CEU Electronic Theses and Dissertations, 2020
| Author | Mandal, Parna |
|---|---|
| Title | Analysis of continuous and discrete mathematical models of malaria propagation |
| Summary | The present dissertation dealing with a compartmental epidemiological model to study the propagation of malaria between two interacting population - human (host) and mosquito(vector), is investigated. The total human population is compartmentalised into four classes, namely, the susceptible, the exposed, the infected and the recovered class. The total mosquito population is classified into three sub classes, e.g., the susceptible, the exposed and the infected class. A region is found out where the model is epidemiologically feasible and mathematically well-posed. The existence of equilibrium along with its stability is derived. The stability criteria do depend on the reproduction number which is calculated by the next-generation matrix technique. For a quantitative insight of the model, a thorough large-scale numerical simulation has been performed and the predicted results are presented graphically. The sequential and Strang-Marchuk splitting schemes together with RK4 numerical method have been leveraged to get the splitting solution of the matrix differential equation. However, the reference solution of the unsplit system is obtained by solving the system of ODEs by the RK4 method. Since the exact solution of the unsplit system considered is not known, this numerical solution is compared with the numerical solution obtained by using the explicit Euler method. The order and accuracy of the methods have been derived both analytically and numerically, and we have also calculated the numerical error (local/global practical error) associated with the methods. Our results agree well with several existing results available in the literature. |
| Supervisor | Faragó, István |
| Department | Mathematics MSc |
| Full text | https://www.etd.ceu.edu/2020/mandal_parna.pdf |
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