We are excited to announce that the repository will soon undergo an upgrade, featuring a new look and feel along with several enhanced features to improve your experience. Please be on the lookout for further updates and announcements regarding the launch date. We appreciate your support and look forward to unveiling the improved platform soon.
dc.contributor.author | Chapwanya, Michael![]() |
|
dc.contributor.author | Lubuma, Jean M.-S.![]() |
|
dc.contributor.author | Lutermann, Heike![]() |
|
dc.contributor.author | Matusse, A.![]() |
|
dc.contributor.author | Nyabadza, F.![]() |
|
dc.contributor.author | Terefe, Y.![]() |
|
dc.date.accessioned | 2022-02-23T08:26:26Z | |
dc.date.issued | 2021 | |
dc.description | This work originated from projects assigned to participants in the 2 nd joint UNISA-UP Work-shop on Mathematical and Theoretical Epidemiology that was held at the University of Pretoria from 2 to 8 March 2015. | en_ZA |
dc.description.abstract | A deterministic mathematical model for the dynamics of cannabis use in a South Africa metropolis of Durban is proposed and analysed. To the analysis the model, the important threshold parameter ℛ0 (the basic reproduction number), is determined. It is proved that the model exhibits multiple cannabis persistent equilibria. For ℛ0 < 1, the model exhibits a backward bifurcation due to double exposure to cannabis sources and re-addiction in the population. More precisely, the locally asymptotically stable cannabis-free equilibrium co-exists with the locally asymptotically stable cannabis persistent equilibrium. Under this situation, the cannabis consumption will remain stay in the population even though ℛ0 < 1. In the absence of double exposure and re-addiction, it is shown that the cannabis-free equilibrium is globally asymptotically stable (GAS) when ℛ0 < 1, while the cannabis persistent equilibrium is GAS when ℛ0 > 1. The model is fitted into the available data and the values of the parameters involved in the model formulation are estimated. Sensitivity analysis of the model, using the parameters involved in the formulation of ℛ0 , is given. Numerical simulation to support the theoretical analysis of the model is provided. | en_ZA |
dc.description.department | Mathematics and Applied Mathematics | en_ZA |
dc.description.department | Zoology and Entomology | en_ZA |
dc.description.embargo | 2022-04-18 | |
dc.description.librarian | hj2022 | en_ZA |
dc.description.sponsorship | The DST/NRF SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences from the University of Pretoria and University of South Africa. | en_ZA |
dc.description.uri | https://www.tandfonline.com/loi/tsms20 | en_ZA |
dc.identifier.citation | M. Chapwanya, J. M. S. Lubuma, H. Lutermann, A. Matusse, F. Nyabadza & Y. Terefe (2021) A mathematical model for the cannabis epidemic in a South African province with a non-linear incidence rate, Journal of Statistics and Management Systems, 24:8, 1627-1647, DOI: 10.1080/09720510.2020.1843274. | en_ZA |
dc.identifier.issn | 0972-0510 (print) | |
dc.identifier.issn | 2169-0014 (online) | |
dc.identifier.other | 10.1080/09720510.2020.1843274 | |
dc.identifier.uri | http://hdl.handle.net/2263/84157 | |
dc.language.iso | en | en_ZA |
dc.publisher | Taylor and Francis | en_ZA |
dc.rights | © Taru Publications. This is an electronic version of an article published in Journal of Statistics and Management Systems, vol. 24, no. 8, pp. 1627-1647, 2021. doi : 10.1080/09720510.2020.1843274. Journal of Statistics and Management Systems is available online at : https://www.tandfonline.com/loi/tsms20. | en_ZA |
dc.subject | Cannabis-free equilibrium | en_ZA |
dc.subject | Cannabis persistent equilibrium | en_ZA |
dc.subject | Backward bifurcation | en_ZA |
dc.subject | Locally asymptotically stable | en_ZA |
dc.subject | Globally asymptotically stable | en_ZA |
dc.title | A mathematical model for the cannabis epidemic in a South African province with a non-linear incidence rate | en_ZA |
dc.type | Postprint Article | en_ZA |