A patchy model for Chikungunya-like diseases

Abstract

BIOMATHEditor-in-Chief: Roumen Anguelov 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 R 2 0 , the basic reproduction number, which may depend on Human movement rates between the patches and on local population sizes. We show that R 0 is bounded from above (below) by the maximum (minimum) of the values of the local basic reproduction numbers. We also show that there exists a disease-free equilibrium E DF that is locally asymptotically stable whenever R 2 0 < 1. Under suitable assumptions, E DF 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 to know where local basic reproduction numbers are large and show that local field interventions can help to control/reduce the spread of the disease. A full analytical study for the 2-patches model and several simulations are provided to illustrate that human movements can either increase or reduce the spreading of the disease.