Modelling Measles Transmission Dynamics in Madagascar: Mixed Vaccination Strategy and Bifurcation Analysis

ABSTRACT In this paper, we developed and implemented an model to investigate the transmission dynamics of measles in Madagascar from 2018. A comprehensive sensitivity analysis was conducted to evaluate the impact of key parameters on the basic reproduction number . The data fitting results indicate that , suggesting that measles is likely to resurge in Madagascar despite the observed decline in reported cases. To mitigate this resurgence, we proposed a mixed vaccination strategy for controlling measles transmission in Madagascar. Theoretical analysis demonstrated the existence, local stability and global stability of infection‐free periodic solutions. Furthermore, numerical simulations were employed to illustrate the presence of non‐trivial periodic solutions. The mixed vaccination strategy framework shows that, with low vaccination coverage and easily achievable vaccination intervals, this strategy can both rapidly contain outbreaks and sustain long‐term disease elimination. By integrating theoretical findings with numerical simulations, we gained clearer insights into the effectiveness of the mixed vaccination strategy. This study provides valuable guidance for designing rational prevention and control measures against measles in Madagascar, with potential applications to other regions as well.