Impact of vaccination and media on a Caputo derivative-based fractional-order epidemic model with PRCC analysis

• Published in: International journal of dynamics and control Vol. 13; no. 9
• Main Authors: Barman, Snehasis, Jana, Soovoojeet, Majee, Suvankar, Patra, Sathi, Kar, Tapan Kumar
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.09.2025
• Subjects: Bifurcations; Computer simulation; Disease control; Epidemics; Equilibrium; Immunization; Optimal control; Parameter sensitivity; Pontryagin principle; Sensitivity analysis
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-025-01800-9

In our current article, we have considered a fractional-order SIR-type epidemic model with media coverage and vaccination control to discuss the disease dynamics. We have thoroughly checked the existence, uniqueness, non-negativity, and boundedness criteria of the solution of the suggested framework. In addition, we have computed the basic reproduction number (ℜ0) and equilibrium points (disease-free and endemic). Based on the values of the basic reproduction number, we have discussed that disease-free equilibrium is asymptotically stable for ℜ0<1 and endemic equilibrium is asymptotically stable for ℜ0>1. Also, we have established a transcritical bifurcation at the threshold ℜ0=1. Furthermore, we have applied fractional-order optimal control to form an objective functional to minimize the effect of the disease and used Pontryagin’s maximum principle to solve it. We have also executed a sensitivity analysis to check the influence of the system parameters on the numerical value of the basic reproduction number. Additionally, some computer simulation work has been done to verify the theoretical studies.