A global mathematical model of malaria transmission dynamics with structured mosquito population and temperature variations

Traoré, Bakary; Koutou, Ousmane; Sangaré, Boureima

doi:10.1016/j.nonrwa.2019.103081

Cited by 22 publications

(17 citation statements)

References 30 publications

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“…The trivial stationary states of system (2.3) are given in the following proposition [8,[11][12][13].…”

Section: Trivial Equilibrium Points Of the Modelmentioning

confidence: 99%

“…The local stability analysis of coexistence equilibrium is given by the following theorem [8,11,12].…”

Section: Coexistence Equilibria Point Of the Modelmentioning

confidence: 99%

“…In this section, we present a sequence of numerical simulations in order to support our mathematical results and to analyze the effect of predation on the dynamics of the two species. We use MATLAB technical computer software [8,12,32]. The values of the parameters are given in Tables 1 and 2.…”

Section: Numerical Experiments and Biological Explanationsmentioning

confidence: 99%

“…These different types of functional responses present a key element for understanding the dynamics of these populations. The main questions concerning population dynamics concern the effects of interaction in the regulation of natural populations, the reduction of their size, the reduction of their natural fluctuations, or the destabilization of the equilibria in oscillations of the states of the population [8][9][10][11][12][13]. The predator-prey relationship is important to maintain the balance between different animal species.…”

Section: Introductionmentioning

confidence: 99%

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A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

2021

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In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.

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“…The trivial stationary states of system (2.3) are given in the following proposition [8,[11][12][13].…”

Section: Trivial Equilibrium Points Of the Modelmentioning

confidence: 99%

“…The local stability analysis of coexistence equilibrium is given by the following theorem [8,11,12].…”

Section: Coexistence Equilibria Point Of the Modelmentioning

confidence: 99%

Section: Numerical Experiments and Biological Explanationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

2021

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“…Several works do exist that are addressing mosquito population dynamics modeling. However, in most of the previous models that have been proposed, the authors have explicitly considered each stage of the vector life cycle when formulating the campartmental model [14,23,25]. To study the impact of time on the dynamics, we skip certain steps in the mosquito's biology and then represent the rest of the steps by a delay parameter.…”

Section: Mathematical Formulation Of the Modelmentioning

confidence: 99%

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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Dynamical Analysis for a Malaria Transmission Model

Zhao

Feng

2022

Qual. Theory Dyn. Syst.

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A global mathematical model of malaria transmission dynamics with structured mosquito population and temperature variations

Cited by 22 publications

References 30 publications

A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

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

Dynamical Analysis for a Malaria Transmission Model

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