Onset of a vector borne disease due to human circulation - uniform, local and network reproduction ratios

We study the effect of human circulation on the onset of an epidemics for a arboviral (mosquito-borne) illness such as dengue. The underlying dynamics on a metapopulation is given by a classical SIR (human)/SI (vector) model. We consider three concepts of reproduction numbers: local (for each isolated subsys- tem), uniform or mixing (disregarding movement and non-uniformity in the whole region), and network (coupling the patches via human circulation). Interrelations between the three concepts are obtained. Depending on the biological contact as- sumptions, two types of network models result. In destination type models, the force of infection depends on mosquito density, relative to human population or to area. In origin based models, it is assumed that the transmission is determined by the behaviour of susceptible humans. Archetypal examples can be found where each node has local reproduction ratio less than one, the uniform reproduction number is also less than one, but the network reproduction number is greater than one. This shows that the disease can propagate among the patches solely as a consequence of human circulation. An estimate about the effect of vector control on a given patch is given. The conceptual framework presented here may help decision makers to plan vector control policies and medical care in case of an outbreak.