ABSTRACT
This chapter looks at mathematical models in which a first order differential equation plays a role. The logistic equation is often used by biologists. Apart from Assumptions (A), (B), and (D) there are also other simplifying assumptions built into it. A mathematical model only requires a qualitative description of the solution of the differential equation concerned, in which case it is not even necessary to solve the differential equation! Many problems in economics lead to mathematical mddels in which differential equations play a prominent role. The chapter considers one case of an epidemic to show the complications that can arise, and especially the analysis to obtain reasonable answers. In the long term the management would like to re-invest a part of the profit annually in the company so that the subsequent profits in future years will increase. Suppose a community is struck by an epidemic. The medical authorities will try to contain the spread of the disease, if possible.
