Modeling and simulation of tax evasion dynamics: Optimal control and its cost-effectivenesss

Bharathi G S; Sagithya Thirumalai; Sekar Elango; Bundit Unyong; Bharathi G S; Sagithya Thirumalai; Sekar Elango; Bundit Unyong

doi:10.3934/math.2026390

AIMS Mathematics

2026, Volume 11, Issue 4: 9398-9438. doi: 10.3934/math.2026390

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Research article

Modeling and simulation of tax evasion dynamics: Optimal control and its cost-effectivenesss

1.
School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, Chennai, 600127, Tamil Nadu, India
2.
Department of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, India
3.
Department of Mathematics and Statistics, Center of Excellence for Ecoinformatics, School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand

Received: 18 January 2026 Revised: 18 March 2026 Accepted: 24 March 2026 Published: 08 April 2026
MSC : 34A08, 49J15, 65L05

Tax evasion remains a significant challenge that undermines government revenue and economic stability. In this paper, we propose proposes a new fractional-order three compartment tax evasion model that highlights the transition from susceptible individuals to honest taxpayers, capturing voluntary compliance driven by awareness and behavioral reinforcement mechanisms. The fundamental properties such as positivity, boundedness, and the existence and uniqueness of solutions, were established for the model. In this study, basic reproduction number $ (R_0) $ was derived to characterize the persistence of tax evasion. Stability analysis showed that the evader-free equilibrium was locally and globally asymptotically stable when the threshold parameter was less than one, and forward bifurcation occurred when the threshold parameter exceeded one, indicating the persistence of tax evasion. Sensitivity analysis using the Partial Rank Correlation Coefficient (PRCC) method identified that the influence rate $ (\beta) $ and the transition rate $ (\alpha) $ are the dominant factors driving tax evasion, whereas audit effectiveness and reformation rate significantly reduce evasion. The model was numerically investigated using the Modified Fractional Euler Method (MFEM) for various combinations of parameters. Two control measures, namely media awareness campaigns ($ u_1 $) and penalties ($ u_2 $), are incorporated to mitigate tax evasion. Pareto and efficiency analyses revealed that penalties are effective when implemented individually, whereas the combined intervention strategy is the most cost-effective and economically viable approach for enhancing tax compliance. The results are presented in the form of figures and tables.
- tax evasion model,
- Caputo fractional derivative,
- PRCC,
- modified fractional Euler method,
- optimal control,
- cost effectiveness
Citation: Bharathi G S, Sagithya Thirumalai, Sekar Elango, Bundit Unyong. Modeling and simulation of tax evasion dynamics: Optimal control and its cost-effectivenesss[J]. AIMS Mathematics, 2026, 11(4): 9398-9438. doi: 10.3934/math.2026390

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Abstract

Tax evasion remains a significant challenge that undermines government revenue and economic stability. In this paper, we propose proposes a new fractional-order three compartment tax evasion model that highlights the transition from susceptible individuals to honest taxpayers, capturing voluntary compliance driven by awareness and behavioral reinforcement mechanisms. The fundamental properties such as positivity, boundedness, and the existence and uniqueness of solutions, were established for the model. In this study, basic reproduction number $ (R_0) $ was derived to characterize the persistence of tax evasion. Stability analysis showed that the evader-free equilibrium was locally and globally asymptotically stable when the threshold parameter was less than one, and forward bifurcation occurred when the threshold parameter exceeded one, indicating the persistence of tax evasion. Sensitivity analysis using the Partial Rank Correlation Coefficient (PRCC) method identified that the influence rate $ (\beta) $ and the transition rate $ (\alpha) $ are the dominant factors driving tax evasion, whereas audit effectiveness and reformation rate significantly reduce evasion. The model was numerically investigated using the Modified Fractional Euler Method (MFEM) for various combinations of parameters. Two control measures, namely media awareness campaigns ($ u_1 $) and penalties ($ u_2 $), are incorporated to mitigate tax evasion. Pareto and efficiency analyses revealed that penalties are effective when implemented individually, whereas the combined intervention strategy is the most cost-effective and economically viable approach for enhancing tax compliance. The results are presented in the form of figures and tables.

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