Abstract
•Propose a deterministic model to describe the importation and local transmission of vector-borne diseases in Florida.•Consider the transmission of viruses between mosquitoes and humans.•Analyze the basic properties of the model with importation terms.•Use the model to mimic the introduction and local outbreak of Zika in Florida in 2016.•Show the existence of a backward bifurcation in the model without importation.•Discuss some effective control and prevention measures.
Chikungunya, dengue, and Zika viruses are all transmitted by Aedes aegypti and Aedes albopictus mosquito species, had been imported to Florida and caused local outbreaks. We propose a deterministic model to study the importation and local transmission of these mosquito-borne diseases. The purpose is to model and mimic the importation of these viruses to Florida via travelers, local infections in domestic mosquitoes by imported travelers, and finally non-travel related transmissions to local humans by infected local mosquitoes. As a case study, the model will be used to simulate the accumulative Zika cases in Florida. Since the disease system is driven by a continuing input of infections from outside sources, orthodox analytic methods based on the calculation of the basic reproduction number are inadequate to describe and predict their behavior. Via steady-state analysis and sensitivity analysis, effective control and prevention measures for these mosquito-borne diseases are tested.
