SAMS Subject Classification Number: 3, 10

Models describing the dynamics of biological phenomena that evolve in stages have been studied extensively using time-delay mathematical models. Recently, these models have evolved into age structured models with age dependent variables. Various mathematical tools have been employed to study these models and investigate the effects of age structure. This work explores two fractional order age structured models to address the issues of latent infection of cells by HIV and the effects of latent TB infection on the dynamics of HIV. The transmission dynamics of HIV by multiple cell types through two transmission routes within-host is modelled by Caputo fractional order derivatives, whereas, the co-epidemic of HIV and TB is modelled by a system of Caputo-Fabrizio derivatives. The equilibrium points are obtained under certain conditions, and the reproduction numbers of each transmission route and each disease are computed. Furthermore, the local asymptotic stability of the disease-free equilibrium for each model is established.