Mathematical modeling of malaria transmission global dynamics: taking into account the immature stages of the vectors

Koutou, Ousmane; Traoré, Bakary; Sangaré, Boureima

doi:10.1186/s13662-018-1671-2

Cited by 28 publications

(29 citation statements)

References 28 publications

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“…It has been highlighted in several studies dealing with mosquito growth dynamic and vector-borne diseases. Mathematical studies have proven that this threshold parameter is highly involved in the transmission dynamics of arboviral diseases such as dengue fever, malaria, chikunguya [12,16,25]. Let τ 0 the critical delay value for the mosquito-free equilibrium.…”

Section: Mathematical Analysis Of the Modelmentioning

confidence: 99%

“…Many diseases such as malaria, dengue, West Nile virus etc, are transmitted by mosquitoes. To achieve a high level of effectiveness in reducing the mosquito population and accordingly the vector-borne diseases, a best understanding of mosquito populations dynamics is necessary [12,18]. Mathematical models have been used for many years to gain insights into the complex underlying the global dynamic of the mosquito populations.…”

Section: Introductionmentioning

confidence: 99%

“…In the existing literatures there are several papers which deal with mosquito populations growth dynamics. In [12], Koutou et al have proposed an autonomous mathematical model of mosquito growth dynamics including the immature stages of the vectors. And more recently, by considering the climate effects and applying the theory of uniform persistence and the Floquet theory, Traoré et al [24] have extended the study proposed by Koutou et al Due to the complexity of the dynamics of mosquito populations, and since only the adult female mosquitoes are responsible for transmitting diseases, therefore in general, models only focus on describing the dynamics of adult female mosquitoes, [7,17].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical analysis of mosquito population global dynamics using delayed-logistic growth

Koutou¹,

Sangaré²,

Diabaté³

2020

Malaya J. Mat

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Malaria is a major public health issue in many parts of the world, and the anopheles mosquitoes which drive transmission are key targets for interventions. Consequently, a best understanding of mosquito populations dynamics is necessary in the fight against the disease. Hence, in this paper we propose a delayed mathematical model of the life cycle of anopheles mosquitoes by using delayed-logistic population growth. The model is formulated by inserting the time delay into the logistic population growth rate, that accounts for the period of growth from eggs to the last aquatic stage, which is pupae. Depending on the system parameters, we establish a threshold for survival and extinction of the anopheles mosquitoes population. Moreover, by choosing the time delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when time delay passes through some critical values. Finally, we perform some numerical simulations and the results are well in keeping with the analytical analysis.

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Section: Mathematical Analysis Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical analysis of mosquito population global dynamics using delayed-logistic growth

Koutou¹,

Sangaré²,

Diabaté³

2020

Malaya J. Mat

Self Cite

View full text Add to dashboard Cite

show abstract

“…There are several studies on factors contributing to malaria transmission using mathematical and statistical modelling [18,19]. These models consist of parameters that vary according to internal factors such as climate and external factors such as demography, geography, and human mobility [20].…”

Section: Introductionmentioning

confidence: 99%

Assessment of environmental variability on malaria transmission in a malaria-endemic rural dry zone locality of Sri Lanka: The wavelet approach

et al. 2020

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Malaria is a global public health concern and its dynamic transmission is still a complex process. Malaria transmission largely depends on various factors, including demography, geography, vector dynamics, parasite reservoir, and climate. The dynamic behaviour of malaria transmission has been explained using various statistical and mathematical methods. Of them, wavelet analysis is a powerful mathematical technique used in analysing rapidly changing time-series to understand disease processes in a more holistic way. The current study is aimed at identifying the pattern of malaria transmission and its variability with environmental factors in Kataragama, a malaria-endemic dry zone locality of Sri Lanka, using a wavelet approach. Monthly environmental data including total rainfall and mean water flow of the "Menik Ganga" river; mean temperature, mean minimum and maximum temperatures and mean relative humidity; and malaria cases in the Kataragama Medical Officer of Health (MOH) area were obtained from the

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“…Our goal is, after having a fundamental understanding of the dynamics for the mosquitoes, to have the mosquito models incorporated into disease transmission models for the mosquito-borne diseases [7]. There have been many elaborate works for the dynamical behavior of the transmission of mosquito-borne diseases [8][9][10], but many of these models do not take into account the metamorphic structure differences of mosquito populations. As we know, individuals differ in size or developmental stage, they also differ in their vital rates.…”

Section: Introductionmentioning

confidence: 99%

A discrete-time mathematical model of stage-structured mosquito populations

2019

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This paper proposes a system of difference equations to model mosquito population. In this study, we develop and analyze the stage-structured models which consist of four distinct mosquito metamorphic stages: eggs, larvae, pupae, and adults. First, a model with constant birth rate is studied, and the inherent net reproduction number 0 of the model is derived. If 0 < 1, the extinction equilibrium is globally asymptotically stable. If 0 > 1, there exists a unique positive equilibrium which is uniformly persistent. When breeding is seasonal for a special case, it indicates that a unique globally asymptotically stable periodic solution is admitted when the net reproductive number is larger than one. When this value is less than one, the mosquito population goes to extinction. Finally, numerical simulations to demonstrate our findings and brief discussion are also provided.At last, we proceed to verifying the last inequality (v). For convenience, we denote m = -bs 3 J 21 J 32 , n = -J 44 . Then (v) is equal to 1b 2 s 2 3 J 2 21 J 2 32 2b 2 s 2 3 J 2 21 J 2 32 J 2 44 --bs 3 J 21 J 32 J 2 44

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Mathematical modeling of malaria transmission global dynamics: taking into account the immature stages of the vectors

Cited by 28 publications

References 28 publications

Mathematical analysis of mosquito population global dynamics using delayed-logistic growth

Mathematical analysis of mosquito population global dynamics using delayed-logistic growth

Assessment of environmental variability on malaria transmission in a malaria-endemic rural dry zone locality of Sri Lanka: The wavelet approach

A discrete-time mathematical model of stage-structured mosquito populations

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