Fractional-calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers

Typhoid fever poses a severe hazard to public health and affects at least 27 million people annually around the globe. It is significant to conceptualize the key factors of the transmission phenomena of this bacterial infection. We formulate a novel epidemic model for typhoid fever with vaccination and carriers via Caputo-Fabrizio operator. The fundamental results of the model are inspected analytically and the basic reproduction value are then assessed. The Jacobian matrix approach has been used to demonstrate the local stability of the infection-free steady-state for R0<1$$ {R}_0<1 $$. We interrogated the uniqueness and existence of the solution of the recommended fractional dynamics of typhoid fever. We illustrated the solution pathways of the recommended system of typhoid fever numerically and demonstrated the dynamics of the infection with variation of different parameters. Our results demonstrated how the dynamical behavior of the typhoid fever infection is influenced by input parameters. The findings highlight the significance and persuasive behavior of fractional order and show that the model's fractional memory effects appear to be a good fit for these kinds of findings. We have shown the most attractive factors of the system for the control and prevention through our study.