Analysis of SIR model with optimal control strategy for a simple traffic congestion process

Ratna Herdiana, Zani Anjani Rafsanjani, R. Heru Tjahjana, Yogi Ahmad Erlangga, Moch. Fandi Ansori

Abstract


Traffic analysis on highways at the macroscopic level is very similar to the analysis of the spread of infectious diseases, namely the susceptible-infected-recover (SIR) model. We propose the SIR model with a control variable. The dynamics with fixed control and stability of the model are analyzed. Sensitivity analysis was also carried out. Variable control is applied as an effort to regulate or change the duration of the green light at an intersection. We obtain an optimal control strategy when the control is time-dependent. Numerical results show the positive impacts of implementing the control to susceptible vehicles and treatment for congested vehicles. We have also done an efficiency analysis, which shows that control is more effective than without control.

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Published: 2024-01-15

How to Cite this Article:

Ratna Herdiana, Zani Anjani Rafsanjani, R. Heru Tjahjana, Yogi Ahmad Erlangga, Moch. Fandi Ansori, Analysis of SIR model with optimal control strategy for a simple traffic congestion process, Commun. Math. Biol. Neurosci., 2024 (2024), Article ID 6

Copyright © 2024 Ratna Herdiana, Zani Anjani Rafsanjani, R. Heru Tjahjana, Yogi Ahmad Erlangga, Moch. Fandi Ansori. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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