Wolbachia infection dynamics by reaction-diffusion equations

Huang, Mugen; Tang, Moxun; Yu, Jianshe

doi:10.1007/s11425-014-4934-8

Cited by 76 publications

(52 citation statements)

References 28 publications

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“…In future research, we will couple our model to a transmission model and analyse the impact that a Wolbachia-infected mosquito population has on the spread of dengue fever, chikungunya, and Zika. Previous studies have shown spatial heterogeneity in the mosquito population can be an important factor in establishing a sustained Wolbachia infected population [5,19,49]. We will also add heterogeneity to our Wolbachia transmission models to better understand the impact of the diffusion of mosquitoes.…”

Section: Discussionmentioning

confidence: 99%

“…Discrete generation models for female mosquitoes were built to understand unstable equilibrium produced by reduced lifespan or lengthened development [52]. Reaction-diffusion and integro-difference equation models have been used to analyse the impact of insect dispersal and infection spread on invasion of Wolbachia [5,19,45,49]. …”

Section: Existing Mosquito-wolbachia Modelsmentioning

confidence: 99%

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Two-sex mosquito model for the persistence ofWolbachia

Xue

Manore

Thongsripong

et al. 2016

Journal of Biological Dynamics

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We develop and analyse an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachiainfected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit some viral mosquito-transmitted diseases, including dengue fever, chikungunya, and Zika. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to establish an endemic infection in a wild mosquito population. Our transmission model for the adult and aquatic-stage mosquitoes takes into account Wolbachia-induced fitness change and cytoplasmic incompatibility. We show that, for a wide range of realistic parameter values, the basic reproduction number, R 0 , is less than one. Hence, the epidemic will die out if only a few Wolbachiainfected mosquitoes are introduced into the wild population. Even though the basic reproduction number is less than one, an endemic Wolbachia infection can be established if a sufficient number of infected mosquitoes are released. This threshold effect is created by a backward bifurcation with three coexisting equilibria: a stable zeroinfection equilibrium, an intermediate-infection unstable endemic equilibrium, and a high-infection stable endemic equilibrium. We analyse the impact of reducing the wild mosquito population before introducing the infected mosquitoes and observed that the most effective approach to establish the infection in the wild is based on reducing mosquitoes in both the adult and aquatic stages. ARTICLE HISTORY

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Section: Discussionmentioning

confidence: 99%

Section: Existing Mosquito-wolbachia Modelsmentioning

confidence: 99%

Two-sex mosquito model for the persistence ofWolbachia

Xue

Manore

Thongsripong

et al. 2016

Journal of Biological Dynamics

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“…However, we should notice that mosquitoes distribute non-uniformly in nature. By considering the impact of the spatial inhomogeneity on Wolbachia invasion dynamics, we developed a reaction-diffusion system to investigate the spatial spread dynamics of Wolbachia (see [10]). Assume that the insects inhabit in a relatively isolated bounded region, like an isolated island, denoted by Ω ⊂ R n , n 1, whose boundary ∂Ω is smooth.…”

Section: Introductionmentioning

confidence: 99%

“…Hu et al [9], Huang et al [10] and Zheng et al [30] concentrated mainly on the dynamics of infected and uninfected populations in two cases: fitness benefit case (κ 1 κ 2 ) and fitness cost case (κ 1 < κ 2 ). Following the line in [10], we study the stability of the steady-states of (1.2).…”

Section: Introductionmentioning

confidence: 99%

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Qualitative analysis for a Wolbachia infection model with diffusion

Huang

et al. 2016

Sci. China Math.

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We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-Schauder degree theory, we investigate the influence of diffusion on the Wolbachia infection dynamics. After identifying the system parameter regions in which diffusion alters the local stability of constant steadystates, we find sufficient conditions under which the system possesses inhomogeneous steady-states. Surprisingly, our mathematical analysis, with the help of numerical simulations, indicates that diffusion is able to lower the threshold value of the infection frequency over which Wolbachia can invade the whole population.

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Transmission dynamics of visceral leishmaniasis with PKDL and periodic delays

Wang

Fan

et al. 2023

Math Methods in App Sciences

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We consider the transmission of visceral leishmaniasis in three populations: humans, dogs and sandflies. To investigate the effects of spatial heterogeneity and temporal periodicity on disease transmission, a nonlocal periodic reaction-diffusion equation model is developed. We introduce the basic reproduction number R 0 and establish the global dynamics. Numerical simulations show that (i) R 0 is overestimated in the absence of spatial heterogeneity; (ii) R 0 is underestimated without considering the effect of temporal seasonality; and (iii) shortening periodic delays of visceral leishmaniasis reduces the risk of disease transmission.

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Wolbachia infection dynamics by reaction-diffusion equations

Cited by 76 publications

References 28 publications

Two-sex mosquito model for the persistence ofWolbachia

Two-sex mosquito model for the persistence ofWolbachia

Qualitative analysis for a Wolbachia infection model with diffusion

Transmission dynamics of visceral leishmaniasis with PKDL and periodic delays

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