A fractional derivative modeling study for measles infection with double dose vaccination

Abstract

This study proposes a novel mathematical framework to study the spread dynamics of diseases. A measles model is developed by dividing the vaccinated compartment into the vaccinated-with-the-first-dose and the-second-dose populations. The model parameters are estimated using the genetic algorithm for measles transmission based on monthly cumulative measles data in Indonesia. The threshold is determined to measure a population’s potential spread of measles. The stability of the equilibria is investigated, and the sensitivity analysis is then presented to find the most dominant parameter on the spread of measles. We extend the classical model into Atangana–Baleanu Caputo (ABC) derivative and consider the effects of the first and second vaccination doses on susceptible and exposed individuals. These outcomes are based on the different fractional parameter values and can be utilized to identify significant disease-control strategies. The yields are graphically exhibited to support our results. The overall finding suggests that taking preventive measures has a significant influence on limiting the spread of measles in the population. Increasing vaccination coverage, in particular, will reduce the number of infected individuals, thereby lowering the disease burden in the population.

Keywords

• Fractional derivative modeling
• Measles infection
• Double dose vaccination
• Atangana–Baleanu operator
• Basic reproduction number
• Fixed point theorem