Epidemic models with differential susceptibility and stagedprogression and their dynamics - James M. Hyman; Jia Li (Mathematical Biosciences and Engineering)
We formulate and study epidemic models with differential susceptibilities andstaged-progressions, based on systems of ordinary differential equations, fordisease transmission where the susceptibility of susceptible individuals varyand the infective individuals progress the disease gradually through stageswith different infectiousness in each stage. We consider the contact rates tobe proportional to the total population or constant such that the infectionrates have a bilinear or standard form, respectively. We derive explicitformulas for the reproductive number $R_0$, and show that the infection-freeequilibrium is globally asymptotically stable if $R_01$.