Spatial‐temporal basic reproduction number and dynamics for a dengue disease diffusion model

Zhu, Dandan; Ren, Jingli; Zhu, Huaiping

doi:10.1002/mma.5085

Cited by 20 publications

(22 citation statements)

References 27 publications

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“…In fact, free boundary value problems have attracted extensive research efforts and remarkable successes have been achieved. They were used to describe spreading phenomena in many fields, such as, wound healing [5], ice melting [22], the transmission of diseases [1,17,32] and species interaction [6,7,15,29,26,28].…”

Section: Jingli Ren Dandan Zhu and Haiyan Wangmentioning

confidence: 99%

Spreading-vanishing dichotomy in information diffusion in online social networks with intervention

Ren

Zhu

Wang³

2019

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, multiple information diffusion in online social networks with free boundary condition is investigated. We prove a spreadingvanishing dichotomy for the problem: i.e., either at least one piece of information lasts forever or all information suspend in finite time. The criterion for spreading and vanishing is established, it is related to the initial spreading area and the expansion capacity. We also obtain several cases of the asymptotic behavior of the information under different conditions. When the information spreads, we provide some upper and lower bounds of the spreading speed corresponding to different cases of asymptotic behavior of the information. In addition, numerical examples are given to illustrate the impacts of the initial spreading area and the expansion capacity on the free boundary, and all cases of the asymptotic behavior of the information.

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Section: Jingli Ren Dandan Zhu and Haiyan Wangmentioning

confidence: 99%

Spreading-vanishing dichotomy in information diffusion in online social networks with intervention

Ren

Zhu

Wang³

2019

Discrete &Amp; Continuous Dynamical Systems - B

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“…Additionally, many vector-borne disease models with spatial structure employ Eq. (1) as a local description of population dynamics, where the emergence and death rates can take on spatial dependence and X(t) is considered to be a spatially-varying population density [28,29]. Our results will also apply this class of model, provided when controls are allowed to take on spatial dependence and are defined at the local level.…”

Section: Uncontrolled Population Dynamicsmentioning

confidence: 97%

Implicit versus explicit control strategies in models for vector-borne disease epidemiology

Demers

Bewick

et al. 2019

Preprint

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Throughout the vector-borne disease modeling literature, there exist two general frameworks for incorporating vector management strategies (e.g. area-wide adulticide spraying and larval source reduction campaigns) into vector population models, namely, the "implicit" and "explicit" control frameworks. The more simplistic "implicit" framework facilitates derivation of mathematically rigorous results on disease suppression and optimal control, but the biological connection of these results to realworld "explicit" control actions that could guide specific management actions is vague at best. Here, we formally define the biological and mathematical relationships between implicit and explicit control, and we provide detailed mathematical expressions relating the strength of implicit control to management-relevant properties of explicit control for four common intervention strategies. These expressions allow optimal control and sensitivity analysis results in existing implicit control studies to be interpreted in terms of real world actions. Our work reveals a previously unknown fact: implicit control is a meaningful approximation of explicit control only when resonance-like synergistic effects between multiple controls have a negligible effect on average population reduction. When non-negligible synergy exists, implicit control results, despite their mathematical tidiness, fail to provide accurate predictions regarding vector control and disease spread. The methodology we establish can be applied to study the interaction of phenological effects with control strategies, and we present a new technique for finding impulse control strategies that optimally reduce a vector population in the presence of seasonally oscillating model parameters. Collectively, these elements build an effective bridge between analytically interesting and mathematically tractable implicit control and the challenging, action-oriented explicit control.

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“…The long run behavior of system (13) Figure 6 depicts the solutions of model (13) when P = 0 (ie with homogeneity in host's distribution), while Figures 7,8,9,and 10 show the solutions of model (13) in a landscape with heterogeneity in hosts distribution (P > 0). Although mosquito population persists over time, its distribution in the domain is not the same.…”

Section: General Dynamicsmentioning

confidence: 99%

“…To investigate the spatial heterogeneity effect on the mosquito dynamics, we take the variation of human distribution. Figures 8,9,and 10 show the influence of the spatial heterogeneity of hosts on the dynamics of female mosquitoes. From these figures, one observes that spatial distribution of females in gonotrophic cycle is strongly influenced by the hosts density.…”

Section: Impact Of Spatial Heterogeneity On Mosquito Spreadmentioning

confidence: 99%

“…At local scales (ie from 100 m to 1 km), mosquito behavior and ecology play an important role in determining the distribution of transmission . The spatial distribution of anopheles has shown great potential to affect malaria transmission intensity . The success and optimal impact of methods for controlling mosquito population (eg sterile insect technique [SIT], genetically modified mosquitoes [GMM] or mechanical control) are based on a good knowledge of the biology and the behavior of mosquitoes, as well as on an accurate modeling of their dispersal.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical analysis of a spatio‐temporal model for the population ecology of anopheles mosquito

Manyombe

Mbang

Tsanou

et al. 2020

Math Methods in App Sciences

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We propose a novel model for the population dynamics of mosquitoes by considering the dispersal states of female mosquitoes of oviposition's cycle and spatial variations. From the modeling perspective, a general functional form of eggs oviposition rate is used including the Malthusian, the Verhlust‐Pearl logistic, the Hassell, and the Maynard‐Smith‐Slatkin functions. From the theoretical and numerical perspectives, the study is done in two steps using the more realistic birth Maynard‐Smith‐Slatkin function. First, we consider an ordinary differential equations model and show that the mosquito‐free equilibrium (MFE) is globally asymptotically stable, whenever the basic offspring number scriptR0ode is less than unity. Using a fluctuation argument, we prove that the unique mosquito‐persistent equilibrium (MPE) is globally attractive, whenever scriptR0ode exceeds the unity. Moreover, the temporal model undergoes a Hopf bifurcation in the absence of density‐dependent mortality in the aquatic stage of mosquitoes. Second, the temporal model is extended into an advection‐reaction‐diffusion model in order to account for the movement of mosquitoes and their spatial source of heterogeneity. We establish the uniform persistence and the existence of at least one positive steady state whenever the spatial basic offspring number scriptR0pde is greater than unity. Finally, for the case study of malaria vector agent (Anopheles mosquito), we construct a nonstandard finite difference scheme that is dynamically consistent with the features of the continuous model to illustrate our results, including the spatial heterogeneity of mosquito resources.

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Spatial‐temporal basic reproduction number and dynamics for a dengue disease diffusion model

Cited by 20 publications

References 27 publications

Spreading-vanishing dichotomy in information diffusion in online social networks with intervention

Spreading-vanishing dichotomy in information diffusion in online social networks with intervention

Implicit versus explicit control strategies in models for vector-borne disease epidemiology

Mathematical analysis of a spatio‐temporal model for the population ecology of anopheles mosquito

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