Mathematical model of malaria transmission dynamics with distributed delay and a wide class of nonlinear incidence rates

Koutou, Ousmane; Traoré, Bakary; Sangaré, Boureima

doi:10.1080/25742558.2018.1564531

Cited by 16 publications

(29 citation statements)

References 32 publications

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“…Figure 3 shows the behavior of dynamics as a function of time. These results show the stability of the dynamics in the absence of cross-diffusion which is in accordance with biological observations [22], [17].…”

Section: B Dynamic Behavior Without the Cross-diffusionsupporting

confidence: 91%

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Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

Ouedraogo¹,

Ouedraogo²,

Sangaré

2019

BIOMATH

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In this paper we propose a nonlinear reaction-diffusion system describing the interaction between toxin-producing phytoplankton and fish population. We analyze the effect of self- and cross-diffusion on the dynamics of the system. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each equilibria based on some conditions on self- and cross-diffusion coefficients. The analytical findings are verified by numerical simulation.

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Section: B Dynamic Behavior Without the Cross-diffusionsupporting

confidence: 91%

“…Proposition III.1. [16], [17], [26] If P(0) ≥ 0 and F(0) ≥ 0, then system (5) has a unique solution defined on the interval [0, ∞). The set {P ≥ 0, F ≥ 0} is positively invariant.…”

Section: Main Theoretical Resultsmentioning

confidence: 99%

Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

Ouedraogo¹,

Ouedraogo²,

Sangaré

2019

BIOMATH

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“…Based on the numerical simulations presented in our paper, we found that large delays would make the steady states unstable because they would lead to oscillations and cyclic behavior that are not observed when delays are very small [1,2,11,22]. However, a delay in negative feedback mechanisms such as intraspecific competition always results in an instability and thus leads to populations cycles or even to populations extinction [11]. We get R m = 7.56 which is greater than unity and τ = 0.76 is greater than the critical value τ 0 .…”

Section: Discussionmentioning

confidence: 87%

“…It usually takes about 1-2 weeks before mosquitoes mature to adulthood, a time frame which is largely relative to the average lifespan of the mosquito. To account for this delay, delay-differential equation models with delay in recruitment are composed [11,24]. Indeed, the three first stages are all aquatic and the adult stage is aerial.…”

Section: Introductionmentioning

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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“…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%

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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Mathematical model of malaria transmission dynamics with distributed delay and a wide class of nonlinear incidence rates

Cited by 16 publications

References 32 publications

Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

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

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

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