On the dynamics of a deterministic and stochastic model for mosquito control

Predescu, Mihaela; Sirbu, George; Levins, Richard; Awerbuch-Friedlander, Tamara

doi:10.1016/j.aml.2006.12.001

Cited by 18 publications

(10 citation statements)

References 9 publications

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“…Moreover, several long-term studies on Ae. aegypti abundance have shown the abundance of this mosquito species to be correlated with different environmental factors, primarily rainfall and temperature (Barrera et al 2011;Dibo et al 2008;Foo et al 1985;Ho et al 1971;Oo et al 2011;Schultz 1993;Scott et al 2000;Tonn et al 1970), but also with "socio-ecological" factors such as unreliable water supply (Barrera et al 1993;Padmanabha et al 2010) or lack of community engagement in proper water container disposal (Predescu et al 2007). Similar patterns of association between mosquito abundance and weather fluctuations have been observed in other Aedes spp.…”

Section: Introductionmentioning

confidence: 99%

Hot temperatures can force delayed mosquito outbreaks via sequential changes in Aedes aegypti demographic parameters in autocorrelated environments

et al. 2014

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Aedes aegypti L. (Diptera: Culicidae) is a common pantropical urban mosquito, vector of dengue, Yellow Fever and chikungunya viruses. Studies have shown Ae. aegypti abundance to be associated with environmental fluctuations, revealing patterns such as the occurrence of delayed mosquito outbreaks, i.e., sudden extraordinary increases in mosquito abundance, following transient extreme high temperatures. Here, we use a two-stage (larvae and adults) matrix model to propose a mechanism for environmental signal canalization into demographic parameters of Ae. aegypti that could explain delayed high temperature induced mosquito outbreaks. We performed model simulations using parameters estimated from a weekly time series from Thailand, assuming either independent or autocorrelated environments. For autocorrelated environments, we found that long delays in the association between the onset of "hot" environments and mosquito outbreaks (10 weeks, as observed in Thailand) can be generated when "hot" environments sequentially trigger a larval survival decrease and over-compensatory fecundity increase, which lasts for the whole "hot" period, in conjunction with a larval survival increase followed by a fecundity decrease when the environment returns to "normal". This result was not observed for independent environments. Finally, we discuss our results implications for prospective entomological research and vector management under changing environments.

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Section: Introductionmentioning

confidence: 99%

Hot temperatures can force delayed mosquito outbreaks via sequential changes in Aedes aegypti demographic parameters in autocorrelated environments

et al. 2014

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“…Lemma 1. Let { , , , } ≥0 be a positive solution of system (4). Parameters are such that 0 < < 1, 0 < < 1, 0 < < 1, and 0 < < 1.…”

Section: Boundedness Of Solutionsmentioning

confidence: 99%

“…Proof. First equation of system (4) gives +1 ≤ +(1− ) ≤ + 1. Thus lim sup → ∞ ≤ 1/(1 − ) and then for any positive number , there exists sufficiently large, such that, for all ≥ ,…”

Section: Boundedness Of Solutionsmentioning

confidence: 99%

“…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]. In a study with three difference equations, we study a system in which the information is related to the number of adult mosquitoes.…”

Section: Introductionmentioning

confidence: 99%

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

Awerbuch-Friedlander

Levins

Predescu

2014

Discrete Dynamics in Nature and Society

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In the case of Dengue transmission and control, the interaction of nature and society is captured by a system of difference equations. For the purpose of studying the dynamics of these interactions, four variables involved in a Dengue epidemic, proportion of infected people (P), number of mosquitoes involved in transmission (M), mosquito habitats (H), and population awareness (A), are linked in a system of difference equations:Pn+1=aPn+1-e-iMn1-Pn,Mn+1=lMne-An+bHn1-e-Mn,Hn+1=cHn/(1+pAn)+1/(1+qAn), andAn+1=rAn+fPn,n=0,1,…. The constraints have socioecological meaning. The initial conditions are such that0≤P0≤1, (M0,H0,A0)≥(0,0,0), the parametersl,a,c,r∈(0,1), and the parametersf, i, b, andpare positive. The paper is concerned with the analysis of solutions of the above system forp=q. We studied the global asymptotic stability of the degenerate equilibrium. We also propose extensions of the above model and some open problems. We explored the role of memory in community awareness by numerical simulations. When the memory parameter is large, the proportion of infected people decreases and stabilizes at zero. Below a critical point we observe periodic oscillations.

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“…The importance of controlling mosquito populations is hard to overstate. It is well known that such diseases as yellow fever, dengue fever, epidemic polyarthritis, Rift Valley fever, Ross River Fever, St. Louis encephalitis, West Nile virus, Japanese encephalitis, LaCross encephalitis, Zika, and malaria are carried and transmitted by mosquitoes, [15,30,34,35,38,45,47,48].…”

Section: Introductionmentioning

confidence: 99%

Diffusing wild type and sterile mosquitoes in an optimal control setting

Fister

McCarthy

Oppenheimer

2018

Mathematical Biosciences

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This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations.

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On the dynamics of a deterministic and stochastic model for mosquito control

Cited by 18 publications

References 9 publications

Hot temperatures can force delayed mosquito outbreaks via sequential changes in Aedes aegypti demographic parameters in autocorrelated environments

Hot temperatures can force delayed mosquito outbreaks via sequential changes in Aedes aegypti demographic parameters in autocorrelated environments

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

Diffusing wild type and sterile mosquitoes in an optimal control setting

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