Per-unit royalty and fixed-fee licensing in a differentiated Stackelberg model

In the present paper we consider a differentiated Stackelberg model, when the leader firm engages in an R&D process that gives an endogenous cost-reducing innovation. The aim is to study the licensing of the cost-reduction by a per-unit royalty and a fixed-fee. We analyse the implications of these types of licensing contracts over the R&D effort, the profits of the firms, the consumer surplus and the social welfare. By using comparative static analysis, we conclude that the degree of the differentiation of the goods plays an important role in the results.

Effects of treatment, awareness and condom use in a coinfection model for HIV and HCV in MSM

We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.