This study focuses on formulating and analyzing the classical fractional order S E I R (susceptible-exposed-infected-recovered) model by incorporating the vaccination compartment with Holling type-II incidence rate to describe the spread of infectious diseases, by using Caputo fractional derivative to capture memory-dependent processes. The mathematical foundation of the proposed S V E I R model has been laid by using some fundamental properties of the operator, along with essential lemmas and validated by existence and boundedness. To calculate the secondary infections, we calculate the reproduction number by using the next generation matrix method and disease persistence and eradication are also given by equilibrium analysis. The sensitivity analysis is performed to identify influential parameters for the reproduction number by using normalized sensitivity index method. The novelty of this work lies in integrating a fractional-order epidemic model with a detailed optimal control framework. Applying Pontryagin’s Maximum Principle to vaccination and treatment interventions, the study identifies optimal strategies that minimize both infection burden and implementation costs. Additionally, a cost-effectiveness assessment is carried out to compare the interventions based on their epidemiological impact and resource use.
Jangir et al. (Tue,) studied this question.