Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays

Hu Zhang, Anwar Zeb, Aying Wan and Zizhen Zhang
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Hu Zhang: School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China
Anwar Zeb: Department of Mathematics, Abbottabad Campus, COMSATS University Islamabad, Islamabad 22060, Pakistan
Aying Wan: School of Mathematics and Statistics, Hulunbuir University, Hulunbuir 021008, China
Zizhen Zhang: School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China

Mathematics, 2022, vol. 10, issue 9, 1-21

Abstract: Synthetic drugs are taking the place of traditional drugs and have made headlines giving rise to serious social issues in many countries. In this work, a synthetic drug transmission model incorporating psychological addicts with two time delays is being developed. Local stability and exhibition of Hopf bifurcation are established analytically and numerically by taking the combinations of the two time delays as bifurcation parameters. The exhibition of Hopf bifurcation shows that it is burdensome to eradicate the synthetic drugs transmission in the population.

Keywords: synthetic drugs transmission; time delays; Hopf bifurcation; local stability; period solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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