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Volume 10, Number 6, 2020, Pages 2682-2703                                                                DOI:10.11948/20200066
Effect of media-induced modification of travel rates on disease transmission in a multiple patch setting
Wei Yang,Chengjun Sun,Julien Arino
Keywords:Epidemiology, Metapopulations, media coverage, nonlinear travel rates, population sizes.
      A general SIS epidemic model is formulated that incorporates media-induced modification of travel rates. Basic local properties of solutions to the model are established. In particular, it is shown that the basic reproduction number does not involve parameters related to the effect of media on travel. The general model is subsequently specialised to two-patch models, with two different scenarios regarding patch population size. Qualitative analyses show that the basic reproduction number acts as a sharp threshold between disease persistence and extinction. The concept of uniform weak persistence is used to prove the existence of an endemic equilibrium and disease uniform strong persistence under a certain condition. Numerical investigations are carried out to gain insight into the analytically tractable and intractable cases, highlighting the importance of considering not only the basic reproduction number but also other measures of disease severity.
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