A Mathematical Model for Mosquito Population Dynamics with Genetics of Insecticide Resistance

In this study, a deterministic mathematical model for mosquito population dynamics is presented. The use of chemical insecticide to control population is incorporated into the model. It is assumed that there is insecticide sensitive (sensitive-type) and insecticide resistant (resistant-type) mosquitoes in the environment. Conditions for the existence and stability of four equilibria of the model have been established. Numerical simulations are carried out to confirm the analytical results and the implications, in terms of mosquito control in the environment, are discussed

Investigation of the Qualitative Behavior of the Equilibrium Points for a Modified Lotka-Volterra Model

We are interested in a modified Lotka-Volterra model to analyze population dynamics of two competing species which are ecologically identical (that is, they use the same resource). The model incorporates a non-linear relationship to represent the interaction between the species. We study the stability of the equilibrium points of the system and compare the qualitative behavior of the equilibrium points in our model with qualitative behavior of the classical Lotka-Volterra equations. Our result suggests that in some cases the modified model may have more than one equilibrium points in the interior of the first quadrant, which biologically means that the two species may co-exist at multiple positive population sizes

Investigation of a Pest Control Method Involving Chemical and Biological Methods Using the Lotka-Volterra Model with Fishing

We are modeling two insect populations which have a prey and preda­tor relationship. If it is not controlled the prey can destroy agricultural fields. To prevent the outbreak of the prey population, pesticides are widely used. The pesticides kill the prey and may also kill the predator. We used the Lotka-Volterra model with fishing (pesticide is the fishing agent) to model the prey-predator relationship, which is dX/dt = { a - e - b Y) X, dY/dt = { dX - c - f) Y. Our results suggest that, in the presence of the predator, predation alone (with out pesticide) can help to keep the prey population at low level. In some situations using pesticides can cause an increase of the prey population and it can cause also seasonal (periodic) pest (prey) outbreaks

Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics: Optimal control analysis

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.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 disease-free 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.National Institute for Mathematical and Biological SynthesisNSF Award # EF-0832858The University of Tennessee, Knoxvill

Mathematics of a single-locus model for assessing the impacts of pyrethroid resistance and temperature on population abundance of malaria mosquitoes

Please read abstract in the article.http://www.keaipublishing.com/en/journals/infectious-disease-modelling/Mathematics and Applied Mathematic

Optimal insecticide-treated bed-net coverage and malaria treatment in a malaria-HIV co-infection model

We propose and study a mathematical model for malaria-HIV co-infection transmission and control, in which malaria treatment and insecticide-treated nets are incorporated. The existence of a backward bifurcation is established analytically, and the occurrence of such backward bifurcation is influenced by disease-induced mortality, insecticide-treated bed-net coverage and malaria treatment parameters. To further assess the impact of malaria treatment and insecticide-treated bed-net coverage, we formulate an optimal control problem with malaria treatment and insecticide-treated nets as control functions. Using reasonable parameter values, numerical simulations of the optimal control suggest the possibility of eliminating malaria and reducing HIV prevalence significantly, within a short time horizon

Mathematics of an epidemiology-genetics model for assessing the role of insecticides resistance on malaria transmission dynamics

Although the widespread use of indoors residual spraying (IRS) and insecticides treated bednets (ITNs; later replaced by long-lasting insecticidal nets (LLINs)) has led to a dramatic reduction of malaria burden in endemic areas, such usage has also resulted in the major challenge of the evolution of insecticide resistance in the mosquito population in those areas. Thus, efforts to combat malaria also include the urgent problem of effectively managing insecticide resistance. This study is based on the design and analysis of a new mathematical model for assessing the impact of insecticides resistance in the mosquito population (due to widespread use of IRS and ITNs) on the transmission dynamics and control of malaria in a community. The model, which couples disease epidemiology with vector population genetics, incorporates several fitness costs associated with insecticide resistance. Detailed rigorous analysis of the model is presented. Using data and parameter values relevant to malaria dynamics in moderate and high malaria transmission settings in some parts of Ethiopia, simulations of the model show that, while the ITNs-IRS strategy can lead to the effective control of the disease in both the moderate and high malaria transmission setting if the ITNs coverage level in the community is high enough (regardless of the level of IRS coverage), it fails to manage insecticide resistance (as measured in terms of the frequency of resistant allele at equilibrium in the community). It is further shown that the effective size of the coverage level of the ITNs and IRS required to effectively control the disease, while effectively managing insecticide resistance in the mosquito population, depends on the magnitude of the level of resistant allele dominance (in mosquitoes with heterozygous genotype) and several fitness costs associated with the insecticide resistance in the vector population. For instance, in a moderate transmission setting, malaria burden can be reduced to low levels of endemicity (even with low coverage of ITNs and IRS), and insecticide resistance effectively managed, if the fitness costs of resistance are at their assumed baseline values. Such reduction is not achievable if the fitness costs of resistance are lower than the baseline values.https://www.elsevier.com/locate/mbshj2020Mathematics and Applied Mathematic

Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics: Optimal control analysis

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 disease-free 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. Keywords: Malaria, Insecticide resistance, ITNs, IRS, Equilibri