Physical Sciences and Mathematics Commons^™

A Two-Strain Tb Model With Multiple Latent Stages, Azizeh Jabbari, Carlos Castillo-Chavez, Fereshteh Nazari, Baojun Song, Hossein Kheiri

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically friendly gamma distributions, a reasonable alternative to the use of exponential distributed waiting periods or to integral equations involving "arbitrary" distributions. The model supports a globally-asymptotically stable disease-free equilibrium when the reproduction number is less than one and an endemic equilibriums, shown to be locally asymptotically stable, or l.a.s., whenever the basic reproduction number is greater than one. Conditions for the existence …