| dc.creator |
Mpande, Leopard |
|
| dc.date |
2019-05-14T11:44:00Z |
|
| dc.date |
2019-05-14T11:44:00Z |
|
| dc.date |
2016-04 |
|
| dc.date.accessioned |
2022-10-25T09:14:50Z |
|
| dc.date.available |
2022-10-25T09:14:50Z |
|
| dc.identifier |
http://dspace.nm-aist.ac.tz/handle/123456789/46 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/94398 |
|
| dc.description |
A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of
Master's in Mathematical and Computer Sciences and Engineering of the Nelson Mandela
African Institution of Science and Technology |
|
| dc.description |
In this research, a metapopulation model is formulated as a system of ordinary differential
equations to study the impact of vaccination on the spread of measles. An expression for the
effective reproduction number 𝑅𝐶 for the metapopulation system and 𝑅𝐶𝑖 (𝑖 = 1,2) for the two
patches when there are no individual movements between them are derived using the next
generation approach for controlling the disease. The disease-free equilibrium is computed and
proved to be locally and globally asymptotically stable if 𝑅𝐶 < 1 and unstable if 𝑅𝐶 > 1. We
show that when there are no movements between the two patches, there exists at least one endemic
equilibrium for all 𝑅𝐶𝑖 > 1 and bifurcation analysis of the endemic equilibrium point proves that
forward (supercritical) bifurcation occurs in each patch. Sensitivity analysis of the basic
reproduction number 𝑅0 for metapopulation system is performed and we found that movement rates
from patch 2 to patch 1 tend to increases measles infection in a metapopulation while movement rates
from patch 1 to patch 2 tend to decrease measles infection in a metapopulation. Numerical simulation
results are also presented to validate analytical results and to show the impact of vaccination on
incidence and prevalence of measles in the metapopulation. |
|
| dc.format |
application/pdf |
|
| dc.language |
en |
|
| dc.publisher |
NM-AIST |
|
| dc.subject |
Research Subject Categories |
|
| dc.title |
Modeling the impact of vaccination on the epidemiology of measles in a metapopulation |
|
| dc.type |
Thesis |
|