Threshold of disease transmission in a patch environment

Wang, Wendi; Mulone, G.

doi:10.1016/s0022-247x(03)00428-1

Cited by 111 publications

(92 citation statements)

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“…In these models, the population size for each species is either assumed to be constant or the per capita birth rate equals the per capita death rate. In other studies, Wang and colleagues [12,14,15] prove global stability of the disease-free and endemic equilibria and verify that the system is uniformly persistent. The Wang and Mulone model [14] is an SIS epidemic model for n patches with a density-dependent births.…”

Section: Introductionmentioning

confidence: 94%

“…In other studies, Wang and colleagues [12,14,15] prove global stability of the disease-free and endemic equilibria and verify that the system is uniformly persistent. The Wang and Mulone model [14] is an SIS epidemic model for n patches with a density-dependent births. For their model, the patch reproduction numbers do not bound the basic reproduction number.…”

Section: Introductionmentioning

confidence: 94%

“…Models that include host demography and stochastic effects are especially important for wildlife diseases due to the wide variability in wildlife population sizes. Deterministic metapopulation models for the spread of disease in a multi-patch system have been studied by others [8][9][10][11][12][13][14][15]. In a review article by Arino and van den Driessche [11], the existence and stability of the disease-free equilibrium or endemic equilibria in a variety of different metapopulation models are summarized.…”

Section: Introductionmentioning

confidence: 99%

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Multi-patch deterministic and stochastic models for wildlife diseases

McCormack

Allen

2007

Journal of Biological Dynamics

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Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique diseasefree equilibrium exists. In these cases, a basic reproduction number R 0 can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers R j , j = 1, . . . , n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Multi-patch deterministic and stochastic models for wildlife diseases

McCormack

Allen

2007

Journal of Biological Dynamics

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“…Applying this method, we systematically investigate the intervention strategies of a general SIRS (susceptible-infected-recovered-susceptible) model, that is appropriate for the spread of an infectious disease in a geographically dispersed metapopulation of individuals. While the qualitative properties of metapopulation (patchy) epidemic models have been widely studied in the literature, evaluating the intervention strategies in these models has received less attention (see, for instance, [2,3,6,11,14,18,19] and the references therein). It is particularly challenging to understand the dependence of movement between populations on the reproduction number [2,4,5].…”

Section: Introductionmentioning

confidence: 99%

A new approach for designing disease intervention strategies in metapopulation models

Knipl

2015

Journal of Biological Dynamics

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We describe a new approach for investigating the control strategies of compartmental disease transmission models. The method rests on the construction of various alternative next-generation matrices, and makes use of the type reproduction number and the target reproduction number. A general metapopulation SIRS (susceptible-infected-recovered-susceptible) model is given to illustrate the application of the method. Such model is useful to study a wide variety of diseases where the population is distributed over geographically separated regions. Considering various control measures such as vaccination, social distancing, and travel restrictions, the procedure allows us to precisely describe in terms of the model parameters, how control methods should be implemented in the SIRS model to ensure disease elimination. In particular, we characterize cases where changing only the travel rates between the regions is sufficient to prevent an outbreak. ARTICLE HISTORY

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“…Developments of SIR models and their extensions continue to be employed to describe various scenarios in mathematical epidemics, cf. Murray [32], Wang and Mulone [41], Wang and Ruan [42], Wang and Zhao [43], Boni and Feldman [5], Lou and Ruggeri [24], Buonomo and Lacitignola [6], Capone [9], Keeling and Rohani [20], Li et al [23], Ma and Li [25], Buonomo and Rionero [7], Buonomo et al [8], Mulone et al [31], Rionero [34], Rionero and Vitiello [35].…”

Section: Introductionmentioning

confidence: 99%

Modelling alcohol problems: total recovery

2012

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. (2013) 'Modelling alcohol problems : total recovery.', Ricerche di matematica., 62 (1). pp. 33-53. Further information on publisher's website:http://dx.doi.org/10.1007/s11587-012-0138-0Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s11587-012-0138-0.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 1We find that the model has two equilibrium points: one without alcohol problems and one where alcohol problems are endemic in the population. We compare our results with those of an existing model that does not allow for total recovery. We show that without total recovery, the threshold for alcohol problems to become endemic in the population is lowered. The endemic equilibrium solution is also affected, with an increased proportion of the population in the treatment class and a decreased proportion in the susceptible class.Including totally recovery does not determine whether the proportion of individuals with alcohol problems increases or decreases, however it does effect the size of the change. Parameter estimates are made from information regarding binge drinking where we find an increase in the recovery rate decreases the proportion of binge drinkers in the population.

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Threshold of disease transmission in a patch environment

Cited by 111 publications

References 10 publications

Multi-patch deterministic and stochastic models for wildlife diseases

Multi-patch deterministic and stochastic models for wildlife diseases

A new approach for designing disease intervention strategies in metapopulation models

Modelling alcohol problems: total recovery

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