The large-scale use of insecticide-treated bednets(ITNs)and indoor residual spraying(IRS),over the last two decades,has resulted in a dramatic reduction of malaria incidence globally.However,the effectiveness of these...The large-scale use of insecticide-treated bednets(ITNs)and indoor residual spraying(IRS),over the last two decades,has resulted in a dramatic reduction of malaria incidence globally.However,the effectiveness of these interventions is now being threatened by numerous factors,such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening(when humans are not protected by the bednets).This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics.A notable feature of the model is that it stratifies the mosquito population in terms of type(wild or resistant to insecticides)and feeding preference(indoor or outdoor).The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial diseasefree equilibrium,the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist).Simulations of the model,using data relevant to malaria transmission dynamics in Ethiopia(a malaria-endemic nation),show that the use of optimal ITNs alone,or in combination with optimal IRS,is more effective than the singular implementation of an optimal IRS-only strategy.Further,when the effect of the fitness cost of insecticide resistance with respect to fecundity(i.e.,assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes)is accounted for,numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease,and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community.展开更多
We investigate the mathematical properties of a“truly nonlinear”oscillator differential equation.In particular,using phase-space methods,it is shown that all solutions are periodic and the fixed-point is a nonlinear...We investigate the mathematical properties of a“truly nonlinear”oscillator differential equation.In particular,using phase-space methods,it is shown that all solutions are periodic and the fixed-point is a nonlinear center.We calculate both exact and approximate analytical expressions for the period,where the exact solution is given in terms of elliptic functions and the method of harmonic balance is used to calculate the approximate formula.展开更多
基金The authors are grateful to National Institute for Mathematical and Biological Synthesis(NIMBioS)for funding theWorking Group on Climate Change and Vector-borne Diseases(VBDs)held from 2013 to 2015.NIMBioS is an Institute sponsored by the National Science Foundation,the U.S.Department of Homeland Security,and the U.S.Department of Agriculture through NSF Award#EF-0832858with additional support from The University of Tennessee,Knoxville.The authors are grateful to the anonymous reviewers for their constructive comments.
文摘The large-scale use of insecticide-treated bednets(ITNs)and indoor residual spraying(IRS),over the last two decades,has resulted in a dramatic reduction of malaria incidence globally.However,the effectiveness of these interventions is now being threatened by numerous factors,such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening(when humans are not protected by the bednets).This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics.A notable feature of the model is that it stratifies the mosquito population in terms of type(wild or resistant to insecticides)and feeding preference(indoor or outdoor).The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial diseasefree equilibrium,the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist).Simulations of the model,using data relevant to malaria transmission dynamics in Ethiopia(a malaria-endemic nation),show that the use of optimal ITNs alone,or in combination with optimal IRS,is more effective than the singular implementation of an optimal IRS-only strategy.Further,when the effect of the fitness cost of insecticide resistance with respect to fecundity(i.e.,assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes)is accounted for,numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease,and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community.
基金supported in part by CAU School of Arts and Sciences Faculty Development Funds.
文摘We investigate the mathematical properties of a“truly nonlinear”oscillator differential equation.In particular,using phase-space methods,it is shown that all solutions are periodic and the fixed-point is a nonlinear center.We calculate both exact and approximate analytical expressions for the period,where the exact solution is given in terms of elliptic functions and the method of harmonic balance is used to calculate the approximate formula.
