Abstract
We consider a n-patches model, to study the impact of human population movements between cities (patches) in the spread of Chikungunya or even Dengue diseases. In previous works, it was showed that the basic reproduction number can vary from place to place, but this result was obtained without taking into account human movements. We provide a theoretical study of the patchy model, and derive the basic reproduction number, which may depend on Human movement rates between the patches and on local population sizes. We show that the basic reproduction number is bounded by the maximum of local basic reproduction number. We also show that there exists a disease-free equilibrium (DFE) that is locally asymptotically stable whenever the basic reproduction number is less than 1. Under suitable assumptions, DFE is even globally asymptotically stable. We emphasize that Human movements are of particular importance to evaluate the spreading or not of Chikungunya or Dengue diseases, and thus movement rates have to be estimated very accurately. We confirm also the importance of the local basic reproduction numbers and show that even local field interventions can be of benefit to control/reduce the spread of a disease. A complete analytical study for a 2-patches model and several examples are provided to illustrate our conclusion.
Highlights
Chikungunya is a vector-borne disease caused by Aedes albopictus
In Reunion Island, 80% of the population being living at the sea level, we assume that the parameters in the human compartments are the same in each patch
Let us recall that in Reunion Island, it was proved that a mutation in the initial strain leads to a new strain that influences the lifespan of the infected mosquito: it is almost halved [27]
Summary
Chikungunya is a vector-borne disease caused by Aedes albopictus. It is an uncommon and not well-known tropical disease whose dynamics and behaviour are yet to be fully understood [32]. A study has been done on the Sterile Insect Technique as a potential vector control tool for the Chikungunya Disease [22]. Another very important point is that two strains of the virus were isolated in Reunion Island. In [25], the authors have revisited how metapopulation processes operate at various spatial scales (individual level, local, and regional epidemics) They have illustrated the resultant spatio-temporal dynamics by a series of case studies which explore diseases metapopulation dynamics at the interface of models and data. We validate our theoretical results with a two patches model
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