Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Recently, new strains of influenza such as bird flu and swine flu have emerged.
These strains have the capacity to infect people on a quite large scale and are
characterized by their resistance to existing influenza treatment and their high
mortality rates.
In this thesis, we consider two models for influenza transmission dynamics that
include both sensitive and resistant strains and accounts for disease induced
mortality. The first model allows for immigration/migration and does not include any
control measure. The second one explores the effects of vaccination and treatment
of the sensitive strain but ignores immigration/migration.
We studied the two models mathematically and numerically. We started with
the model without any control measures; we calculated the basic reproductive
numbers, determined the equilibrium points and investigated their stability.
Our analysis showed that when the basic reproduction numbers of both strains
are less than one then the two strains will die out. When at least one of the
basic reproduction numbers is greater than one, then the strain with the higher
basic reproduction number is the one that will persist. Numerical simulations
were carried out to confirm the stability results and a bifurcation diagram
was given. We also studied numerically the impact of the mortality rate of
influenza on the dynamics of the disease. Especially, we investigated the effect
of the mortality rate on the time needed for the pandemic to reach its peak,
the value at the peak for each strain and, when eradication is possible, the
time it takes for the disease to be eradicated.
For the model with control, we also calculated the control reproductive number
and the equilibrium points. The stability analysis was carried out numerically
and bifurcation diagrams with vaccination and treatment parameters were
given to determine the regions where eradication of the disease is possible.
Our results suggest that in the presence of a resistant strain, treating more
infected individuals will not eradicate the disease as the resistant strain will
always persist. In such a case vaccination and antiviral treatment should be
implemented simultaneously. / AFRIKAANSE OPSOMMING: Geen opsomming
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/20050 |
| Date | 03 1900 |
| Creators | Mathebula, Dephney |
| Contributors | Ouifki, Rachid, Rewitzky, Ingrid, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 64 p. : ill. |
| Rights | Stellenbosch University |
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