COVID-19 simulation models are mathematical infectious disease models for the spread of COVID-19.[1] The list should not be confused with COVID-19 apps used mainly for digital contact tracing.
Note that some of the applications listed are website-only models or simulators, and some of those rely on (or use) real-time data from other sources.
Models with the most scientific backing
The sub-list contains simulators that are based on theoretical models. Due to the high number of pre-print research created and driving by the COVID-19 pandemic,[2] especially newer models should only be considered with further scientific rigor.[3][4][5]
Simulations and models
- Chen et al. simulation based on Bats-Hosts-Reservoir-People (BHRP) model (simplified to RP only)[6]
- CoSim19[7] - Prof Lehr, based on SEIRD model
- COVID-19 MOBILITY MODELING[8] - Stanford based on SEIR model[9]
- COVID-19 Simulator[10] - Harvard Medical School based on a validated system dynamics (compartment) model[11]
- COVID-19 Surge[12] - CDC[13]
- COVIDSIM[14] - by Mark Kok Yew Ng et al.
- CovidSim - Imperial College London, MRC Centre for Global Infectious Disease Analysis, Neil Ferguson et al.
- CovidSim[15] - Research project by Munich University of Applied Sciences, Prof Köster
- COVIDSim[16] - written in MATLAB[17] by Ng and Gui[18]
- CovidSIM.eu[19] - Martin Eichner, Markus Schwehm supported by University of Tübingen and sponsored by the German Federal Ministry of Education and Research.
- CovidSIM[20] - Schneider et al.
- CovRadar[21] - for molecular surveillance of the Corona spike protein[22][23]
- De-Leon and Pederiva - A dynamic particle Monte Carlo algorithm based on the basic principles of statistical physics.[24][25]
- Dr. Ghaffarzadegan’s model[26][27][28]
- Event Horizon - COVID-19[29] - HU Berlin based on SIR-X model[30]
- Evolutionary AI[31] - "Non-pharmaceutical interventions (NPIs) that the AI generates for different countries and regions over time, their predicted effect."[32][33][34]
- IHME model - Institute for Health Metrics and Evaluation COVID model
- MEmilio[35] - an open source high performance Modular EpideMIcs simuLatIOn software based on hybrid graph-SIR-type model[36] with commuter testing between regions[37] and vaccination strategies[38] and agent-based models
- OpenCOVID[39][40] - Swiss Tropical and Public Health Institute (Swiss TPH) - Open access individual-based transmission model of SARS-CoV-2 infection and COVID-19 disease dynamics implemented in R.
- OxCGRT[41] - The Oxford COVID-19 Government Response Tracker[42][34]
- SC-COSMO[43] - Stanford-CIDE Coronavirus Simulation Model
- SDL-PAND: A digital Twin of the pandemic situation in Catalonia.[44]
- SECIR[45][46][47][48] - Model by Helmholtz Centre for Infection Research
- SEIR model on a small-world network used estimate the effect of non-pharmaceutical interventions on the structure of the transmission network[49]
- SIAM's Epidemiology Collection[50]
- SIRSS model that combines the dynamics of social stress with classical epidemic models.[51] Social stress is described by the tools of social physics.
- Smart Investment of Virus RNA Testing Resources to Enhance Covid-19 Mitigation[52][53]
- Youyang Gu COVID model
- MechBayes COVID model[54]
Genome databases
Several of these models make use of genome databases, including the following:
Consortia, research clusters, other collections
- CDC list of Forecast Inclusion and Assumptions[55] - large list with different models, etc.
- CORSMA - EU consortium (COVID-19-Outbreak Response combining E-health, Serolomics, Modelling, Artificial Intelligence and Implementation Research)[56]
- COVID-19 Forecast Hub[57] - Serves as a central repository of forecasts and predictions from over 50 international research groups.[58][59]
- Nextstrain - Open-source project to harness the scientific and public health potential of pathogen genome data[60]
- See also Nextstrain SARS-CoV-2 resources[61]
- SIMID[62] - Simulation Models of Infectious Diseases - Belgium research consortium
- RAMP - Rapid Assistance in Modelling the Pandemic[63] (UK)
- UT Austin COVID-19 Modeling Consortium[64]
- Computational Approaches to Foster Innovation in the Treatment and Diagnosis of Infectious Diseases by Frontiers
Vaccination monitors, models or dashboards
Note: The following (additional) resources are mostly based on actual data, not simulation. They might include predictive features, e. g. vaccination rate estimation, but in general are not based on theoretical or modeling grounds as the main list of this article. Nonetheless, forecasting remains important.[65] (See for example the COVID-19 Forecast Hub)[66]
- COVID-19 Dashboard[67] - Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU)[68][69]
- COVIDVaxView by the CDC[70]
- Datahub Novel Coronavirus 2019 dataset[71][72] - COVID-19 dataset Coronavirus disease 2019 (COVID-19) time series listing confirmed cases, reported deaths and reported recoveries.
- Impfdashboard.de - Germany's vaccination monitor[73]
- Simulation der COVID19-Impfkampagne[74] - Monitor for vaccination-campaign in Germany by Zi Data Science Lab
- The Institute for Health Metrics and Evaluation (IHME) COVID-19 Projections[75]
Models with less scientific backing
The following models are purely for educational purposes only.
- Cellular Defense Automata model[76]
- Overview of SARS-CoV-2 variants and mutations that are of interest[77]
- Covid-19 Simulator[78]
- COVID19: Top 7 - A curated list[79] posted on Medium
- github.com/topics: covid-19[80]
- ISEE Systems COVID-19 Simulator[81]
- nCoV2019.live[82] - "Numbers you need at a quick glance" by Schiffmann/Conlon
- cov19.cc- by Conlon[83]
- Simul8 - COVID-19 Simulation Resources[84]
- Simulating coronavirus with the SIR model[85]
- Virus Spread Simulation[86]
Other related simulations, models or data sources
- (American Chemical Society) CAS COVID-19 BIOINDICATOR EXPLORER[87]
- CDC's COVID Data Tracker[88]
- Civil Society Partners in Solidarity against COVID-19 (CSPAC): Full, live, global, COVID-19 Status Report for 251 locales & 71 Ships[89]
- Cornell Institute for Social & Economic Research (CISER): COVID-19 Data Sources[90]
- Eulerian–Lagrangian multiphase modeling, e. g. for transmission of COVID-19 in elevators based on CFD[91]
- Onset of Symptoms of COVID-19 simulation (Stochastic Progression Model) by Larsen et al.[92]
- Our World in Data's Coronavirus Source Data[93]
- The Atlantic's COVID 19 Tracking Project[94]
- Vadere - Open Source Framework for Pedestrian and Crowd Simulation[95]
- WHO Coronavirus (COVID-19) Dashboard[96]
Trainings and other resources
- Infectious Disease Modelling Specialization - provided on Coursera by Imperial College London
- Introducing the COVID-19 Simulator and Machine Learning Toolkit for Predicting COVID-19 Spread - AWS Machine Learning Blog
See also
References
- ↑ Adam D (April 2020). "Special report: The simulations driving the world's response to COVID-19". Nature. 580 (7803): 316–318. Bibcode:2020Natur.580..316A. doi:10.1038/d41586-020-01003-6. PMID 32242115. S2CID 256820433.
- ↑ Brierley L. "The role of research preprints in the academic response to the COVID-19 epidemic". Authorea Preprints. doi:10.22541/au.158516578.89167184.
- ↑ "Another 178,000 deaths? Scientists' latest virus projection is a warning". NBC News. 24 September 2020. Retrieved 2021-02-22.
- ↑ Tufekci Z (2020-04-02). "Don't Believe the COVID-19 Models". The Atlantic. Retrieved 2021-02-22.
- ↑ Gonçalves B (2020-09-09). "Epidemic Modeling 102: All CoVID-19 models are wrong, but some are useful". Medium. Retrieved 2021-02-22.
- ↑ Chen TM, Rui J, Wang QP, Zhao ZY, Cui JA, Yin L (February 2020). "A mathematical model for simulating the phase-based transmissibility of a novel coronavirus". Infectious Diseases of Poverty. 9 (1): 24. doi:10.1186/s40249-020-00640-3. PMC 7047374. PMID 32111262.
- ↑ "CoSim Online". shiny.covid-simulator.com. Retrieved 14 December 2023.
- ↑ "COVID-19 Mobility Network Modeling". covid-mobility.stanford.edu. Retrieved 14 December 2023.
- ↑ Chang S, Pierson E, Koh PW, Gerardin J, Redbird B, Grusky D, Leskovec J (January 2021). "Mobility network models of COVID-19 explain inequities and inform reopening". Nature. 589 (7840): 82–87. Bibcode:2021Natur.589...82C. doi:10.1038/s41586-020-2923-3. PMID 33171481.
- ↑ "Home - COVID-19 Simulator". covid19sim.org. Retrieved 14 December 2023.
- ↑ "Policy Simulator Methodology". COVID-19 Simulator. Retrieved 2021-02-21.
- ↑ "Healthcare Workers". Centers for Disease Control and Prevention. 11 February 2020. Retrieved 14 December 2023.
- ↑ CDC (2020-02-11). "Healthcare Workers". Centers for Disease Control and Prevention. Retrieved 2021-02-22.
- ↑ Ng MK. "SEIRS-based COVID-19 Simulation Package". markusng.com. Retrieved 14 December 2023.
- ↑ "Research project - CovidSim - Modeling and simulation of covid infection spread in crowds in system relevant infrastructures - HM Hochschule München University of Applied Sciences". Hochschule München. Retrieved 14 December 2023.
- ↑ Ng M (24 September 2023). "COVIDSim — SEIRS-based COVID-19 Simulation Package". GitHub. Retrieved 14 December 2023.
- ↑ Ng M (2020-12-23), nkymark/COVIDSim, retrieved 2021-03-09
- ↑ Ng KY, Gui MM (October 2020). "COVID-19: Development of a robust mathematical model and simulation package with consideration for ageing population and time delay for control action and resusceptibility". Physica D: Nonlinear Phenomena. 411: 132599. arXiv:2004.01974. Bibcode:2020PhyD..41132599N. doi:10.1016/j.physd.2020.132599. PMC 7282799. PMID 32536738.
- ↑ "CovidSIM". covidsim.eu. Retrieved 2021-03-13.
- ↑ Schneider KA, Ngwa GA, Schwehm M, Eichner L, Eichner M (November 2020). "The COVID-19 pandemic preparedness simulation tool: CovidSIM". BMC Infectious Diseases. 20 (1): 859. doi:10.1186/s12879-020-05566-7. PMC 7675392. PMID 33213360.
- ↑ "CovRadar". covradar.net. Retrieved 14 December 2023.
- ↑ Wittig A, Miranda F, Hölzer M, Altenburg T, Bartoszewicz JM, Dieckmann MA, et al. (2021-04-06). "CovRadar: Continuously tracking and filtering SARS-CoV-2 mutations for molecular surveillance". bioRxiv 10.1101/2021.02.03.429146v2.
- ↑ "Molecular surveillance of SARS-CoV-2 spike protein mutations using CovRadar". News-Medical.net. 2021-02-07. Retrieved 2021-04-25.
- ↑ De-Leon H, Pederiva F (August 2020). "Particle modeling of the spreading of coronavirus disease (COVID-19)". Physics of Fluids. 32 (8): 087113. arXiv:2005.10357. Bibcode:2020PhFl...32h7113D. doi:10.1063/5.0020565. PMC 7441410. PMID 32848352.
- ↑ De-Leon H, Pederiva F (July 2021). "Statistical mechanics study of the introduction of a vaccine against COVID-19 disease". Physical Review E. 104 (1): 014132. arXiv:2012.07306. Bibcode:2021PhRvE.104a4132D. doi:10.1103/PhysRevE.104.014132. PMID 34412259. S2CID 229155979.
- ↑ "Dr. Ghaffarzadegan's model - Simulate your university's covid-19 cases". forio.com. Retrieved 2 May 2021.
- ↑ Ghaffarzadegan N (2021-02-01). "Simulation-based what-if analysis for controlling the spread of Covid-19 in universities". PLOS ONE. 16 (2): e0246323. Bibcode:2021PLoSO..1646323G. doi:10.1371/journal.pone.0246323. PMC 7850497. PMID 33524045.
- ↑ "COVID-19 simulation model creates scenarios". www.vtnews.vt.edu. Archived from the original on 2021-03-06. Retrieved 2021-02-21.
- ↑ "Event Horizon - COVID-19". rocs.hu-berlin.de. Retrieved 14 December 2023.
- ↑ Maier BF, Brockmann D (May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492): 742–746. arXiv:2002.07572. Bibcode:2020Sci...368..742M. doi:10.1126/science.abb4557. PMC 7164388. PMID 32269067.
- ↑ "Evolutionary AI". evolution.ml. Retrieved 14 December 2023.
- ↑ "Evolutionary AI". evolution.ml. Retrieved 2021-04-26.
- ↑ Miikkulainen R, Francon O, Meyerson E, Qiu X, Sargent D, Canzani E, Hodjat B (2020-08-01). "From Prediction to Prescription: Evolutionary Optimization of Non-Pharmaceutical Interventions in the COVID-19 Pandemic". arXiv:2005.13766 [cs.NE].
- 1 2 "Can Computer Models Select the Best Public Health Interventions for COVID-19?". IEEE Spectrum: Technology, Engineering, and Science News. 5 January 2021. Retrieved 2021-04-26.
- ↑ Abele D, Kühn MJ, Koslow W, Rack K, Siggel M, Kleinert J, et al. (2022-01-01). "MEmilio - a high performance Modular EpideMIcs simuLatIOn software". GitHub.
- ↑ Kühn MJ, Abele D, Mitra T, Koslow W, Abedi M, Rack K, et al. (September 2021). "Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution". Mathematical Biosciences. 339: 108648. doi:10.1016/j.mbs.2021.108648. PMC 8243656. PMID 34216635.
- ↑ Kühn MJ, Abele D, Binder S, Rack K, Klitz M, Kleinert J, et al. (2021-04-28). "Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants". medRxiv 10.1101/2021.04.23.21255995.
- ↑ Koslow W, Kühn MJ, Binder S, Klitz M, Abele D, Basermann A, et al. (2021-11-29). "Appropriate relaxation of non-pharmaceutical interventions minimizes the risk of a resurgence in SARS-CoV-2 infections in spite of the Delta variant". medRxiv 10.1101/2021.07.09.21260257.
- ↑ Shattock AJ, Le Rutte EA, Dünner RP, Sen S, Kelly SL, Chitnis N, Penny MA (March 2022). "Impact of vaccination and non-pharmaceutical interventions on SARS-CoV-2 dynamics in Switzerland". Epidemics. 38 (7): 100535. Bibcode:2021PLSCB..17E9146H. doi:10.1016/j.epidem.2021.100535. PMC 8669952. PMID 34923396.
- ↑ "Git-repository with open access source-code for OpenCOVID". GitHub. Swiss TPH. 2022-01-31. Retrieved 2022-02-15.
- ↑ "COVID-19 Government Response Tracker". www.bsg.ox.ac.uk. 18 March 2020. Retrieved 14 December 2023.
- ↑ "COVID-19 Government Response Tracker". www.bsg.ox.ac.uk. 18 March 2020. Retrieved 2021-04-26.
- ↑ "sc-cosmo – Stanford-CIDE COronavirus Simulation MOdel". Retrieved 14 December 2023.
- ↑ "SDL PAND - Mapa global". pand.sdlps.com. Retrieved 2023-05-20.
- ↑ Khailaie S, Mitra T, Bandyopadhyay A, Schips M, Mascheroni P, Vanella P, et al. (2020-04-07). "Estimate of the development of the epidemic reproduction number Rt from Coronavirus SARS-CoV-2 case data and implications for political measures based on prognostics". medRxiv 10.1101/2020.04.04.20053637v1.
- ↑ "simm / covid19 / SECIR". GitLab. Retrieved 2021-07-05.
- ↑ "Report · Wiki · simm / covid19 / SECIR". GitLab. Retrieved 2021-07-05.
- ↑ "Our research". Helmholtz Centre for Infection Research. Retrieved 2021-07-05.
- ↑ Syga S, David-Rus D, Schälte Y, Hatzikirou H, Deutsch A (November 2021). "Inferring the effect of interventions on COVID-19 transmission networks". Scientific Reports. 11 (1): 21913. arXiv:2012.03846. Bibcode:2021NatSR..1121913S. doi:10.1038/s41598-021-01407-y. PMC 8578219. PMID 34754025.
- ↑ "Epidemiology Collection". epubs.siam.org.
- ↑ Kastalskiy IA, Pankratova EV, Mirkes EM, Kazantsev VB, Gorban AN (November 2021). "Social stress drives the multi-wave dynamics of COVID-19 outbreaks". Scientific Reports. 11 (1): 22497. arXiv:2106.08966. Bibcode:2021NatSR..1122497K. doi:10.1038/s41598-021-01317-z. PMC 8602246. PMID 34795311.
- ↑ "COVID-19 Simulation Tool". corona-lab.ch. Retrieved 28 April 2021.
- ↑ Gorji H, Arnoldini M, Jenny DF, Hardt WD, Jenny P (2020-12-02). "Smart Investment of Virus RNA Testing Resources to Enhance Covid-19 Mitigation". medRxiv 10.1101/2020.11.30.20239566.
- ↑ GIBSON GC, REICH NG, SHELDON D (24 December 2020). "Real-Time Mechanistic Bayesian Forecasts of Covid-19 Mortality". MedRxiv: The Preprint Server for Health Sciences: 2020.12.22.20248736. doi:10.1101/2020.12.22.20248736. PMC 7781348. PMID 33398305.
- ↑ "CDC list of Forecast Inclusion and Assumptions". www.cdc.gov/coronavirus.
- ↑ "CORESMA". CORESMA. Retrieved 2021-07-05.
- ↑ "Home - COVID 19 forecast hub". covid19forecasthub.org. Retrieved 14 December 2023.
- ↑ Best R, Boice J (2020-05-01). "Where The Latest COVID-19 Models Think We're Headed — And Why They Disagree". FiveThirtyEight. Retrieved 2021-02-21.
- ↑ "Home - COVID 19 forecast hub". covid19forecasthub.org. Retrieved 2021-02-21.
- ↑ "Nextstrain". nextstrain.org. Retrieved 2021-04-26.
- ↑ "Nextstrain". nextstrain.org. Retrieved 14 December 2023.
- ↑ "SIMID – Simulation Models of Infectious Diseases". Retrieved 14 December 2023.
- ↑ "Rapid Assistance in Modelling the Pandemic: RAMP | Royal Society". royalsociety.org. Retrieved 2021-03-09.
- ↑ "UT COVID-19 Modeling Consortium". covid-19.tacc.utexas.edu. Retrieved 14 December 2023.
- ↑ CDC (2020-02-11). "Coronavirus Disease 2019 (COVID-19) - COVID-19 Forecasting: Background Information". Centers for Disease Control and Prevention. Retrieved 2021-10-03.
- ↑ "About the Hub - COVID 19 forecast hub". covid19forecasthub.org. Retrieved 2021-10-03.
- ↑ "COVID-19 Map". Johns Hopkins Coronavirus Resource Center. Retrieved 14 December 2023.
- ↑ "COVID-19 Map". Johns Hopkins Coronavirus Resource Center. Retrieved 2021-04-26.
- ↑ Dong E, Du H, Gardner L (May 2020). "An interactive web-based dashboard to track COVID-19 in real time". The Lancet. Infectious Diseases. 20 (5): 533–534. doi:10.1016/S1473-3099(20)30120-1. PMC 7159018. PMID 32087114.
- ↑ "COVIDVaxView | CDC". www.cdc.gov. 2021-09-23. Retrieved 2021-10-03.
- ↑ Datopian, Open Knowledge International. "Novel Coronavirus 2019". DataHub.io. Retrieved 2021-05-02.
- ↑ datasets/covid-19, Data Packaged Core Datasets at GitHub, 2021-05-02, retrieved 2021-05-02
- ↑ Bundesministerium für Gesundheit. "Das offizielle Dashboard zur Impfkampagne der Bundesrepublik Deutschland". impfdashboard.de (in German). Retrieved 2021-06-07.
- ↑ "Simulation der COVID19-Impfkampagne". www.zidatasciencelab.de. Retrieved 14 December 2023.
- ↑ "IHME | COVID-19 Projections". Institute for Health Metrics and Evaluation. Retrieved 14 December 2023.
- ↑ "Cellular Defense Automata model". thememeticist.github.io.
- ↑ "CoVariants (CoVariants] - Overview of SARS-CoV-2 variants and mutations that are of interest)". covariants.org. Retrieved 14 December 2023.
- ↑ "Covid-19 Simulator". www.coronasimulator.com. Retrieved 28 April 2021.
- ↑ Prabowo A (3 May 2020). "COVID19: Top 7 online interactive simulations, curated". Medium. Retrieved 2021-02-21.
- ↑ "Build software better, together (topics/covid-19)". GitHub. Retrieved 14 December 2023.
- ↑ "COVID-19 Simulator". exchange.iseesystems.com. Retrieved 14 December 2023.
- ↑ "Coronavirus Dashboard". ncov2019.live. Retrieved 14 December 2023.
- ↑ "cov19.cc". Retrieved 18 August 2023.
- ↑ "COVID-19 Simulation Resources". Retrieved 2020-02-21.
- ↑ "Simulating coronavirus with the SIR model". fatiherikli.github.io. Archived from the original on 2021-04-19. Retrieved 2021-02-21.
- ↑ "Covid-19 Spread Simulation". c19model.com. Retrieved 14 December 2023.
- ↑ "CAS COVID-19 Resources". CAS. Retrieved 2021-06-02.
- ↑ "COVID Data Tracker". Centers for Disease Control and Prevention. 28 March 2020. Retrieved 14 December 2023.
- ↑ "Full, live, global, COVID-19 Status Report for 251 locales & 71 Ships". civilsocietysolidarityagainstcovid19.com. Retrieved 2021-07-01.
- ↑ Bohan J. "LibGuides: Cornell Institute for Social & Economic Research (CISER): COVID-19 Data Sources". guides.library.cornell.edu. Retrieved 14 December 2023.
- ↑ Dbouk T, Drikakis D (January 2021). "On airborne virus transmission in elevators and confined spaces". Physics of Fluids. 33 (1): 011905. Bibcode:2021PhFl...33a1905D. doi:10.1063/5.0038180. PMC 7984422. PMID 33790526.
- ↑ Larsen JR, Martin MR, Martin JD, Kuhn P, Hicks JB (2020). "Modeling the Onset of Symptoms of COVID-19". Frontiers in Public Health. 8: 473. doi:10.3389/fpubh.2020.00473. PMC 7438535. PMID 32903584.
- ↑ Mathieu E, Ritchie H, Rodés-Guirao L, Appel C, Giattino C, Hasell J, Macdonald B, Dattani S, Beltekian D, Ortiz-Ospina E, Roser M (5 March 2020). "Coronavirus Pandemic (COVID-19)". Our World in Data. Retrieved 14 December 2023.
- ↑ "The COVID Tracking Project". The COVID Tracking Project. Retrieved 14 December 2023.
- ↑ "Vadere – Open Source Framework for Pedestrian and Crowd Simulation". www.vadere.org. Retrieved 14 December 2023.
- ↑ "WHO Coronavirus (COVID-19) Dashboard". covid19.who.int. Retrieved 2021-07-01.
Further reading
Articles
- Adam D (April 2020). "Special report: The simulations driving the world's response to COVID-19". Nature. 580 (7803): 316–318. Bibcode:2020Natur.580..316A. doi:10.1038/d41586-020-01003-6. PMID 32242115. S2CID 214771531.
- Alper J. "WXML 2020 covid-modeling learning guide". Department of Mathematics. Seattle, Washington: University of Washington.
- Fuller J (March 2021). "What are the COVID-19 models modeling (philosophically speaking)?". History and Philosophy of the Life Sciences. 43 (2): 47. doi:10.1007/s40656-021-00407-5. PMC 7994354. PMID 33770267.
- Roberts M, Driggs D, Selby I, Sala E, Schönlieb CB (1 June 2021). "Fighting a Pandemic with Medical Imaging and Machine Learning: Lessons Learned from COVID-19". SIAM News.
Books
- Basavarajaiah D, Murthy BN (2022-04-25). COVID Transmission Modeling: An Insight into Infectious Diseases Mechanism (1 ed.). Boca Raton: Chapman and Hall/CRC. doi:10.1201/9781003204794. ISBN 978-1-00-320479-4. Retrieved 2022-07-23.
- Prabha S, Karthikeyan P, Kamalanand K, Selvaganesan N (7 July 2021). Computational Modelling and Imaging for SARS-CoV-2 and COVID-19 (1st ed.). CRC Press. doi:10.1201/9781003142584. ISBN 978-1-00-314258-4. S2CID 237802484.
- Azar AT, Hassanien AE, eds. (2022). Modeling, Control and Drug Development for COVID-19 Outbreak Prevention. Studies in Systems, Decision and Control. Vol. 366. Cham: Springer International Publishing. doi:10.1007/978-3-030-72834-2. ISBN 978-3-030-72833-5. S2CID 240429840. Retrieved 2022-07-23.
- Pani SK, Dash S, dos Santos WP, Bukhari SA, Flammini F, eds. (2022). Assessing COVID-19 and Other Pandemics and Epidemics using Computational Modelling and Data Analysis. Cham: Springer International Publishing. doi:10.1007/978-3-030-79753-9. ISBN 978-3-030-79752-2. S2CID 245119014.
- Martcheva M (2015). An Introduction to Mathematical Epidemiology. Texts in Applied Mathematics. Vol. 61. Boston, MA: Springer US. doi:10.1007/978-1-4899-7612-3. ISBN 978-1-4899-7611-6. Retrieved 2022-09-12.
- Li MY (2018). An Introduction to Mathematical Modeling of Infectious Diseases. Cham: Springer International Publishing. doi:10.1007/978-3-319-72122-4. ISBN 978-3-319-72121-7. Retrieved 2022-09-12.
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