Dynamics and spreading speed of a reaction-diffusion system with advection modeling West Nile virus

Cheng, Chengcheng; Zhang, Zheng

doi:10.1016/j.jmaa.2020.124507

Cited by 9 publications

(7 citation statements)

References 31 publications

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“…and Lemma 2.6 in [20], we give the rough estimates about the supper and lower bound of U (x, t), V (x, t), g (t)…”

Section: Assume That (Umentioning

confidence: 99%

“…Tarboush et al [19] studied a WNv model which incorporates a Partial differential equation and an ordinary differential equation with moving boundaries. Cheng and Zheng [20] considered a reaction-advection-diffusion WNv model with double free boundaries and studied the influence of advection term on the boundary asymptotic spreading speeds.…”

Section: Introductionmentioning

confidence: 99%

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Spatial and temporal dynamics of an almost periodic reaction-diffusion system for West Nile virus

Cheng,

Zheng

2020

Preprint

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In current paper, we put forward a reaction-diffusion system for West Nile virus in spatial heterogeneous and time almost periodic environment with free boundaries to investigate the influences of the habitat differences and seasonal variations on the propagation of West Nile virus. The existence, uniqueness and regularity estimates of the global solution for this disease model are given. Focused on the effects of spatial heterogeneity and time almost periodicity, we apply the principal Lyapunov exponent λ(t) with time t to get the initial infected domain threshold L * to analyze the long-time dynamical behaviors of the solution for this almost periodic West Nile virus model and give the spreading-vanishing dichotomy regimes of the disease. Especially, we prove that the solution for this West Nile virus model converges to a time almost periodic function locally uniformly for x in R when the spreading occurs, which is driven by spatial differences and seasonal recurrence. Moreover, the initial disease infected domain and the front expanding rate have momentous impacts on the permanence and extinction of the epidemic disease. Eventually, numerical simulations identify our theoretical results.

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“…and Lemma 2.6 in [20], we give the rough estimates about the supper and lower bound of U (x, t), V (x, t), g (t)…”

Section: Assume That (Umentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatial and temporal dynamics of an almost periodic reaction-diffusion system for West Nile virus

Cheng,

Zheng

2020

Preprint

Self Cite

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“…In fact, the relevant research works on reaction–advection–diffusion model have begun to study the impact of advection on disease transmission (Gu et al. 2014 , 2015a , b ; Tian and Ruan 2018 ; Cheng and Zheng 2021 ). In 2018, Tian and Ruan ( 2018 ) studied the traveling wave of an advection–reaction–diffusion competition system with double free boundaries modeling invasion and competition of and mosquitoes.…”

Section: Introductionmentioning

confidence: 99%

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Wu,

Salmaniw,

Wang

2024

J. Math. Biol.

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Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number $${\mathcal {R}}_0$$ R 0 and show that the disease-free periodic solution is globally attractive when $${\mathcal {R}}_0<1$$ R 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when $${\mathcal {R}}_0>1$$ R 0 > 1 . Moreover, we find that $${\mathcal {R}}_0$$ R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

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“…These models are all governed by a series of ordinary differential equations. Since Lewis et al 12 initiated the investigation of the temporal‐spatial spreading of the diseases, there have been extensive reaction‐diffusion equations for WNV considering the movement of birds and mosquitoes (see Lin et al, 13 Tarboush et al, 14 Wang et al, 15 Lin et al, 16 and Cheng et al 17 ). All the above models are deterministic.…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions for near‐optimal controls of a stochastic West Nile virus system with spatial diffusion

Min-na

Zhang

Zhao

2022

Math Methods in App Sciences

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Near‐optimal controls are as meaningful as optimal controls given both theory and applications; however, they are usually much easier to be obtained than optimal ones, which are simply impossible to be obtained in many complicated systems. Therefore, this paper focuses on the near‐optimal control problems of a stochastic West Nile virus system with spatial diffusion describing the virus transmission among the bird, mosquito, and human populations. First, we introduce two control variables, namely, antimosquito and the treatment of the infected humans, into the system and prove the existence and uniqueness of the global positive solution of the system. Second, the necessary and sufficient conditions for two controls to be near‐optimal are acquired in terms of a Hamiltonian function and a small parameter ε$$ \varepsilon $$ based on the Ekeland principle, the adjoint equation, and some prior estimates. Finally, we use numerical simulations to illustrate the theoretical results and conclude that mosquito control is the most critical factor preventing West Nile virus.

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Dynamics and spreading speed of a reaction-diffusion system with advection modeling West Nile virus

Cited by 9 publications

References 31 publications

Spatial and temporal dynamics of an almost periodic reaction-diffusion system for West Nile virus

Spatial and temporal dynamics of an almost periodic reaction-diffusion system for West Nile virus

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Necessary and sufficient conditions for near‐optimal controls of a stochastic West Nile virus system with spatial diffusion

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