A  Fractional SIR Model for Hepatitis A Virus: Lyapunov Stability and Effects of Awareness and Vaccination

Burhanuddin Safi; Agniva Das; A.H. Hasmani

doi:10.5614/cbms.2025.8.2.4

Authors

Burhanuddin Safi Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat 388120, India & Department of Mathematics, Kabul University, Kart-e-Char, Kabul 1001, Afghanistan
Agniva Das Department of Statistics, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat 390002, India
A.H. Hasmani Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat 388120, India

DOI:

https://doi.org/10.5614/cbms.2025.8.2.4

Keywords:

Caputo derivatives, Hepatitis A virus, awareness, vaccination, lyapunov function, estimation

Abstract

Although Hepatitis A Virus (HAV) causes non-chronic infection, it poses serious health threats, particularly among children and older individuals due to poor sanitation and weak immunity. To better capture the memory-dependent progression of HAV, a novel SIR-type epidemic model is developed using Caputo fractional derivatives. The model incorporates awareness campaigns and a precautionary vaccination strategy represented by a Holling type-II functional response. We analytically established positivity, boundedness, and both local and global stability of equilibrium points using Jacobian matrices and Lyapunov functions are presented. Realworld data from the United States are used to estimate possible parameters through mean absolute error (MAE) minimization. Additionally, numerical simulations were perforemd to support the qualitative results revealing that fractional-order dynamics offer more accurate and realistic forecasts compared to classical integer-order models. Moreover, sensitivity analysis further identified the infection rate and recruitment rate as dominant drivers of HAV spread. Overall, the findings confirm that combining awareness and vaccination substantially reduces the infection levels and that fractional modelling provides critical advantages in disease forecasting and control planning.

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