SNF 2020 | ABS-261 | Jakarta, Indonesia, 20 June 2020

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The Relation between ABM (Agent-Based
Model) and SIR (Susceptible-Infected-
Recovered) Model for Spread of Disease
A. Susandi1,2,*, I. Taufik2, P. Aditiawati2, S. Viridi2
1Badan Intelijen Negara Republik Indonesia
2Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
*armi@meteo.itb.ac.id

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Outline
• Agent-based Model (ABM) and its applications
• Mathematical modelling of infectious disease
• SIR model
• AMB-SIR
• Case 1, 2, 3
• The 2nd wave
• Conclusion (and future plan)

3. Agent-Based Model (ABM)
• Simulation of many individuals
• Each individual can interact to other individual
• Individual can also interact to enviroment
• Rule of interaction can be so abstract
• Each agent is updated in random order
• Individual can breed, mutate, die, etc..
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4. Applications of ABM
Large scale
• Optimization in spatial planning [1]
• Predicting future of a city [2]
Mesoscale
• Human interactions in evacuation [3]
• Multilane traffic flow [4]
• Farming system [5]
• Customer behaviour in car purchasing [6]
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5. Applications of ABM (cont.)
Microscale
• Mechanics of cells and tissues [7]
• Interaction among red blood cells, macro-
phages, and neutrophils in immune system
during infection [8]
Molecular / atomic scale
• Simulation of state of matter [9]
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6. Mathematical modelling of infectious disease
For COVID-19
• SIR [10]
• SIRD [11]
• SEIR [12]
• SEIRD [13]
• SEIQRD [14]
• SIDARTHE [15]
Terms
• Susceptible
• Infected
• Recovered
• Death
• Exposed
• Quarantine
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susceptible (S), infected (I), diagnosed (D), ailing (A),
recognized (R), threatened (T), healed (H), extinct (E)
Compartments

7. Susceptible-Infected-Recovered
• Simple, discrete form, normalized
• Two final states: non-epidemic & epidemic
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iiii isss 1 iiiii iisii  1 iii irr 1
1 iii ris
0.0
0.2
0.4
0.6
0.8
1.0
0 15 30 45 60 75 90
t
s
i
r
0.0
0.2
0.4
0.6
0.8
1.0
0 15 30 45 60 75 90
t
s
i
r

8. SIR-ABM
• World in square grid □
• Represented in matrix form
• Can move only one □ in direction ← ↑ ↓ →
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9. Case 1: ABM can, SIR can’t
• Infected agent surrounded by recovered ones
ABM predicts no infection spread
• SIR will still predict infection spread, since it
does not take into account spatial factor
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10. Case 2: ABM clear, SIR not clear
• One in-
fected
agent will
spread
infection
differently
in ABM
• But still the same in SIR, except we change
value of β
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same time t >>

11. Case 3: Four connected cities
• Infection begins at North-West city, propaga-
ted to South-West city, then to South-East city,
and finally arrives in North-East city
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time t >>
NW NE
SW SE

12. • The pandemic is
propagated
from city to city
Case 3: ..
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0.0
0.2
0.4
0.6
0.8
1.0
0 15 30 45 60 75 90 105 120 135 150
t
s
i
r
0.0
0.2
0.4
0.6
0.8
1.0
0 15 30 45 60 75 90 105 120 135 150
t
s
i
r
0.0
0.2
0.4
0.6
0.8
1.0
0 15 30 45 60 75 90 105 120 135 150
t
s
i
r
0.0
0.2
0.4
0.6
0.8
1.0
0 15 30 45 60 75 90 105 120 135 150
t
s
i
r
NW
SW
SE
NE

13. Sum all data from the four cities
• We get the 2nd wave phenomenon, which is
bigger!
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0.0
0.2
0.4
0.6
0.8
1.0
0 15 30 45 60 75 90 105 120 135 150
t
s
i
r

14. Conclusions
• ABM gives more details information than SIR
• Phenomenon of second wave can observed
when data of four cities are summed up
Future plan
• Study the network of interaction between
agent: first
infection is
agent 000
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References
1. A. Ligtenberg, R. J. A. van Lammeren, A. K. Bregt and A. J. M. Beulens,
Comput. Environ. Urban Syst. 34, 424-434 (2010).
2. F. Hosseinali, A. A. Alesheikh and F. Nourian, Cities 31, 105-113 (2013).
3. E. Bonabeau, PNAS 99, 7280-7287 (2002).
4. R. Sugihakim and H. Alatas, Phys. Lett. A 380, 147-155 (2016).
5. S. Viridi, P. Premadi, P. Aditiawati, E. S. Maqdir, T. Suheri, J. Halid, K. N.
Sari, U. S. Pasaribu, N. M. Sudaryani, N. Latifah and S. Rahimah, IOP
Conf. Ser.: Earth Environ. Sci. 230, 012118 (2019).
6. M. G. Mueller and P. de Haan, Energy Policy 37, 1072-1082 (2009).
7. P. Van Liedekerke, "Quantitative modeling of cell and tissue mechanics
with agent-based models", Biological Physics [physics.bio-ph], Inria
Paris, Sobonne Université, Mar 2019, HAL Id: tel-02064216, url
https://hal.inria.fr/tel-02064216.

16. References (cont.)
8. Z. Z. Shi, C.-H. Wu and D. Ben-Arieh, Open J. Model. Simul. 2, 12-22
(2014).
9. S. Viridi and F. Haryanto, IOP Conf. Ser. Mat. Sci. Eng. 599, 012008
(2019).
10. M. S. Boudrioua and A. Boudrioua, medRxiv 20079467v6 06 Jun 2020.
11. J. Fernández-Villaverde, C. I. Jones, NBER Working Paper 27128, May
2020.
12. E. Soewono, Commun. Biomath. Sci. 3, 9-18, (2020).
13. I. Korolev, SSRN 3569367, 20 Apr 2020.
14. A. G. M. Selvam and D. Vignesh, Alochana Chakra J. 9, 217-221 (2020).
15. G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di
Matteo and M. Colaneri, Nat. Med., (2020).
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Thank you