Robert D. Holt*, Andrew P. Dobson, Michael Begon, Roger G. Bowers and Eric M. Schauber Department of Zoology, University of Florida, Gainesville, FL 32611, USA Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08540, USA Department of Environmental and Evolutionary Biology, Liverpool L69 3BX, UK Department of Applied Mathematics and Theoretical Physics, Univers...

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R0 is computed and shown ...

This paper deals with the nonlinear dynamics of a susceptible-infectious-recovered (SIR) epidemic model with nonlinear incidence rate, vertical transmission, vaccination for the newborns of susceptible and recovered individuals, and the capacity of treatment. It is assumed that the treatment rate is proportional to the number of infectives when it is below the capacity and constant when the num...

A semi-stochastic model for schistosomiasis was developed based on the immune response built up by human host after elapsing a fixed period of time L from the first infection, and on the parasite infection with multiple occurrences. Both acquired immunity and multiple parasite infections reproduced a great endemic stability for the disease and a high value for the basic reproduction ratio.

In many epidemiological models of microparasitic infections it is assumed that the infection process is governed by the mass-action principle, i.e. that the infection rate per host and per parasite is a constant. Furthermore, the parasite-induced host mortality (parasite virulence) and the reproduction rate of the parasite are often assumed to be independent of the infecting parasite dose. Howe...

We define a linear physiologically structured population model by two rules, one for reproduction and one for “movement” and survival. We use these ingredients to give a constructive definition of next-population-state operators. For the autonomous case we define the basic reproduction ratio R0 and the Malthusian parameter r and we compute the resolvent in terms of the Laplace transform of the ...

Recently, de-Camino-Beck and Lewis (Bull Math Biol 69:1341-1354, 2007) have presented a method that under certain restricted conditions allows computing the basic reproduction ratio R₀ in a simple manner from life cycle graphs, without, however, giving an explicit indication of these conditions. In this paper, we give various sets of sufficient and generically necessary conditions. To this end,...

The maintenance of disease-free status from Foot-and-Mouth Disease is of significant socio-economic importance to countries such as the UK. The imposition of bans on the movement of susceptible livestock following the discovery of an outbreak is deemed necessary to prevent the spread of what is a highly contagious disease, but has a significant economic impact on the agricultural community in i...

We present a method to estimate basic reproduction ratio R0 from transmission experiments. By using previously published data of experiments with Classical Swine Fever Virus more extensively, we obtained smaller confidence intervals than the martingale method used in the original papers. Moreover, our method allows simultaneous estimation of a reproduction ratio within pens R0w and a modified r...

This paper addresses the spread of tuberculosis through one-strain and two-strain models. We first present a basic model that incorporates fast and slow progression, effective chemoprophylaxis and therapeutic treatment. The system exhibits the traditional behavior. We prove that if the basic reproduction ratio R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable on the no...