The effect of nonreproductive groups on persistent sexually transmitted diseases
Daniel Maxin Fabio Augusto Milner
Mathematical Biosciences & Engineering 2007, 4(3): 505-522 doi: 10.3934/mbe.2007.4.505
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. We then modify these models to include groups isolated from sexual contact and analyze their potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels.
keywords: population models. sexually transmitted diseases isolation
How Do Nonreproductive Groups Affect Population Growth?
Fabio Augusto Milner
Mathematical Biosciences & Engineering 2005, 2(3): 579-590 doi: 10.3934/mbe.2005.2.579
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.
keywords: population models isolation nonreproductive groups exponential growth rate.
A deterministic model of schistosomiasis with spatial structure
Fabio Augusto Milner Ruijun Zhao
Mathematical Biosciences & Engineering 2008, 5(3): 505-522 doi: 10.3934/mbe.2008.5.505
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. In this paper, the authors establish a model with spatial structure that characterizes the density change of parasites following the flush-away of larvae. It is shown that the reproductive number, which is an indicator of prevalence of parasitism, is a decreasing function of the river current velocity. Moreover, numerical simulations suggest that the mean parasite load is low when the velocity of river current flow is sufficiently high.
keywords: delay differential equations. reproductive numbers schistosomiasis

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