Tuesday, February 2, 2016

Modeling Illicit Drug Use Dynamics and Its Optimal Control Analysis

The global burden of death and disability attributable to illicit drug use, remains a significant threat to public health for both developed and developing nations. 

This paper presents a new mathematical modeling framework to investigate the effects of illicit drug use in the community. In our model the transmission process is captured as a social “contact” process between the susceptible individuals and illicit drug users. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. 

Using our model, we present illustrative numerical results with a case study in Cape Town, Gauteng, Mpumalanga and Durban communities of South Africa. In addition, the basic model is extended to incorporate time dependent intervention strategies.

Below:  Model system (2) fitted to data for individuals seeking treatment due to illicit drug use. The blue circles indicate the actual data and the solid line indicates the model fit to the data.

Below:  Dynamics of system (C.3) showing the effects of optimal control strategies on eliminating or reducing illicit drug use in the community

Full article at:   http://goo.gl/swAlzU

University of Zimbabwe, Department of Mathematics, P.O. Box MP 167, Harare, Zimbabwe
*Steady Mushayabasa: Email: moc.liamg@ayahsumydaets

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