Spatial-Temporal Dynamics in Nonlocal Epidemiological Models

Ruan, Shigui

doi:10.1007/978-3-540-34426-1_5

Cited by 84 publications

(89 citation statements)

References 52 publications

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“…Also, approximately 60% of the 1,500 malaria cases occur each year in the United States are among US travelers (Newman et al, 2004). Therefore, it is more reasonable to consider the combined effect of incubation periods and spatial structure in modeling vectorhost interactions (see Ruan, 2006;Ruan and Xiao, 2004 and the references cited therein) in order to understand the spatial spread of malaria. The prevalence levels decrease as the per capita mortality rate of mosquitoes is increased.…”

Section: Discussionmentioning

confidence: 99%

On the Delayed Ross–Macdonald Model for Malaria Transmission

2008

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The feedback dynamics from mosquito to human and back to mosquito involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a delayed RossMacdonald model. Then we calculate the basic reproduction number R 0 and carry out some sensitivity analysis of R 0 on the incubation periods, that is, to study the effect of time delays on the basic reproduction number. It is shown that the basic reproduction number is a decreasing function of both time delays. Thus, prolonging the incubation periods in either humans or mosquitos (via medicine or control measures) could reduce the prevalence of infection.

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Section: Discussionmentioning

confidence: 99%

On the Delayed Ross–Macdonald Model for Malaria Transmission

2008

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“…In addition, if we wish to consider, as pointed out in Ruan (2007), the effect of spatial heterogeneity (geographical movement), non-local interaction and time delay such as latent period on the spread of the disease, we need to examine an even more general model of the following form:…”

Section: ∂ ∂T I (X T) = D I (X T) + S (X T)mentioning

confidence: 99%

Travelling waves of a diffusive Kermack–McKendrick epidemic model with non-local delayed transmission

Wang

2009

Proc. R. Soc. A.

124

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We obtain full information about the existence and non-existence of travelling wave solutions for a general class of diffusive Kermack-McKendrick SIR models with nonlocal and delayed disease transmission. We show that this information is determined by the basic reproduction number of the corresponding ordinary differential model, and the minimal wave speed is explicitly determined by the delay (such as the latent period) and non-locality in disease transmission, and the spatial movement pattern of the infected individuals. The difficulty is the lack of order-preserving property of the general system, and we obtain the threshold dynamics for spatial spread of the disease by constructing an invariant cone and applying Schauder's fixed point theorem.

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“…Epidemiology: Spatial point processes have been used to model the spread of foot and mouth disease [26]. Kendall [54] proposed the first spatial epidemic PDE model based on the Kermack-McKendrick nonspatial compartment model, and this has been extended to the Diekmann-Thieme model where traits of individuals affect both their susceptibility to infection and their infectiveness to other individuals [77]. Networking: There is a substantial amount of work on mobility models, both at the analytical level and experimentally through traces in the domain of networking [14,69].…”

Section: Applications Of Continuous Spacementioning

confidence: 99%

Spatial Representations and Analysis Techniques

Galpin

2016

Formal Methods for the Quantitative Evaluation of Collective Adaptive Systems

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Abstract. Space plays an important role in the dynamics of collective adaptive systems (CAS). There are choices between representations to be made when we model these systems with space included explicitly, rather than being abstracted away. Since CAS often involve a large number of agents or components, we focus on scalable modelling and analysis of these models, which may involve approximation techniques. Discrete and continuous space are considered, for both models of individuals and models of populations. The aim of this tutorial is to provide an overview that supports decisions in modelling systems that involve space.

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Spatial-Temporal Dynamics in Nonlocal Epidemiological Models

Cited by 84 publications

References 52 publications

On the Delayed Ross–Macdonald Model for Malaria Transmission

On the Delayed Ross–Macdonald Model for Malaria Transmission

Travelling waves of a diffusive Kermack–McKendrick epidemic model with non-local delayed transmission

Spatial Representations and Analysis Techniques

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