MARKOV CHAINS MODELS FOR EPIDEMICS
| dc.contributor.advisor | Srinivasan, Raj | |
| dc.contributor.advisor | Soteros, Chris | |
| dc.contributor.committeeMember | Soteros, Chris | |
| dc.contributor.committeeMember | Lui, Juxin | |
| dc.contributor.committeeMember | Khan, Shahedul | |
| dc.creator | Asamoah, Isaac Dante | |
| dc.date.accessioned | 2024-04-19T14:39:31Z | |
| dc.date.available | 2024-04-19T14:39:31Z | |
| dc.date.copyright | 2024 | |
| dc.date.created | 2024-04 | |
| dc.date.issued | 2024-04-19 | |
| dc.date.submitted | April 2024 | |
| dc.date.updated | 2024-04-19T14:39:32Z | |
| dc.description.abstract | In this thesis, we review and explore the stochastic models of epidemics developed by researchers in recent years. These stochastic models encompass both discrete and continuous time Markov chain models, particularly emphasizing stochastic Susceptible Infected Susceptible (SIS) and Susceptible Infected Recovered (SIR) models. These models are compared with their deterministic counterparts regarding dynamics, behavior, and outcomes, assuming a constant population size. The comparison involves quantitative and qualitative analyses, focusing on the asymptotic dynamics, the mean of the stochastic process versus the deterministic solution and the differing properties, such as the final size of an epidemic, particularly for when the basic reproduction number, R0, exceeds 1. Significant observations include the bimodal nature of probability distributions in stochastic models when the basic reproduction number, R0, exceeds 1. The two modes correspond respectively to disease elimination and disease persistence. This highlights the qualitative differences in the asymptotic dynamics between deterministic and stochastic models. The occurrence of disease elimination in the SIS stochastic models as time approaches infinity stands in contrast to the SIS deterministic model. Similarly, the potential for disease elimination during the peak period in the SIR stochastic model contrasts with the SIR deterministic model. The thesis also investigates the impact of factors like initial infection numbers, basic reproduction number, and population size on the epidemic’s duration and final size. For the models studied, it is observed that larger populations lead to longer epidemic durations, and the size of the epidemic increases when the initial number of infectives increased. Further, the thesis conducts a comparative analysis between stochastic and deterministic SIR models specifically for a model of COVID-19. A vaccination parameter, presumed to be 100% effective, is introduced to evaluate its impact on the expected time until disease extinction. Findings reveal that vaccination significantly accelerates the eradication of epidemics. Overall, this study highlights the crucial role of stochastic models in capturing uncertainties and variations that real-world epidemics may have, arising from factors like the unpredictable nature of interpersonal contact. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | https://hdl.handle.net/10388/15618 | |
| dc.language.iso | en | |
| dc.subject | Stochastic models | |
| dc.subject | Deterministic models | |
| dc.subject | Markov chain | |
| dc.subject | Asymptotic dynamics | |
| dc.subject | Reproduction number | |
| dc.subject | Disease elimination. | |
| dc.title | MARKOV CHAINS MODELS FOR EPIDEMICS | |
| dc.type | Thesis | |
| dc.type.material | text | |
| thesis.degree.department | Mathematics and Statistics | |
| thesis.degree.discipline | Statistics | |
| thesis.degree.grantor | University of Saskatchewan | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.Sc.) |