Fractional-order modeling of vaccination strategies for measles transmission incorporating immune memory

This study explores how vaccination, immune memory, and long-term immunity shape the transmission dynamics of measles by developing a fractional-order mathematical model.

Caputo-Fabrizio fractional-order SEITR-VL model is formulated, in which population is divided into susceptible, exposed, infectious, treated, recovered, vaccinated, and lifelong immunity classes. The model incorporates memory effects so that past disease and immunity states can influence current transmission behavior. Basic mathematical properties such as positivity, boundedness, and the existence of solutions are verified. The effective reproduction number is derived using the next-generation matrix approach, and numerical solutions are obtained through the Laplace-Adomian Decomposition Method.

Numerical experiments showed that increasing vaccination coverage, as well as improving recovery rates, leads to a clear decline in infection levels. In addition, the fractional-order structure introduces memory effects that moderate sharp epidemic peaks and slow the overall spread of the disease, resulting in smoother outbreak patterns. Since some parameters are not estimated from data, these findings are interpreted mainly at a qualitative level.

The results emphasize the importance of vaccination and immune memory in controlling measles transmission. While the fractional-order framework provides a useful way to capture long-term and memory-dependent effects, further validation using real epidemiological data would be necessary for predictive or policy-oriented applications.