Homelessness and drug misuse in developing countries: A mathematical approach

• A model to analyse homeless and drug misuse is presented.
• The effects of each of them on the other are explored.
• Results from model analysis show homelessness and drug-misuse positively enhances, the growth of each other.

Homelessness and drug-misuse are known to exist like siamese twins. We present a model to capture the dynamics in the growth in the number of homeless (street kids and street adults) and drug misusers. The reproduction numbers of the model are determined and analyzed. Results from this study suggests that adult peer pressure plays a more significant role in the growth of drug-misuse and the number of street kids. This result suggests that in resource constrained settings intervention strategies should be tailor made to target adults whose behaviour influence others to misuse drugs and abuse children. Furthermore, numerical simulations show that homelessness and drug-misuse positively enhances, the growth of each other. Thus, to effectively control these two social problems require strategies targeting both of them.