Fuzzy based Mathematical Model of Measles with Double-Dose Vaccination under Epidemiological Parameter Uncertainty

Source abstract

This study develops a fuzzy-based mathematical model for the transmission dynamics of measles incorporating double-dose vaccination and treatment under epidemiological parameter uncertainty. The model extends a deterministic measles framework by representing selected parameters, including the transmission, vaccination, treatment and recovery rates, as triangular fuzzy numbers. Basic properties of the model are established, and the disease-free equilibrium and basic reproduction number are derived. The $r$-cut approach is employed to obtain interval-valued representations of the uncertain parameters and the fuzzy basic reproduction number. The results show that the uncertainty interval of the reproduction number decreases as the $r$-cut level increases and converges to the deterministic reproduction number at $r=1$. Intervention analysis further shows that a combined reduction in disease transmission with increased vaccination coverage and treatment can reduce both the deterministic reproduction number and the upper bound of the fuzzy reproduction number below unity. The proposed framework therefore provides a useful approach for assessing measles transmission and control when epidemiological parameters are imprecisely known.