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Subfield · Mathematics

Modeling and Simulation research

Modeling and Simulation is a subfield of Mathematics. Science Explorer counts 106k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

In short: use of models – physical, mathematical, or otherwise logical representation of a system, entity, phenomenon, or process – as a basis for simulations – methods for implementing a model (either statically or) over time.

Research works
106k
fractional, since 1950
In the world top 10%
11k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Topics
6
Growth, 2018-21 → 2022-25
+9%
the tick is no change
Largest producer
China
28% of the 10 largest, 2022-now
Modeling and Simulation

What is Modeling and Simulation research about, and what is growing?

By the world's output in 2021-25, its most used keywords are Modeling, COVID-19, transmission dynamics, Anomalous Diffusion, Fractional Calculus, Mathematical Modeling. Gaining share since 2011-15: COVID-19, transmission dynamics, Modeling. Losing share: Social Entrepreneurship, Space Exploration, Mathematical Modeling, Interpolation.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2021-25 in the topics tagged with each word; colour compares the word's share of this field with 2011-15. Each links to the topic it comes from most.

All 14 words, with their numbers
  1. Modeling24k▲ 2.8×2 topics
  2. COVID-1924k▲ 2.9×1 topic
  3. transmission dynamics24k▲ 2.9×1 topic
  4. Anomalous Diffusion13k▼ 0.69×1 topic
  5. Fractional Calculus13k▼ 0.69×1 topic
  6. Mathematical Modeling4,479▼ 0.35×2 topics
  7. Cancer Growth3,864▼ 0.51×1 topic
  8. Tumor Invasion3,864▼ 0.51×1 topic
  9. Engineering Students1,108▼ 0.46×1 topic
  10. Mathematics Support1,108▼ 0.46×1 topic
  11. Social Entrepreneurship616▼ 0.12×1 topic
  12. Space Exploration616▼ 0.12×1 topic
  13. Interpolation158▼ 0.44×1 topic
  14. Mathematica158▼ 0.44×1 topic

Which countries lead Modeling and Simulation research?

On research quality in 2022-now, the United States, China and the United Kingdom rank highest in Modeling and Simulation. By volume, China and the United States publish the most (5.4k and 4.2k works in 2022-now).

By research quality, 2022-now

  1. 1 United States #1 all time 1.10× citation excellence · 1.60× journals · 100% breadth 11.3% top 10% · 3.8k works
  2. 2 China #2 all time 1.00× citation excellence · 1.02× journals · 100% breadth 10.7% top 10% · 4.8k works
  3. 3 United Kingdom #3 all time 1.29× citation excellence · 1.47× journals · 100% breadth 13.3% top 10% · 1k works
  4. 4 Germany #4 all time 1.24× citation excellence · 1.40× journals · 100% breadth 11.7% top 10% · 610 works
  5. 5 France #5 all time 1.03× citation excellence · 1.26× journals · 100% breadth 9.1% top 10% · 627 works
  6. 6 Canada #8 all time 1.12× citation excellence · 1.20× journals · 100% breadth 11.3% top 10% · 552 works
  7. 7 Australia #6 all time 1.27× citation excellence · 1.20× journals · 100% breadth 13.6% top 10% · 424 works
  8. 8 Netherlands #12 all time 1.25× citation excellence · 1.45× journals · 100% breadth 12.5% top 10% · 207 works
  9. 9 India #13 all time 0.78× citation excellence · 0.42× journals · 100% breadth 7.1% top 10% · 2.9k works
  10. 10 Italy #11 all time 1.12× citation excellence · 0.68× journals · 100% breadth 10.9% top 10% · 722 works

The track on each row is that row's top-10% rate. The ranking itself is the quality score, which compares the rate with what each place's own topics predict, adds its share of papers in the Nature Index journals, and counts output and breadth too.

Of 33 countries ranked in Modeling and Simulation. Ranked on the quality score for 2022-now; the bracket is the all-time rank.

All countries ranked in Modeling and Simulation

By volume, 2022-now

  1. 1 China 5.4k works
  2. 2 United States 4.2k works
  3. 3 India 3.2k works
  4. 4 Saudi Arabia 1.2k works
  5. 5 United Kingdom 1.1k works
  6. 6 Türkiye 885 works
  7. 7 Pakistan 841 works
  8. 8 Italy 781 works
  9. 9 Iran 753 works
  10. 10 Nigeria 688 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 28.2%United States: 22.2%India: 16.9%Saudi Arabia: 6.3%6 others listed: 26.4%28%largest
China5,406 · 28.2%United States4,248 · 22.2%India3,242 · 16.9%Saudi Arabia1,205 · 6.3%6 others listed5,053 · 26.4%

Shares of the rows listed above, not of the whole node.

Which institutions lead Modeling and Simulation research?

Harvard University (United States) ranks first in Modeling and Simulation on research quality in 2022-now, followed by University of Oxford and United States Department of Health and Human Services.

By research quality, 2022-now

  1. 1 Harvard University United States · Cambridge · #1 all time 18.3% top 10% · 77 works
  2. 2 University of Oxford United Kingdom · Oxford · #2 all time 16.8% top 10% · 76 works
  3. 3 United States Department of Health and Human Services United States · Washington · #10 all time 16.6% top 10% · 74 works
  4. 4 Johns Hopkins University United States · Baltimore · #4 all time 16.8% top 10% · 70 works
  5. 5 Centre National de la Recherche Scientifique France · Paris · #7 all time 7.7% top 10% · 202 works
  6. 6 Chinese Academy of Sciences China · Beijing · #3 all time 13.8% top 10% · 70 works
  7. 7 University College London United Kingdom · London · #20 all time 14.1% top 10% · 61 works
  8. 8 Harbin Institute of Technology China · Harbin · #18 all time 7.4% top 10% · 64 works
  9. 9 King Abdulaziz University Saudi Arabia · Jeddah · #23 all time 10.9% top 10% · 90 works
  10. 10 University of North Carolina at Chapel Hill United States · Chapel Hill · #68 all time 3.8% top 10% · 98 works

The track on each row is that row's top-10% rate. The ranking itself is the quality score, which compares the rate with what each place's own topics predict, adds its share of papers in the Nature Index journals, and counts output and breadth too.

Of 17 institutions above the floor of 40 fractional works in Modeling and Simulation.

Top 100 Modeling and Simulation institutions

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 216 works
  2. 2 Russian Academy of SciencesRussia 155 works
  3. 3 Vellore Institute of Technology UniversityIndia 128 works
  4. 4 University of North Carolina at Chapel HillUnited States 105 works
  5. 5 King Abdulaziz UniversitySaudi Arabia 97 works
  6. 6 King Saud UniversitySaudi Arabia 94 works
  7. 7 Islamic Azad University, TehranIran 91 works
  8. 8 University of OxfordUnited Kingdom 83 works
  9. 9 Harvard UniversityUnited States 83 works
  10. 10 Qassim UniversitySaudi Arabia 80 works

Who are the leading researchers in Modeling and Simulation?

Counting only their work in Modeling and Simulation, Cecile G. Viboud, Benjamin John Cowling and Neil M. Ferguson have the most papers in the world top 10% for their subfield and year beyond the 10% expected.

  1. 1 Cecile G. Viboud United States · #3,328 worldwide overall 40.9 of 81 papers here in the top 10%
  2. 2 Benjamin John Cowling China · #81,671 worldwide overall 38.5 of 124 papers here in the top 10%
  3. 3 Neil M. Ferguson United Kingdom · #7,169 worldwide overall 32.2 of 64 papers here in the top 10%
  4. 4 Ralf Metzler Germany · #9,068 worldwide overall 31.8 of 62 papers here in the top 10%
  5. 5 Alessandro Vespignani United States · #2,173 worldwide overall 29.4 of 54 papers here in the top 10%
  6. 6 W. John Edmunds United Kingdom · #5,025 worldwide overall 27.5 of 52 papers here in the top 10%
  7. 7 Sebastian Funk United Kingdom · #64 worldwide overall 26.5 of 55 papers here in the top 10%
  8. 8 Marc Lipsitch United States · #6,726 worldwide overall 25.7 of 50 papers here in the top 10%
  9. 9 Ji‐Huan He China · #310,349 worldwide overall 45.1 of 82 papers here in the top 10%
  10. 10 Dumitru Bǎleanu Türkiye · #1,922,304 worldwide overall 138.5 of 542 papers here in the top 10%

Ranked on their work in Modeling and Simulation alone: how many more of their papers here reached the world top 10% for their subfield and year than the 10% expected, among 342,975 ranked researchers with a paper here. Each paper counts once, so many strong papers outrank one famous one, and a long record of ordinary papers does not climb. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Modeling and Simulation researchers

What are the most cited papers in Modeling and Simulation?

The most cited paper in Modeling and Simulation is "Characteristics of and Important Lessons From the Coronavirus Disease 2019 (COVID-19) Outbreak in China" (Zunyou Wu, Jennifer M. McGoogan, 2020), with 18,071 citations. Next come "Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia" (18,005) and "The global distribution and burden of dengue" (10,418).

Most cited papers
#PaperReleasedCitations
1 Characteristics of and Important Lessons From the Coronavirus Disease 2019 (COVID-19) Outbreak in China Zunyou Wu, Jennifer M. McGoogan · JAMA Open access 24 Feb 2020 18,071
2 Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia Qun Li et al. · New England Journal of Medicine Open access 29 Jan 2020 18,005
3 The global distribution and burden of dengue Samir Bhatt, Peter W. Gething, Oliver J. Brady et al. · Nature Open access Apr 2013 10,418
4 Active contours without edges Tony Fan-Cheong Chan, Luminita A. Vese · IEEE Transactions on Image Processing 2001 10,394
5 Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1 Neeltje van Doremalen, Trenton Bushmaker, Dylan H. Morris et al. · New England Journal of Medicine Open access 17 Mar 2020 10,255
All 100 most cited papers, with filters and sorting

Where is Modeling and Simulation research done?

The largest centres of Modeling and Simulation research in 2022-now are Beijing (China), London (United Kingdom), Riyadh (Saudi Arabia) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Malakand, ash-Shalif and Beni Mellal.

Largest cities, 2022-now

  1. 1 BeijingChina 652 works
  2. 2 LondonUnited Kingdom 380 works
  3. 3 RiyadhSaudi Arabia 360 works
  4. 4 ShanghaiChina 336 works
  5. 5 ParisFrance 264 works
  6. 6 MoscowRussia 255 works
  7. 7 New DelhiIndia 238 works
  8. 8 NanjingChina 237 works
  9. 9 TehranIran 235 works
  10. 10 GuangzhouChina 226 works

Where it is the local speciality

  1. MalakandPK · 47.1 works31×
  2. ash-ShalifDZ · 22.2 works21×
  3. Beni MellalMA · 77.1 works17×
  4. ZeytinburnuTR · 24.2 works14×
  5. OsogboNG · 37.7 works14×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Modeling and Simulation than the world average.

See Modeling and Simulation on the map

Modeling and Simulation research by country

The best places for Modeling and Simulation research inside each country, with that country's researchers and world standing.

Where is the best place to study Modeling and Simulation?

Among universities, judged by research, Harvard University, University of Oxford and Johns Hopkins University score highest, combining standing in the field's ranking, citation excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 15.28%fractional works in this field (log) →share of work in the world top 10% →Harvard UniversityJohns Hopkins Univer…University of OxfordLondon School of Hyg…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Standingthis field's institution ranking, three quarters all time and a quarter 2022-now
50%
Citation excellenceshare of its work in the world top 10%, 2022-now and all time averaged
20%
Specialisationhow much of its work is in this field, counted up to 10× the world share
5%
Sizeits output in this field, on a log scale
15%
Growthoutput growth, counted from -20% to +20%
5%
Internationalshare of its work with a co-author abroad
5%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreRank in field (all time)Top 10%SpecialisationWorksGrowth
1Harvard UniversityUnited States 77.0#1 (#1)18.1%0.9×83 -25.4%
2University of OxfordUnited Kingdom 69.2#2 (#2)16.7%2.1×83 -10.4%
3Johns Hopkins UniversityUnited States 59.3#4 (#4)17.0%1.7×76 -4.7%
4London School of Hygiene & Tropical MedicineUnited Kingdom 47.6- (#8)12.9%10.9×49 -22.5%
5University of Hong KongChina 44.7- (#9)16.8%1.8×48 -13.8%
6University College LondonUnited Kingdom 43.8#7 (#20)14.2%1.4×65 +9.7%
7Stanford UniversityUnited States 43.1- (#5)13.3%1.1×44 -20.2%
8King Abdulaziz UniversitySaudi Arabia 42.4#9 (#23)10.5%6.4×98 -9.1%
9Harbin Institute of TechnologyChina 40.5#8 (#18)7.6%1.5×70 +29.4%
10Lebanese American UniversityLebanon 39.3-25.7%19.8×62 +2490.8%

Universities only. The score blends standing (50%), citation excellence (20%), size (15%), specialisation (5%), growth (5%), international reach (5%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise. Standing is the score in this field's institution ranking, three quarters over all time and a quarter 2022-now; excellence averages the two windows too. Four years alone undercount fields such as AI, where many conference and arXiv papers from 2022 on carry no affiliation in the data.

Every institution in Modeling and Simulation, country by country

Is Modeling and Simulation research growing?

Output in 2022-2025 was 9% higher than in 2018-2021, peaking in 2021. The fastest-growing topics are Mathematics Education and Programs, Mathematical and Computational Methods and Mathematical Biology Tumor Growth.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Modeling and Simulation as a percentage of every work published that year, 0.12% in 2024.

still counting0.10%0.20%0.30%Modeling and Simulation0.11% in 202519801990200020102020

Fractional works of Modeling and Simulation over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Modeling and Simulation10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

  1. Mathematics Education and Programs+35%
  2. Mathematical and Computational Methods+26%
  3. Mathematical Biology Tumor Growth+19%
  4. Fractional Differential Equations Solutions+17%
  5. COVID-19 epidemiological studies+2%
  6. Advanced Research in Science and Engineering-11%
← shrinkingno changegrowing →

Growth in output from 2018-21 to 2022-25. Every topic is a page of its own.

What does Modeling and Simulation include?

COVID-19 epidemiological…40kCOVID-19 epidemiological studies: 40k fractional worksFractional Differential …37kFractional Differential Equations Solutions: 37k fractional worksMathematical Biology Tum…15kMathematical Biology Tumor Growth: 15k fractional worksAdvanced Research in Science and Engineering: 7,718 fractional worksMathematics Education and Programs: 5,694 fractional worksMathematical and Computational Methods: 1,134 fractional works

Area is fractional works in that topic. Every name below is a page of its own.

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Who leads Modeling and Simulation, on Science Explorer

A card with the countries and institutions that lead Modeling and Simulation, for a post or a slide.

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1200 × 630 PNG, sized for social posts, drawn from the latest snapshot.

The leading institutions' badges6Each links to that institution's page and updates with every snapshot

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