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Mathematical models of Ebola virus disease with socio-economic dynamics
Thesis (PhD)--Stellenbosch University, 2019.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2019
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| _version_ | 1867613932449955840 |
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| access_status_str | Open Access |
| author | Djiomba Njankou, Sylvie Diane |
| author2 | Nyabadza, Farai |
| author_browse | Djiomba Njankou, Sylvie Diane Nyabadza, Farai |
| author_facet | Nyabadza, Farai Djiomba Njankou, Sylvie Diane |
| author_sort | Djiomba Njankou, Sylvie Diane |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2019. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/105726 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:43:59.926Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/105726 Mathematical models of Ebola virus disease with socio-economic dynamics Djiomba Njankou, Sylvie Diane Nyabadza, Farai Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics. Ebola virus disease -- Mathematical models Ebola epidemic Diseases -- Social aspects -- Africa Diseases -- Economic aspects -- Africa Human migration -- Mathematical models UCTD Thesis (PhD)--Stellenbosch University, 2019. ENGLISH ABSTRACT : West Africa hosted the deadliest Ebola virus disease epidemic from 2013 to 2016 and one of the common characteristics of the affected countries is their status of being developing countries. Poor economic and social living conditions is a reality in these countries and they have deeply affected the fight against Ebola virus disease. In this work, we focus on the potential impact of socio-economic factors on Ebola virus disease dynamics. First, we use a compartmental model to study the dynamics of Ebola virus disease when there is a limited number of beds for patients. We use a non linear hospitalisation rate and formulate the rate at which the time dependent number of available beds evolves. The results suggest that a timely supply of sufficient beds to Ebola treatment units, limits the spread of the disease by keeping the infectious in one place, during their infectious period. Second, we formulate a mathematical model of Ebola virus disease that considers human behaviour through an exponential non linear incidence rate. Suitable Lyapunov functions are built and the proofs of the global stability of equilibria are presented. The results advocate for an immediate and efficacious behaviour change, as a control measure to rapidly control an Ebola virus disease epidemic. Third, we build a mathematical model of Ebola virus disease dynamics, that describes the introduction of a new strain of Ebola virus, through continuous or impulsive immigration of infectives. The results suggest controlled movements of people between countries that have had Ebola outbreaks. Finally, we develop a model of Ebola virus disease that considers two patches with different economic statuses represented by the respective gross-national incomes of these patches. We assume that susceptible, exposed and recovered individuals from the poorer patch move to the rich patch. The results indicate a decrease of the number of infected individuals in the rich patch when movements of populations are limited through the improvement of the economy in the poor patch. We conclude that the improvement of the economy of poorer countries may be critical in avoiding potential outbreaks of Ebola virus disease. The results in this thesis point to the need to consider socio-economic factors in Ebola virus disease epidemic models. AFRIKAANSE OPSOMMING : Wes-Afrika het die dodelikste epidemie van die Ebola-virus siekte vanaf 2013 tot 2016 gehad en een van die algemene kenmerke van die geaffekteerde lande is hul status as ontwikkelende lande. Swak ekonomiese en sosiale lewensomstandighede is in hierdie lande ’n werklikheid en het die stryd teen Ebola-virus siektes erg beïnvloed. In hierdie tesis het ons gekies om te fokus op die moontlike impak van sosio-ekonomiese faktore op die dinamika van die Ebola-virus siekte. Eerstens gebruik ons ’n kompartementele model om die dinamika van Ebola-virus siekte te bestudeer wanneer daar ’n beperkte aantal beddens vir pasiënte is. Ons gebruik ’n nie-lineêre hospitalisasie koers en formuleer die koers waarteen die tyd afhanklike aantal beskikbare beddens ontwikkel. Die resultate dui daarop dat ’n tydige voorsiening van voldoende beddens vir Ebola-behandelingseenhede die verspreiding van die siekte beperk deur die aansteeklikes op een plek te hou gedurende hul aansteeklike tydperk. Tweedens formuleer ons ’n wiskundige model van Ebola-virus siekte wat menslike gedrag oorweeg deur ’n eksponensiële nie-lineêre voorkomsskoers. Geskikte Lyapunov funksies word gebou en die bewyse van die globale stabiliteit van ewewig word aangebied. Resultate argumenteer vir ’n onmiddellike en doeltreffende gedragsverandering as ’n beheermaatreël om ’n Ebolavirus siekte-epidemie vinnig te beheer. Derdens bou ons ’n wiskundige model van Ebola-virus sindinamika, wat die bekendstelling van ’n nuwe stam Ebola-virus beskryf, deur middel van deurlopende of impulsiewe immigrasie van infektiewe. Resultate dui op beheerde bewegings van mense tussen lande wat Ebola-uitbrake gehad het. Ten slotte, ons ontwikkel ’n model van Ebola-virus siekte wat twee gebiede met verskillende ekonomiese statusse beskou, verteenwoordig deur die onderskeie bruto nasionale inkomste van hierdie gebiede. Ons aanvaar dat vatbare, blootgestelde en verhaalde individue van die armer gebied na die ryk gebied beweeg. Resultate dui ’n afname aan in die aantal besmette individue in die ryk gebied wanneer bewegings van bevolkings beperk word deur die verbetering van die ekonomie in die arm gebied. Ons kom tot die gevolgtrekking dat die verbetering van die ekonomie van armer lande krities kan wees om potensiële uitbrake van Ebola-virus siektes te vermy. Die resultate in hierdie proefskrif dui op die noodsaaklikheid om sosio-ekonomiese faktore in Ebola-virus siekte epidemiese modelle te oorweeg. Doctoral 2019-01-12T22:16:57Z 2019-04-17T08:10:26Z 2019-01-12T22:16:57Z 2019-04-17T08:10:26Z 2019-04 Thesis http://hdl.handle.net/10019.1/105726 en_ZA Stellenbosch University xiii, 193 pages : illustrations (chiefly colour), 1 map application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Ebola virus disease -- Mathematical models Ebola epidemic Diseases -- Social aspects -- Africa Diseases -- Economic aspects -- Africa Human migration -- Mathematical models UCTD Djiomba Njankou, Sylvie Diane Mathematical models of Ebola virus disease with socio-economic dynamics |
| title | Mathematical models of Ebola virus disease with socio-economic dynamics |
| title_full | Mathematical models of Ebola virus disease with socio-economic dynamics |
| title_fullStr | Mathematical models of Ebola virus disease with socio-economic dynamics |
| title_full_unstemmed | Mathematical models of Ebola virus disease with socio-economic dynamics |
| title_short | Mathematical models of Ebola virus disease with socio-economic dynamics |
| title_sort | mathematical models of ebola virus disease with socio economic dynamics |
| topic | Ebola virus disease -- Mathematical models Ebola epidemic Diseases -- Social aspects -- Africa Diseases -- Economic aspects -- Africa Human migration -- Mathematical models UCTD |
| url | http://hdl.handle.net/10019.1/105726 |
| work_keys_str_mv | AT djiombanjankousylviediane mathematicalmodelsofebolavirusdiseasewithsocioeconomicdynamics |