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Non-linear difference equation models are employed in biology to describe the dynamics of certain populations and their interaction with the environment. In this paper we analyze a non-linear system describing community intervention in mosquito control through management of their habitats. The system takes the general form:where the function h ∈ C 1 ([0, ∞) → [0, 1]) satisfying certain properties, will denote either h(t) = h 1 (t) = e −t and/or h(t) = h 2 (t) = 1/(1 + t). We give conditions in terms of parameters for boundedness and stability. This enables us to explore the dynamics of prevalence/community-activity systems as affected by the range of parameters.

In this work, we analyze a system of nonlinear difference equations describing community intervention in mosquito control. More specifically, we extend the model given in [M. Predescu, R. Levins, T. Awerbuch, Analysis of a nonlinear system for community intervention in mosquito control, Discrete Contin. Dyn. Syst. Ser. B 6 (3) (2006) 605-622] to allow for consciousness to be created in an ongoing way by educational efforts that are independent of the presence of mosquito breeding sites. In order to quantify the effect of random external events, such as weather or public concerns, we consider a stochastic version of the model. Numerical simulations show that the stochastic model is consistent with the deterministic one.

In this paper, we formulate a nonlinear system of difference equations that models the three-stage life cycle of the deer tick over four seasons. We study the effect of seasonality on the stability and oscillatory behavior of the tick population by comparing analytically the seasonal model with a non-seasonal one. The analysis of the models reveals the existence of two equilibrium points. We discuss the necessary and sufficient conditions for local asymptotic stability of the equilibria and analyze the boundedness and oscillatory behavior of the solutions. A main result of the mathematical analysis is that seasonality in the life cycle of the deer tick can have a positive effect, in the sense that it increases the stability of the system. It is also shown that for some combination of parameters within the stability region, perturbations will result in a return to the equilibrium through transient oscillations. The models are used to explore the biological consequences of parameter variations reflecting expected environmental changes.

BackgroundEthnic density (the proportion of ethnic minority populations in a geographic area) has emerged as an important factor determining population health. By examining the relationship between mortality rates and the proportion of aboriginal population in Taiwan, this ecological approach highlights the pressing need to understand why aboriginal health remains relatively disadvantaged affecting the population as a whole, especially given the provision of universal health coverage.MethodsUsing combined data from various government departments in Taiwan, we first compare overall mortality rates between aboriginal people and the general population in Taiwan’s 21 administrative locations during the years 2010 and 2011. Then we describe the associations between ethnic density and the relative risk of 40 different causes of death.ResultsAboriginal people in Taiwan on average have higher overall mortality rates than the general population. The proportion of aboriginal population is associated with a higher risk of death for overall mortality, homicide, vehicle crashes, tuberculosis, and several alcohol-related diseases such as peptic ulcer, chronic liver disease, and cirrhosis. These affect the health of the general population in counties where aborigines are abundant.ConclusionThe proportion of aboriginal population may play an essential role in determining Taiwan’s population health. When universal health coverage is in place, the root causes (for example, alcoholism, culture, and socioeconomic disadvantages) of health disparities between aboriginal populations and general populations need to be addressed.