Spatial models of vector-host epidemics with directed movement of vectors over long distances

Fitzgibbon, W. E.; Morgan, Joseph A.; Webb, Glenn; Wu, Yixiang

doi:10.1016/j.mbs.2019.04.003

Cited by 8 publications

(3 citation statements)

References 43 publications

(55 reference statements)

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“…There are a large number of research studies, conference proceedings and monograph in both PDE and ODE models in the literature. We list only some of them here as examples, e.g., [2,3,11,18,35] for the SIR ODE models and [1,13,17,24,32,41] for the SIR PDE models. Many more references can be found in a SIAM Review paper by Hethcote [23] and the monograph by Busenberg and Cooke [7], Cantres and Cosner [8], Daley and Gani [11], Lou and Ni [32], etc.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis for a Nonlinear Reaction-Diffusion System Modeling an Infectious Disease

Yin¹,

Zou²

2022

Preprint

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In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human hosts may lose a lifetime immunity and could be infected again. Another important feature in the model is that the mobility for each species is allowed to be dependent upon both the location and time. With the whole population assumed to be susceptible with the bacteria, the model is a strongly coupled nonlinear reaction-diffusion system. We prove that the nonlinear system has a unique solution globally in any space dimension under some natural conditions on the model parameters and the given data. Moreover, the long-time behavior and stability analysis for the solutions are carried out rigorously. In particular, we characterize the precise conditions on variable parameters about the stability or instability of all steady-state solutions. These new results provide the answers to several open questions raised in the literature.

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Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis for a Nonlinear Reaction-Diffusion System Modeling an Infectious Disease

Yin¹,

Zou²

2022

Preprint

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“…Bluetongue is listed as a notifiable disease by the World Organisation for Animal Health (OIE) [21]. The mechanisms for the introduction of BTV from endemic to disease-free areas include movements of infected animals and the passive flight of infected midges by wind [10]. Controlling BTV outbreaks locally and globally are a big concern to the ruminant livestock sector.…”

Section: Introductionmentioning

confidence: 99%

Optimal control analysis of bluetongue virus transmission in patchy environments connected by host and wind-aided midge movements

Mugabi

Duffy

Mugisha

et al. 2021

J. Appl. Math. Comput.

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Bluetongue, a midge-borne disease of ruminants caused by the bluetongue virus (BTV) can rapidly spread from one region (patch) to another by host and/or midge movements, making its control difficult. A multi-patch deterministic model for BTV is formulated and analysed to evaluate the effectiveness of vaccination, quarantine, insecticide spraying and the use of repellent control strategies in reducing the within and between-patches transmission. By using optimal control theory, the effectiveness of these strategies is established. Incremental cost-effectiveness ratios are calculated to determine the most cost-effective strategy. In a single patch, vaccination, insecticide spraying and the use of repellents are all highly effective in minimising transmission, but the most cost-effective is vaccination. In patches connected by host and midge movements, if any of these controls is applied in a high-risk patch, a disease-free status is achieved in both patches, but if implemented in a low-risk patch, it is not attained in any patch. If hosts and midges move, quarantine has no effect, but for no midge movement, the effect can be large in a low-risk patch if it's internally imposed.

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“…Modelling studies on the spread of infection include analyses simulating the movement of people and pathogens in such 2-D spaces akin to the horizontal flow and dispersion of physical substances (Smallman-Raynor, Cliff & Barford, 2015;Haggett, 1976;Reluga, Medlock & Galvani, 2006;Birrell et al, 2016;Simoes, 2005;Chen et al, 2005;Fitzgibbon et al, 2019). For example, Simoes (2005) used an agent-based model (ABM) focused on infected individuals and Fitzgibbon et al (2019) used a geographical information system (GIS)-based model. However, a limited number of such studies, clearly describe the system of time evolution equations underlying their model.…”

Section: Introductionmentioning

confidence: 99%

Verification of Infection Prevention Control Using a Spatial Random Walk Model

Ichinose

Tian²,

Li³

2020

IJSSS

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To stop pandemic of the 2019 novel coronavirus (COVID-19), "an 80 percent reduction of person to person contact opportunities" was proposed by the Japanese government. This guideline was based on the result of macroscopic differential equation model akin to the SIR (Susceptible-Infected-Recovered) model. For the purpose of indicating person to person’s infection mechanism intuitively, we built a new model to calculate infections between two persons who are in contact each other. This model adopted a spatial random walk model to express random movement of people in a specific 2-D geographical space. This model was applied to verify the effect of the proposed infection control procedure, "80 percent reduction". The result of the numerical simulation supported a proposed infection control procedure of "an 80 percent reduction" derived by the SIR model.

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Spatial models of vector-host epidemics with directed movement of vectors over long distances

Cited by 8 publications

References 43 publications

Asymptotic Analysis for a Nonlinear Reaction-Diffusion System Modeling an Infectious Disease

Asymptotic Analysis for a Nonlinear Reaction-Diffusion System Modeling an Infectious Disease

Optimal control analysis of bluetongue virus transmission in patchy environments connected by host and wind-aided midge movements

Verification of Infection Prevention Control Using a Spatial Random Walk Model

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