Mathematical Modelling of Disease Outbreak
Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study...
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Technological University Dublin
2024-12-01
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| Series: | SURE Journal: (Science Undergraduate Research Experience Journal) |
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| Online Access: | https://arrow.tudublin.ie/sure_j/vol6/iss1/4 |
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| author | Favour Christian Matthew Molloy |
| author_facet | Favour Christian Matthew Molloy |
| author_sort | Favour Christian |
| collection | DOAJ |
| description | Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.
The models are designed around a zombie outbreak in which the zombie virus is spread through a susceptible population. The SIR model developed by Kermack and McKendrick in 1927 as a means of predicting the spread of an infection in a susceptible population is the basic model of choice. The two main methods used in this study are Eulers first order method of solving ordinary differential equations, and the SZR variation of the SIR model, where the Infected class (I) is replaced by the Zombie class (Z).
The study showed that without the resurrection mechanism, the classes do not interact with each other and after the resurrection mechanism was included, the susceptible population reduces exponentially upon interaction with infected individuals. Varying parameters were applied to the model, and this resulted in different interactions dependent on the parameter values. The final model included a cure for the zombies, and more susceptible individuals survived proportional to the value assigned to the rate of the spread of the cure. The effect of the difference in parameter values on the amount of time it took for zombies to overtake the susceptible population, with and without a cure were measured using colour coding. Finally, the model design was used to successfully predict the spread of infection of influenza in a boarding school in England in 1978 using the data obtained from the first day of the infection.
This model proved efficient in the analysis of different parameters associated with a zombie outbreak even with the inclusion of a cure. The model was even able to be applied to real-world cases as in the 1978 influenza outbreak. |
| format | Article |
| id | doaj-art-528f363d005742bda13e03cc30d0393a |
| institution | Kabale University |
| issn | 2990-8167 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Technological University Dublin |
| record_format | Article |
| series | SURE Journal: (Science Undergraduate Research Experience Journal) |
| spelling | doaj-art-528f363d005742bda13e03cc30d0393a2025-01-31T10:28:14ZengTechnological University DublinSURE Journal: (Science Undergraduate Research Experience Journal)2990-81672024-12-016110.21427/2nsb-6a52Mathematical Modelling of Disease OutbreakFavour Christian0Matthew Molloy1Dundalk Institute of TechnologyDundalk Institute of TechnologyEstablishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations. The models are designed around a zombie outbreak in which the zombie virus is spread through a susceptible population. The SIR model developed by Kermack and McKendrick in 1927 as a means of predicting the spread of an infection in a susceptible population is the basic model of choice. The two main methods used in this study are Eulers first order method of solving ordinary differential equations, and the SZR variation of the SIR model, where the Infected class (I) is replaced by the Zombie class (Z). The study showed that without the resurrection mechanism, the classes do not interact with each other and after the resurrection mechanism was included, the susceptible population reduces exponentially upon interaction with infected individuals. Varying parameters were applied to the model, and this resulted in different interactions dependent on the parameter values. The final model included a cure for the zombies, and more susceptible individuals survived proportional to the value assigned to the rate of the spread of the cure. The effect of the difference in parameter values on the amount of time it took for zombies to overtake the susceptible population, with and without a cure were measured using colour coding. Finally, the model design was used to successfully predict the spread of infection of influenza in a boarding school in England in 1978 using the data obtained from the first day of the infection. This model proved efficient in the analysis of different parameters associated with a zombie outbreak even with the inclusion of a cure. The model was even able to be applied to real-world cases as in the 1978 influenza outbreak.https://arrow.tudublin.ie/sure_j/vol6/iss1/4epidemiologymathematical modellingsimulationordinary differential equations |
| spellingShingle | Favour Christian Matthew Molloy Mathematical Modelling of Disease Outbreak SURE Journal: (Science Undergraduate Research Experience Journal) epidemiology mathematical modelling simulation ordinary differential equations |
| title | Mathematical Modelling of Disease Outbreak |
| title_full | Mathematical Modelling of Disease Outbreak |
| title_fullStr | Mathematical Modelling of Disease Outbreak |
| title_full_unstemmed | Mathematical Modelling of Disease Outbreak |
| title_short | Mathematical Modelling of Disease Outbreak |
| title_sort | mathematical modelling of disease outbreak |
| topic | epidemiology mathematical modelling simulation ordinary differential equations |
| url | https://arrow.tudublin.ie/sure_j/vol6/iss1/4 |
| work_keys_str_mv | AT favourchristian mathematicalmodellingofdiseaseoutbreak AT matthewmolloy mathematicalmodellingofdiseaseoutbreak |