Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction Rate

Kouokam, Etienne; Auger, Pierre; Hbid, Hassan; Tchuenté, Maurice

doi:10.1007/s10441-008-9036-y

Cited by 10 publications

(8 citation statements)

References 11 publications

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“…when the two patches are the same from an epidemiological point of view, an interesting result holds for the mass action transmission law: the global reproductive number is smaller than the local ones. This result is similar to that obtained in Kouokam et al (2008) for a two patch SIRS autonomous model with fast migration, which was extended in that contribution to a set of N [ 2 patches. On the contrary, considering the frequency dependent transmission law yields global reproduction number greater than local ones.…”

Section: Discussionsupporting

confidence: 86%

“…In most of these works migration and epidemic processes are assumed to act at the same time scale. A work were time scales are explicitly considered is Kouokam et al (2008): a spatial SIRS model with migrations being faster than disease transmission and recovery. In the present work we also study a two time scales model coupling migrations and local disease spread but letting migration, transmission and recovery rates to be represented by periodic functions of time.…”

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confidence: 99%

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Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on Two Time Scales

2011

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In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated, system. We derive global reproduction numbers governing the general spatially distributed nonautonomous system through the aggregated system. We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected.

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Section: Discussionsupporting

confidence: 86%

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confidence: 99%

Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on Two Time Scales

2011

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“…Finally, we were able to note that the numerical simulations con�rm the analytical results we have exhibited in this paper. Another track will be to complete our model in order to extent it to more age groups and other compartmental models, such as SEIR or SEIRS [13,34,35]. Finally the effect of spatialization in such models can be investigated as it has been done in [33,34].…”

Section: Discussionmentioning

confidence: 99%

Disease Control in Age Structure Population

Kouokam

Zucker²,

Fondjo

et al. 2013

ISRN Epidemiology

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We combine the Leslie model and its derivatives with the classical compartmental SIRS models to build a model of transmission of infected diseases, in a population of hosts, whether opened or closed systems. We calculate the basic reproductive rate R 0 . Under certain conditions, when 0 < 1, there is a disease-free equilibrium that is locally asymptotically stable. In contrast, when 0 > 1, this equilibrium is unstable. en, through an example, we show how we can de�ne public health strategies to tackle an endemic. �inally we carry a global sensitivity analysis based on this basic reproduction rate to exhibit the most in�uential parameters of our model that are applied to in�uenza.

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“…Due to population dispersal an epidemic model was proposed to describe the dynamics of disease spread among patches in [13]. In [14] the authors considered two-patches where the individuals can move from one patch to another. But the interactions are governed by a classical S I RS model.…”

Section: Mathematical Epidemic Modelmentioning

confidence: 99%

Patches Approach to Investigate the Populational Dynamics in Dengue

Santos

2017

Tend. Mat. Apl. Comput.

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In areas where resources are located in patches or discrete locations, human dispersal is more conveniently modeled, in which the population is divided into discrete patches. In this work we develop a general discrete model to analyze the spread of Dengue disease. In the process of mathematical modeling we take into account the human populations and the circulation of a single serotype of dengue mosquitoes. The movements of susceptible, infected and recovered humans among all patches are considered. Aquatic phases with different carrying capacities are considered within the patches. Also an arbitrary number of patches can be used to simulate the spread of dengue disease. In this paper we performed numerical experiments to show the applicability of this methodology to investigate the dengue disease problem. The general discrete space model was developed for solving epidemiological problems whereas the human-vector interactions and human mobilities play an important role. Based on our numerical results, we may recommend the general patches model for solving epidemiological problems in Population Dynamics.

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Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction Rate

Cited by 10 publications

References 11 publications

Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on Two Time Scales

Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on Two Time Scales

Disease Control in Age Structure Population

Patches Approach to Investigate the Populational Dynamics in Dengue

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