## 1992-Kenney, Emelie - Differential equations and the AIDS epidemic: a lecture for Calculus II Students

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Kenney, Emelie A. 1992. Differential equations and the AIDS epidemic: a lecture for Calculus II Students. *PRIMUS*. 2(4): 386-392.

Article Abstract: This paper describes a lecture for Calculus II students in which the Acquired Immune Deficiency Syndrome was used to motivate study of first-order linear differential equations and the derivative as a rate of change. Some figures for study were obtained from the U. S. Center for Disease Control the day before the lecture was given in order to add to the sense of currency of the application.

When I started the journal *PRIMUS – Problems, Resources, and Issues in Mathematics Undergraduate Studies* in 1991 I was looking to publish nuts and bolts, here is what we did in class type pieces. This article is just that.

The author goes through exactly how she uses the material in class and included some items for students (and faculty) in a List of Things to Think About that provides truly thought provoking opportunities for students.

There is data presented from the CDD on the early (and hence exponentially growing) stages of the epidemic; hence the model *P*(*t*) = *P*(0)*e*^{ − kt}. From a differential equation point of view the model is *P*(*t*) = *k**P*(*t*) and from the table of data (weekly # of AIDS cases) provided here from the CDC the students are encouraged to estimate *k*, by approximating *P*(*t*) using differences and then dividing by *P*(*t*) to obtain an estimate of *k*.

The reader and the student are then left to build the model, *P*(*t*) = *P*(0)*e*^{ − kt} , using the estimated *k* and then compare the model’s prediction with the actual data, at least at the start of the epidemic.

The author succeeds in engaging the reader to examine how he/she might engage in modeling in a differential equations class – just what we want in SIMIODE!

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