This approximation is most accurate at the beginning of the epidemic and when partnerships are short. Lastly, the model is generalized to allow dependencies among partnerships. This generalization permits proportional mixing with an arbitrary distribution on the number of partners. Elsevier Science Inc. Ail rights reserved. Threshold results for the existence of endemic states are established for most cases.
Uniqueness is shown in each case.
Threshold used are explicitly computable in terms of demographic and epidemiological parameters of the model. Elsevier Science Inc. All rights reserved.