Time-continuous and time-discrete SIR models revisited: theory and applications.
COVID-19
Difference equations
Existence and uniqueness
Mathematical epidemiology
Nonlinear ordinary differential equations
Numerical analysis
SIR model
Well-posedness
Journal
Advances in difference equations
ISSN: 1687-1839
Titre abrégé: Adv Differ Equ
Pays: Germany
ID NLM: 101670234
Informations de publication
Date de publication:
2020
2020
Historique:
received:
12
05
2020
accepted:
22
09
2020
entrez:
12
10
2020
pubmed:
13
10
2020
medline:
13
10
2020
Statut:
ppublish
Résumé
Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people-infectious people-recovered people) model. For this purpose, we first introduce its continuous variant with time-varying transmission and recovery rates and, as our first contribution, discuss thoroughly its properties. With respect to these results, we develop different possible time-discrete SIR models, we derive our implicit time-discrete SIR model in contrast to many other works which mainly investigate explicit time-discrete schemes and, as our main contribution, show unique solvability and further desirable properties compared to its continuous version. We thoroughly show that many of the desired properties of the time-continuous case are still valid in the time-discrete implicit case. Especially, we prove an upper error bound for our time-discrete implicit numerical scheme. Finally, we apply our proposed time-discrete SIR model to currently available data regarding the spread of COVID-19 in Germany and Iran.
Identifiants
pubmed: 33042201
doi: 10.1186/s13662-020-02995-1
pii: 2995
pmc: PMC7538854
doi:
Types de publication
Journal Article
Langues
eng
Pagination
556Informations de copyright
© The Author(s) 2020.
Déclaration de conflit d'intérêts
Competing interestsThe authors declare that they have no competing interests.
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