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...

The role of stray dogs in the persistence of domestic dog rabies, and whether removal of such dogs is beneficial, remains contentious issues for control programs seeking to eliminate rabies. While a community might reach the WHO vaccination target of 70% for dogs that can be handled, the stray or neighborhood dogs that are too wary of humans to be held are a more problematic population to vacci...

This paper is devoted to the study of two advection-dispersion-reaction models arising from the dynamics of harmful algae and zooplankton in flowingwater habitats where a main channel is coupled to a hydraulic storage zone, representing an ensemble of fringing coves on the shoreline. For the system modeling the dynamics of algae and their toxin that contains little limiting nutrient, we establi...

Optimal control theory is applied to a system of ordinary differential equations modeling Buruli ulcer transmission in population. We apply controls on mass treatment, insecticide and mass education to minimize the number of infected hosts and infected vectors as well as infected fishes. The model takes into account human, water bug and fish populations as well as MU in the environment. The hos...

Wemodel the spread of an SI (Susceptible→ Infectious) sexually transmitted infection on a dynamic homosexual network. The network consists of individuals with a dynamically varying number of partners. There is demographic turnover due to individuals entering the population at a constant rate and leaving the population after an exponentially distributed time. Infection is transmitted in partners...