Modelling the-spread-of-sars-cov-2
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The document discusses the importance of mathematical modeling and simulation in understanding the spread of SARS-CoV-2 and the implications of COVID-19 in Austria. It highlights the reliability and uncertainty of epidemiological models, emphasizing that while these models are simplified, they are crucial for informing policy decisions regarding the pandemic. Additionally, it explores the various types of epidemiological models and challenges faced in accurate forecasting due to data errors and the evolving nature of the virus.
Modelling the-spread-of-sars-cov-2
- 1. Modelling the spread of SARS-CoV-2: How reliable are simulated forecasts? Dr. Martin Bicher 1,2 1TU Wien, Institute for Information Systems Engineering 2dwh GmbH, dwh simulation
- 2. Overview • What is and why do we need mathematical modelling and simulation? • What‘s the secret behind epidemiological models? • What‘s the uncertainty of epidemiological models?
- 3. MATHEMATICAL MODELLING AND SIMULATION What is and why do we need
- 4. Mathematical Modelling and Simulation Question Answer ?
- 5. Mathematical Modelling and Simulation Question Answer Experiment
- 6. Mathematical Modelling and Simulation Question Answer Experiment Theory
- 7. Mathematical Modelling and Simulation Question Answer Experiment Theory
- 8. Mathematical Modelling and Simulation Question Answer Experiment Theory Modelling and Simulation
- 9. Mathematical Modelling and Simulation Abstract Example Does the paper plane fly further than 5m?
- 10. Mathematical Modelling and Simulation Abstract Example Experiments 5m Does the paper plane fly further than 5m?
- 11. Mathematical Modelling and Simulation Abstract Example Experiments In 80% of all cases. 5m Does the paper plane fly further than 5m?
- 12. Mathematical Modelling and Simulation Abstract Example 5m Does the paper plane fly further than 5m? Experiments In 70% of all cases.
- 13. Mathematical Modelling and Simulation Abstract Example 5m Does the paper plane fly further than 5m? Experiments In 70% of all cases. General Paper Plane Theory: „Arrow-type paper planes fly ... dependent on their wing span...“
- 14. Mathematical Modelling and Simulation Abstract Example Does the paper plane fly further than 5m? General Paper Plane Theory: „Arrow-type paper planes fly ... dependent on their wing span...“ In 90% of all cases.
- 15. Mathematical Modelling and Simulation Abstract Example I need to know it in advance No arrow-type Does the paper plane fly further than 5m? General Paper Plane Theory: „Arrow-type paper planes fly ... dependent on their wing span...“
- 16. Mathematical Modelling and Simulation Abstract Example Mathematical paper plane model 𝑒 = 𝑢2 2 + 𝑝 𝜌 + 𝑔𝑧 • Findings from „ General Paper Plane Theory“ • Data from experiments • Additional knowledge like Physikal laws, ... Does the paper plane fly further than 5m? General Paper Plane Theory: „Arrow-type paper planes fly ... dependent on their wing span...“ I need to know it in advance No arrow-type
- 17. Mathematical Modelling and Simulation Abstract Example Simulation Does the paper plane fly further than 5m? General Paper Plane Theory: „Arrow-type paper planes fly ... dependent on their wing span...“ I need to know it in advance No arrow-type Mathematical paper plane model 𝑒 = 𝑢2 2 + 𝑝 𝜌 + 𝑔𝑧 In 2% of all cases.
- 18. Mathematical Modelling and Simulation Abstract Example Simulation Model Uncertainty: • Previous knowledge cannot be used directly • Impossible to model all influence factors • ... Does the paper plane fly further than 5m? General Paper Plane Theory: „Arrow-type paper planes fly ... dependent on their wing span...“ I need to know it in advance No arrow-type Mathematical paper plane model 𝑒 = 𝑢2 2 + 𝑝 𝜌 + 𝑔𝑧 In 2% of all cases... probably
- 19. Mathematical Modelling and Simulation COVID-19 How is SARS-CoV-2 going to spread in Austria? What consequences will the epidemic of COVID-19 have on the population?
- 20. Mathematical Modelling and Simulation COVID-19 • Italy ≠ Austria General knowledge about Influenza, other corona viruses, and the health care system • SARS CoV-2 ≠ Influenza Unintentional „experiments“: data from countries in which the virus has started spreading earlier How is SARS-CoV-2 going to spread in Austria? What consequences will the epidemic of COVID-19 have on the population?
- 21. Mathematical Modelling and Simulation COVID-19 • Italy ≠ Austria General knowledge about Influenza, other corona viruses, and the health care system • SARS CoV-2 ≠ Influenza Unintentional „experiments“: data from countries in which the virus has started spreading earlier How is SARS-CoV-2 going to spread in Austria? What consequences will the epidemic of COVID-19 have on the population? COVID-19 simulation model e.g.: 𝑆′ = −𝛼𝐼𝑆 𝐼′ = 𝛼𝐼𝑆 − 𝛽𝐼 𝑅′ = 𝛽𝐼 • Information / data from countries with more „COVID-19 experience“ • General knowledge about the spread of infectious diseases in Austria • Additional causal knowledge about the spread of infectious diseases (SIR)
- 22. Mathematical Modelling and Simulation COVID-19 • Italy ≠ Austria General knowledge about Influenza, other corona viruses, and the health care system • SARS CoV-2 ≠ Influenza Unintentional „experiments“: data from countries in which the virus has started spreading earlier How is SARS-CoV-2 going to spread in Austria? What consequences will the epidemic of COVID-19 have on the population? COVID-19 simulation model e.g.: 𝑆′ = −𝛼𝐼𝑆 𝐼′ = 𝛼𝐼𝑆 − 𝛽𝐼 𝑅′ = 𝛽𝐼 • Information / data from countries with more „COVID-19 experience“ • General knowledge about the spread of infectious diseases in Austria • Additional causal knowledge about the spread of infectious diseases (SIR) Model Uncertainty ?
- 24. What are the secrets behind epidemiological models? data based models causal models • much data • little logic • (a little bit) less data • much logic • extrapolation of current trends • good fit of current numbers • statistical methods, machine learning, ... • good qualitative forecasting capabilities • Status quo more difficult to fit • uses meta information about the system
- 25. What are the secrets behind epidemiological models? data based models causal models • much data • little logic • (a little bit) less data • much logic • extrapolation of current trends • good fit of current numbers • statistical methods, machine learning, ... • good qualitative forecasting capabilities • Status quo more difficult to fit • uses meta information about the system data method solution causalities method solution data
- 26. What are the secrets behind epidemiological models? data-based models causal models macroscopic/aggregated models susceptible persons infectious persons resistant persons new infections per day recoveries per day • SIR Strategy • Most famous model by Kermack and McKendrick (~1927)
- 27. What are the secrets behind epidemiological models? susceptible new infections per day exposed persons becoming infectious per day infectious resistant persons recovering per day • SEIR Strategy • „Exposed“ = persons within latency time • time-delayed epidemics behaviour data-based models causal models macroscopic/aggregated models
- 28. What are the secrets behind epidemiological models? susceptible exposed infectious resistant asymptomatic infectious deceased home quarantined hospitalised severe hospitalised critical • Compartment model strategy leaves space for any kind of model extension (SIRS,SEIRS,SIR-X,SIS,...) data-based models macroscopic/aggregated models
- 29. What are the secrets behind epidemiological models? macroscopic/ aggregated models microscopic models (microsimulations) susceptible person resistant person infectious person infection recovery • agent-based models • Markov Models • DES Models data-based models causal models
- 30. What are the secrets behind epidemiological models? macroscopic/ aggregated models microscopic models • „No-Free-Lunch“ All model types have advantages and disadvantages • Every model is developed for a certain purpose It should only be used for this purpose and only within its range of validity data-based models causal models
- 31. DWH/TU Wien COVID-19 Model Population Module Contact Module Disease Module Policy Module Responsible for creating and managing agents as well as death and birth processes Responsible for creating agent- agent contacts Responsible for modelling the disease progression Responsible for modelling of policies
- 32. DWH/TU Wien COVID-19 Model Key concept: Every real inhabitant is repesented by a statistically representative virtual inhabitant (a so called agent) Sampling
- 33. DWH/TU Wien COVID-19 Model Key concept: Every real inhabitant is repesented by a statistically representative virtual inhabitant (a so called agent) Sampling
- 34. DWH/TU Wien COVID-19 Model visit locations households schools workplaces leisure-time contacts at locations who contacts whom? contactmodule • Contacts between agents are not direct but agent- location-agent contacts • Location types: households, schools, workplaces • Additonal agent-agent leisure time contacts
- 35. DWH/TU Wien COVID-19 Model • Disease progression is handled in form of a flow-chart • Each agent uses is own discrete-event simulator age 54 male age 38 female infectious
- 36. How about uncertainty? • Italy ≠ Austria General knowledge about Influenza, other corona viruses, and the health care system • SARS CoV-2 ≠ Influenza Unintentional „experiments“: data from countries in which the virus has started spreading earlier How is SARS-CoV-2 going to spread in Austria? What consequences will the epidemic of COVID-19 have on the population? COVID-19 simulation model e.g.: 𝑆′ = −𝛼𝐼𝑆 𝐼′ = 𝛼𝐼𝑆 − 𝛽𝐼 𝑅′ = 𝛽𝐼 • Information / data from countries with more „COVID-19 experience“ • General knowledge about the spread of infectious diseases in Austria • Additional causal knowledge about the spread of infectious diseases (SIR) Model Uncertainty ?
- 37. How about uncertainty? Model Uncertainty Model Errors. • Every model is a simplified version of reality: potentially important mechanisms might not included or insuffiently known Data Errors • All data sources for COVID-19 are heavily biased Forecast Uncertainty Feedback Loop. • Every forecasts is only valid for a system that does not change • Even published forecasts might change the system behaviour NEWS „ ... scientists forecast Millions of infected persons...“ NEWS „ ... government reacts on forecasts and introduces lockdown measures ...“ NEWS „ ... all prognoses were wrong! Can we trust the scientists?“
- 38. Summary Though the uncertainty is huge, computer models and simulations are currently our only way to get an idea of what lies ahead of us. Consequently they are and will remain a vital element for decision support of COVID-19 policy makers 0 2000 4000 6000 8000 10000 12000 14000 16000 2020-02-19T00:00 2020-02-22T00:00 2020-02-25T00:00 2020-02-28T00:00 2020-03-02T00:00 2020-03-05T00:00 2020-03-08T00:00 2020-03-11T00:00 2020-03-14T00:00 2020-03-17T00:00 2020-03-20T00:00 2020-03-23T00:00 2020-03-26T00:00 2020-03-29T00:00 2020-04-01T00:00 2020-04-04T00:00 2020-04-07T00:00 2020-04-10T00:00 2020-04-13T00:00 2020-04-16T00:00 2020-04-19T00:00 2020-04-22T00:00 2020-04-25T00:00 2020-04-28T00:00 2020-05-01T00:00 2020-05-04T00:00 2020-05-07T00:00 2020-05-10T00:00 2020-05-13T00:00 2020-05-16T00:00 2020-05-19T00:00 2020-05-22T00:00 2020-05-25T00:00 2020-05-28T00:00 2020-05-31T00:00 2020-06-03T00:00 2020-06-06T00:00 2020-06-09T00:00 2020-06-12T00:00 2020-06-15T00:00 2020-06-18T00:00 2020-06-21T00:00 2020-06-24T00:00 2020-06-27T00:00 2020-06-30T00:00 2020-07-03T00:00 2020-07-06T00:00 2020-07-09T00:00 2020-07-12T00:00 2020-07-15T00:00 2020-07-18T00:00 2020-07-21T00:00 2020-07-24T00:00 2020-07-27T00:00 2020-07-30T00:00 2020-08-02T00:00 2020-08-05T00:00 2020-08-08T00:00 2020-08-11T00:00
- 39. Dr. Martin Bicher 1,2 1TU Wien, Institute for Information Systems Engineering 2dwh GmbH, dwh simulation Thank you for your attention Modelling the spread of SARS-CoV-2: How reliable are simulated forecasts?