Modelling the potential role of control strategies on Ebola virus disease dynamics

Njankou, Sylvie Diane Djiomba (2015-12)

Thesis (MSc)--Stellenbosch University, 2015

Thesis

ENGLISH ABSTRACT : The most deadly Ebola disease epidemic ever was still ongoing as of June 2015 in West Africa. It started in Guinea, where the first cases were recorded in March 2014. Control strategies, aiming at stopping the transmission chain of Ebola disease were publicised through national and international media and were successful in Liberia. Using two different approaches, the dynamics of Ebola disease is described in this thesis. First, a six compartments mathematical model is formulated to investigate the role of media campaigns on Ebola transmission. The model includes tweets or messages sent by individuals with different disease status through the media. The media campaigns reproduction number is computed and used to investigate the stability of the disease free steady state. The presence of a backward bifurcation as well as a forward bifurcation are shown together with the existence and local stability of the endemic equilibrium. We concluded through numerical simulations, that messages sent through media have a time limited beneficial effect on the reduction of Ebola cases and media campaigns must be spaced out in order to be more efficacious. Second, we use a seven compartments model to describe the evolution of the disease in the population when educational campaigns, active case-finding and pharmaceutical interventions are implemented as controls against the disease. We prove the existence of an optimal control set and analyse the necessary and sufficient conditions, optimality and transversality conditions. Using data from affected countries, we conclude using numerical analysis that containing an Ebola outbreak needs early and long term implementation of the joint control strategies.

AFRIKAANSE OPSOMMING : In Junie 2015 was die dodelikste Ebola-epidemie ooit steeds voortslepend inWes-Afrika. Dit het in Guinee uitgebreek, waar die eerste gevalle in Maart 2014 opgeteken is. Beheerstrategieë daarop gemik om die oordragsketting van Ebola te stop is deur die nasionale en internasionale media gepubliseer en was suksesvol in Liberië. In hierdie tesis word die dinamika van Ebola aan die hand van twee verskillende benaderings beskryf. Eerstens is ’n sesvak- wiskundige model geformuleer om die rol van mediaveldtogte in Ebola-oordrag te ondersoek. Die model sluit twiets of boodskappe gestuur deur individue met wisselende siektestatus deur die media in. Die mediaveldtogweergawenommer is bereken en gebruik om die stabiliteit van die siektevry - ewewigstoestand te bespreek. Die teenwoordigheid van ’n terugwaartse bifurkasie asook ’n voorwaartse bifurkasie is getoon, tesame met die voorkoms en plaaslike stabiliteit van die endemie-ewewig. Ons gevolgtrekking deur middel van numeriese simulasies is dat boodskappe wat deur die media gestuur is ’n tydsbeperkte voordelige uitwerking op die vermindering van Ebola-gevalle het en dat mediaveldtogte gespasieer moet word om meer doeltreffend te wees. Tweedens is ’n sewevak-model gebruik om die evolusie van die siekte onder die bevolking te beskryf as opvoedkundige veldtogte, aktiewe gevalopsporing en farmaseutiese intervensies as beheermaatreëls teen die siekte geïmplementeer word. Die studie bewys die bestaan van ’n optimale beheerstel en ontleed die nodige en doeltreffende toestande, optimaliteit en transversaliteitsvoorwaardes. Met behulp van data van lande wat deur die siekte geraak is, is die bevinding ná numeriese analise dat vroegtydige en langtermyn-implementering van die gesamentlike beheerstrategieë nodig is om die uitbreek van Ebola te beheer.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/97813
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