Nonlinear dynamics of the observed HIV-positive population size in Fiji

In this paper, the reported numbers of HIV-positive individuals in Fiji between and including the years 1989 and 2002 have been used to study the dynamics of the observed HIV-positive population size. The Fiji data showed a pattern that appears to begin to approximate the "S" shaped growth pattern. It is well-known in the mathematics literature that this nonlinear pattern is a natural growth phenomenon and that there are suitable mathematical equations--from the classical Verhulst equation to the recent Tsoularis equation--that can be used to study it. These equations generate two-dimensional curves, the uses of which are case-dependent. In this paper, the curves used are the Logistic Curve and the Gompertz Curve, which are known to be relatively accurate in predicting the short-term behaviour of the observed HIV-positive population size at the initial stages of growth. This study showed that the curves, based on the 1989-2002 data, gave the scenarios in which new reported cases could stabilize by 2005 or 2013. Based on the 1989-2001 data, both curves gave the worst-case scenario of continuous increase till the year 2020 when the numbers could begin to stabilize.