Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments

[摘要] ENGLISH ABSTRACT : Substance abuse is a major problem globally with immeasurable consequences tothe health of users. Rehabilitation is one of the strategies that can help to fightagainst substance abuse. It is divided into two forms: in-patient and out-patient rehabilitation.In this study, we consider a compartmental model of substance usersin rehabilitation, where a periodic function is included to illustrate seasonal oscillationsof drug users entering rehabilitation. In this thesis, we derive two basic reproductionnumbers R0 and [R0], where R0 is the model with periodicity and [R0]the model without periodicity. We show that the model has a drug-free equilibriumwhen the basic reproduction number R0 is less than one and drug persistentequilibrium when R0 is greater than one. We fit the model to data and obtainedsneak preview of the future of these forms of rehabilitation. Our results indicatethat when R0 is less than one, the in- and out-patient populations decrease quicklyand when R0 is greater than one drugs persists and after a long period of time, individuals in rehabilitation approaches w-periodic solution. Sensitivity analysis isperformed and the results show that control measures should focus on the effectivecontact rate between susceptibles and drug users so as to control the epidemic.These results have significant implications on the management and planning of rehabilitationprograms in South Africa.

[发布机构] Stellenbosch University