Pezzella, Mario (2023) Infectious Disease Outbreak Simulation: Accurate and Dynamically Consistent Numerical Methods for Integro-Differential Epidemic Models. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Infectious Disease Outbreak Simulation: Accurate and Dynamically Consistent Numerical Methods for Integro-Differential Epidemic Models. |
| Autori: | Autore Email Pezzella, Mario mario.pezzella@unina.it |
| Data: | 11 Dicembre 2023 |
| Numero di pagine: | 156 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 36 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda gioconda.moscariello@unina.it |
| Tutor: | nome email Festa, Paola [non definito] |
| Data: | 11 Dicembre 2023 |
| Numero di pagine: | 156 |
| Parole chiave: | Epidemic models. Age-of-infection. Volterra integro-differential equations. Non-standard Finite Differences. Direct Quadrature. Dynamical consistency. Asymptotic behavior. Discrete models. |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/08 - Analisi numerica |
| Depositato il: | 19 Dic 2023 18:12 |
| Ultima modifica: | 09 Mar 2026 14:38 |
| URI: | http://www.fedoa.unina.it/id/eprint/15674 |
Abstract
The age-of-infection integro-differential model, originally proposed by Kermack and McKendrick, offers a versatile yet computationally challenging framework for a comprehensive description of various infectious disease outbreak scenarios. This work addresses the challenges posed by the long-time simulation of the aforementioned model and of its extensions through the introduction of dynamically consistent numerical methods. Specifically, unconditionally positive and high-order schemes based on Non-Standard Finite Difference and Direct Quadrature methods are here devised. A thorough investigation of the asymptotic behavior of the numerical solutions is carried out and the convergence of the discrete final size to the continuous counterpart is rigorously proved.
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