Effects of Heterogeneity on the Spread of HIV/AIDS among Intravenous Drug Users in a Spatially Structured Environment

John R. D'Souza, International Institute for Population Sciences (IIPS)
Lysander M. Menezes, International Institute for Population Sciences (IIPS)

We study a simple configuration model of the spread of HIV and AIDS among a population of injecting drug users that includes a parameter for the dimensions of a spatially structured environment. Our blocks are two important papers written by Kaplan (Rev. Infect. Dis. 11: 289-298, 1989) and Greenhalgh (Math. Biosci. 136: 141-186, 1996). The model postulates the existence of “artificial agents”, each of who can be an Altruist or an Egoist. An altruist injecting drug user is one who confers a benefit on the next user by cleaning the syringe after use. An egoist injecting drug user on the other hand does not clean the syringe after using it. We allow for the comparison of disease spread in a spatially non-structured environment with environments where the agents were distributed over a circle. In the model addicts are assumed to gather in locations where needles are shared sequentially. We explicitly represent the following sharing behavior: (a) persistence and (b) rearrangement. Persistent needle sharing behavior would imply a fixed ordering of the sequence in which needles are shared. Rearranging behavior would entail a random switching of positions in the sequence after each time step. Susceptibles entering the population of injecting drug users choose their actions by the learning mechanism of imitation. For various purposes it would be helpful to have information about the spatial contact dynamics of the susceptible class in the presence of such sharing behavior. The technique of clustering (Möbius 2002) is used to characterize the stochastic dynamics that predict the behavior of such a rational epidemic. The impact of spatially dependent intervention strategies is compared with a nonspatially dependent one. This work was motivated by close observation of injecting drug-using behavior in a neighborhood in Mumbai, India as well as insight obtained from Esther Welp (Cluster Infectious Diseases, Municipal Health Service, Amsterdam, Netherlands) regarding the mixing, for the purpose of obtaining drugs, among intravenous drug users located in two areas in Amsterdam: the main city and the outskirts.