Spatial Deterministic Epidemics

Rass, Linda; Radcliffe, John

doi:10.1090/surv/102

Cited by 107 publications

(93 citation statements)

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“…The classical SIR (susceptible/infected/removed) model is one of the cornerstones of mathematical epidemiology, describing the dynamics of infection in a single population [18,5]. The analysis of infection spread through linked systems of populations such as urban centres is of great importance [20] and attracts considerable interest, in particular for planning the response to emerging pandemic diseases. An excellent review of a huge literature on spatial epidemic models can be found in [15].…”

Section: Introductionmentioning

confidence: 99%

The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

Sazonov

Kelbert

Gravenor

2008

Math. Model. Nat. Phenom.

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Abstract. A one-dimensional lattice of SIR (susceptible/infected/removed) epidemic centres is considered numerically and analytically. The limiting solutions describing the behaviour of the standard SIR model with a small number of initially infected individuals are derived, and expressions found for the duration of an outbreak. We study a model for a weakly mixed population distributed between the interacting centres. The centres are modelled as SIR nodes with interaction between sites determined by a diffusion-type migration process. Under the assumption of fast migration, a one-dimensional lattice of SIR nodes is studied numerically with deterministic and random coupling, and travelling wave-like solutions are found in both cases. For weak coupling, the main part of the travelling wave is well approximated by the limiting SIR solution. Explicit formulae are found for the speed of the travelling waves and compared with results of numerical simulation. Approximate formulae for the epidemic propagation speed are also derived when coupling coefficients are randomly distributed, they allow us to estimate how the average speed in random media is slowed down.

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Section: Introductionmentioning

confidence: 99%

The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

Sazonov

Kelbert

Gravenor

2008

Math. Model. Nat. Phenom.

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“…For continuous time systems, the analysis of epidemic spread in terms of traveling waves and spreading speeds have been studied by many authors (see e.g. [17] and references therein. )…”

Section: Introductionmentioning

confidence: 99%

A discrete time model for epidemic spread: traveling waves and spreading speeds

Aydogmus¹

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. In this paper, we aim to study spread of an epidemic in a spatially strati…ed population with non-overlapping generations. We consider mean …eld equation of an endemic chain-binomial process and allow individuals to disperse in the spatial habitat. To be able to model the spatial movement, we used an averaging kernel. The existence of traveling waves for traveling wave speeds greater than a certain minimum is proved. In addition, an explicit formula for the critical wave speed is given in terms of the moment generating function of the dispersal kernel and the basic reproductive ratio of the infectives.

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“…As the medical program to diminish such a threat, the vaccination seems to be the most likely method to control and prevent the infectious disease spread. Mathematical models have become important tools in analyzing the infectious spread and in constructing the vaccination program [2][3][4][5][6][7][8][9][10][11]. In the past, various kinds of the infectious disease models with vaccination have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Optimal Vaccination Problems for the Stochastic SIR Model with Saturated Treatment

Ishikawa

2013

Stochastic Systems Theory and its Applications (SSS)

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This paper is concerned with the control strategy by vaccination of the infectious disease spread in the populations consisting of the susceptible, the infected and the recovered (SIR). In the realistic spread of the infectious disease, changes in the environment and the weather cause some kinds of random fluctuations in the infection and the recovery rates, etc. Moreover, medical facilities have generally the maximal capacity for treatment of diseases. Taking these facts into consideration, we propose the stochastic infectious model with vaccination and saturated treatment, and we consider the stochastic optimal vaccination problem for the SIR model with saturated treatment using the stochastic maximum principle and the four-step scheme.

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Spatial Deterministic Epidemics

Cited by 107 publications

References 0 publications

The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

A discrete time model for epidemic spread: traveling waves and spreading speeds

Optimal Vaccination Problems for the Stochastic SIR Model with Saturated Treatment

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