Sex-biased prevalence in infections with heterosexual, direct, and vector-mediated transmission: A theoretical analysis.

Three deterministic Kermack-McKendrick-type models for studying the transmission dynamics of an infection in a two-sex closed population are analyzed here. In each model it is assumed that infection can be transmitted through heterosexual contacts, and that there is a higher probability of transmission from one sex to the other than vice versa. The study is focused on understanding whether and how this bias in transmission reflects in sex differences in final attack ratios (i.

An SEIQR model for childhood diseases.

It has been shown that the inclusion of an isolated class in the classical SIR model for childhood diseases can be responsible for self-sustained oscillations. Hence, the recurrent outbreaks of such diseases can be caused by autonomous, deterministic factors. We extend the model to include a latent class (i.

The role of sexually abstained groups in two-sex demographic and epidemic logistic models with non-linear mortality.

We describe several gender structured population models governed by logistic growth with non-linear death rate. We extend these models to include groups of people isolated from sexual activity and individuals exposed to a mild and long-lasting sexually transmitted disease, i.e.

A Mathematical model of Schistosoma mansoni in Biomphalaria glabrata with control strategies.

We describe and analyze a mathematical model for schistosomiasis in which infected snails are distinguished from susceptible through increased mortality and no reproduction. We based the model on the same derivation as Anderson and May (J. Anim.

A deterministic model of schistosomiasis with spatial structure.

It has been observed in several settings that schistosomiasis is less prevalent in segments of river with fast current than in those with slow current. Some believe that this can be attributed to flush-away of intermediate host snails. However, free-swimming parasite larvae are very active in searching for suitable hosts, which indicates that the flush-away of larvae may also be very important.

The effect of nonreproductive groups on persistent sexually transmitted diseases.

We describe several population models exposed to a mild life long sexually transmitted disease, i.e. without significant increased mortality among infected individuals and providing no immunity/recovery.

The application of an age-structured model with unbounded mortality to demography.

We carry out a simulation of the female population of the USA using the non-autonomous Lotka-McKendrick model with finite maximum age and recent demographic data. The most important contributions in our study are the identification of the mortality rate (including the maximum age) and the design and analysis of a numerical method that works efficiently with unbounded mortality rates. We also consider the effect in the population projections produced by different ways to choose the vital rates and we present a sensitivity analysis with respect to the mortality.

How do nonreproductive groups affect population growth?

I describe several models of population dynamics, both unstructured and gender structured, that include groups of individuals who do not reproduce. I analyze the effect that the nonreproductive group may have on the dynamics of the whole population in terms of the vital rates and the proportion of nonreproductive individuals, and we provide specific examples for real populations.

Schistosomiasis models with density dependence and age of infection in snail dynamics.

New models for schistosomiasis are developed. These models incorporate several realistic features including drug treatment for human hosts, an infection age in snail hosts, density-dependent birth rate of snails, distribution of schistosomes within human hosts, and disease-induced mortality in both human and snail hosts. The qualitative and quantitative mathematical properties of the models are studied, their biological consequences and some control strategies are discussed, and the results of the new models are compared with those of simpler models.