Meulenbroeks, Mark (2024) The number of infections at the time of first detection in a SIR epidemic model for large populations. Bachelor's Thesis, Mathematics.
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Abstract
The SIR epidemic model is a foundational framework in epidemiology for understanding the spread of infectious diseases. In 2009 Trapman and Bootsma proved that the distribution of the infective population at the time of first detection is geometric by relating the SIR epidemic model to a M/G/1-PS queue. This paper expands on their work by using the Poisson superposition theorem to prove that the number of infections is also geometrically distributed. Furthermore, it describes models that account for an infectivity and a detectivity that change based on the time since infection and relates these to a M/G/1-queue with a waiting time based service discipline. In an effort to give a convincing argument that in this extended model the number of infectives at the time of first detection is also geometrically distributed, an intuitive argument is given and statistical tests are developed. This conjecture could provide valuable insight into the spreading capacity of disease before their first detection.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Trapman, J.P. and Szabo, R. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 30 Jul 2024 08:59 |
| Last Modified: | 30 Jul 2024 08:59 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33740 |
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