodent populations may lead to spillover infection in humans.

A habitat-based model for the spread of hantavirus between reservoir and spillover species.

New habitat-based models for spread of hantavirus are developed which account for interspecies interaction. Existing habitat-based models do not consider interspecies pathogen transmission, a primary route for emergence of new infectious diseases and reservoirs in wildlife and man. The modeling of interspecies transmission has the potential to provide more accurate predictions of disease persistence and emergence dynamics. The new models are motivated by our recent work on hantavirus in rodent communities in Paraguay. Our Paraguayan data illustrate the spatial and temporal overlaps among rodent species, one of which is the reservoir species for Jabora virus and others which are spillover species. Disease transmission occurs when their habitats overlap. Two mathematical models, a system of ordinary differential equations (ODE) and a continuous-time Markov chain (CTMC) model, are developed for spread of hantavirus between a reservoir and a spillover species. Analysis of a special case of the ODE model provides an explicit expression for the basic reproduction number, R(0), such that if R(0)<1, then the pathogen does not persist in either population but if R(0)>1, pathogen outbreaks or persistence may occur. Numerical simulations of the CTMC model display sporadic disease incidence, a new behavior of our habitat-based model, not present in other models, but which is a prominent feature of the seroprevalence data from Paraguay. Environmental changes that result in greater habitat overlap result in more encounters among various species that may lead to pathogen outbreaks and pathogen establishment in a new host.

The basic reproduction number in epidemic models with periodic demographics.

Patterns of contact in social behaviour and seasonality due to environmental influences often affect the spread and persistence of diseases. Models of epidemics with seasonality and patterns in the contact rate include time-periodic coefficients, making the systems nonautonomous. No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models. However, for some epidemic models with periodic coefficients and constant population size, the time-averaged basic reproduction number has been shown to be a threshold for disease extinction. We extend these results by showing that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic. The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains.