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Is it possible to break the host-vector chain of transmission when there isan influx of infectious hosts into a na\"{i}ve population and competent vector?To address this question, a class of vector-borne disease models with anarbitrary number of infectious stages that account for immigration of infectiveindividuals is formulated. The proposed model accounts for forward and backwardprogression, capturing the mitigation and aggravation to and from any stages ofthe infection, respectively. The model has a rich dynamic, which depends on thepatterns of infected immigrant influx into the host population and connectivityof the transfer between infectious classes. We provide conditions under whichthe answer of the initial question is positive.

Effects of migration on vector-borne diseases with forward and backward stage progression