Abstract
In epidemiological modeling, the basic reproduction number is usually defined as being the spectral radius of the next-generation matrix evaluated at the trivial equilibrium. The global stability of the trivial equilibrium point was determined by the left eigenvector associated with that next-generation matrix. More recently, the fraction of susceptible individuals was also obtained from the next generation matrix. The gross reproduction number and the fraction of susceptible individuals were calculated by revisiting the drug-sensitive and resistant tuberculosis model. Hence, the next-generation matrices shed light on the evolution of the dynamics: the beginning of the epidemic via the basic reproduction number and approaching the epidemic’s steady-state via the susceptible individuals’ asymptotic fraction.
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