Infectious diseases continue to have a major impact on individuals, populations, and the economy, even though some of them have been eradicated (e.g. small pox). Unlike many other ecological systems, many infectious diseases are well documented by spatio-temporal data sets of occurrence and impact. In addition, in particular for childhood diseases, the dynamics of the disease in a single individual are fairly well understood and fairly simple. As such, infectious diseases are a great field for mathematical modeling, and for connecting these models to data. In this article, we concentrate on three issues, namely (1) comparative childhood disease dynamics and vaccination, (2) spatio-temporal disease dynamics, and (3) evolution in diseases with multiple strains. The mathematical techniques used in the analysis of disease models contain bifurcation theory for ODEs, wavelet analysis, stochastic simulations and various forms of data fitting.
This paper offers a simple approach to the theory of decentralizing inventory and pricing decisions within a distribution system. We consider an upstream manufacturer selling to two outlets, which compete as differentiated duopolists and face uncertain demand. Demand spillovers between the outlets arise in the event of stock-outs. The price mechanism, in which each outlet simply pays a wholesale price and chooses price and inventory, never coordinates incentives efficiently. Contracts that can elicit first-best decisions include resale price floors or buy-back policies (retailer-held options to sell inventory back to the manufacturers) with fixed fees. The combination of a buy-back option plus a resale price ceiling elicits the first-best without the need for a fixed fee and is robust to asymmetry in information about demand at the time of contracting.