The effect of density dependent emigration on spread of infectious diseases: a modelling study

In this study, we proposed and analyzed an SIS mathematicalmodel by considering population densitydependent emigration. It is assumed that the diseaseis transmitted by direct contact of infective and susceptiblepopulations. We also assumed that the rate ofcontact is emigration dependent i.e. contact rate is variablewhich depends on the current population of habitatas well as on non-emigrating population density of habitat.The equilibria and their stability are studied by usingthe stability theory of differential equations and simulation.The model analysis shows that the spread of infectiousdisease in habitat decreases if the rate of emigrationincreases but it increases as the population density of nonemigratingpopulation increases. The simulation study ofthe model confirms these analytical results