ArticleAdvances in difference equations2020
Time-continuous and time-discrete SIR models revisited: theory and applications.
Article in Advances in difference equations, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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10 citing papers in PubMed.
- Survey on mathematical modeling of infectious disease dynamics: insights and applications.BMC infectious diseases · 2026Review
- Article
- Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19.Viruses · 2023Article
- Analysis and simulation of a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures: A case study of the outbreak in Urumqi, China in August 2022.Infectious Disease Modelling · 2023Article
- A mathematical system of COVID-19 disease model: Existence, uniqueness, numerical and sensitivity analysis.MethodsX · 2023Review
- Combining formal methods and Bayesian approach for inferring discrete-state stochastic models from steady-state data.PloS one · 2023Article
- Trade-Off between COVID-19 Pandemic Prevention and Control and Economic Stimulus.International journal of environmental research and public health · 2022Article
- Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19.Scientific reports · 2022Article
- Time-discrete SIR model for COVID-19 in Fiji.Epidemiology and infection · 2022Article
- Inverse problem for adaptive SIR model: Application to COVID-19 in Latin America.Infectious Disease Modelling · 2022Article
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2 authors.
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Abstract
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.
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