Analysis of a nonlinear system for community intervention in mosquito control

Abstract

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.

Assessing changing weather and the El Niño Southern Oscillation impacts on cattle rabies outbreaks and mortality in Costa Rica (1985–2016)

“…An additional reason could be that surveillance and prevention might be less effective in the Atlantic basin of Costa Rica. For example, underreporting could delay appropriate action and promote a reduced coverage of cattle rabies vaccination, which in turn might lead to larger outbreaks, given an increased susceptibility in host populations without rabies vaccination, as predicted by mathematical models dealing with risk perception and infectious disease transmission prevention [ 70 ]. Actually, the large 1985 outbreak occurred when no control programme was in operation.…”

Codynamics of Four Variables Involved in Dengue Transmission and Its Control by Community Intervention: A System of Four Difference Equations

“…The above graph is generated with parameter values = 0.5, = 0.5, = 5, = 0.6, = 0.5, = 0.5, = 0.5, and = 20 (the parameters are placed in the region where > (1 − )(1 − )). One can see that the solutions display oscillatory behavior for smaller values of .examples of such functions (used in the previous work,[3]) are for instance ℎ 1 ( ) = 1/(1 + ) and ℎ 2 ( ) = 1/(1 + ).…”

“…Mathematical models may serve at designing policy interventions and provide a better understanding of phenomena at study [3]. Because at times interventions are implemented when consciousness is prompted by an increase in the incidence of sick people, one can work with the original system in a form as such:…”

“…In previous work, we studied the dynamics of a discrete time system in which we modeled the awareness as a factor that is triggered by the formation of potential breeding sites and the response was aimed at eliminating them. The system was studied by a pair of two difference equations [3]. By expanding the model to introduce an ongoing educational program, our new model predicted that high consciousness over time kept the number of breeding sites low [4].…”

Beyond buzzing: mosquito watching stimulates malaria bednet use—a household-based cluster-randomized controlled assessor blind educational trial

“…When people hear the sound of buzzing, it is only natural to seek defense against mosquito bites. 2 , 3 , 4 Insecticidal treated bednets (ITNs), especially long-lasting insecticide-treated nets, are effective in preventing malaria and widely used in developing countries. 5 , 6 , 7 ITNs contributed to the dramatic reduction of malaria deaths and cases over the past 10 years.…”