A Refined Difference Equation for Malaria Parasite development

Suggested by Periodic and Chaotic Host-Parasite Interactios in Human Malaria, Dominic Kwiatkowski, Martin Nowak, Proceedings of the National Academy of Sciences of the United States of America, Vol. 88, No. 12 (Jun. 15, 1991), pp. 5111-5113.

The Model:

yt+1 = d1xtf(xt)
xt+1 = rd2ytg(xt)

where

Experimental evidence indicates that

f(xt)>g(xt)
(fever is more harmful to older parasites). The result?

"Initially, the parasite population replicates asynchronously, with a multiplication rate R = rd1d2 every two days. When parasite density increases beyond a certain level, significant fever occurs. This exerts a negative feedback force, terminating exponential growth and causing parasite density to oscillate."

Here's a lisp file that illustrates the effect, and the web version (below). See the paper for the definitions of these parameters. The starting parameters are those of Figure 2.