We consider age-of-infection epidemic models to describe multiple-
stage epidemic models, including treatment. We derive an expression for the
basic reproduction number $R_0$ in terms of the distributions of periods of stay
in the various compartments. We find that, in the model without treatment,
$R_0$ depends only on the mean periods in compartments, and not on the form
of the distributions. In treatment models, $R_0$ depends on the form of the dis-
tributions of stay in infective compartments from which members are removed
for treatment, but the dependence for treatment compartments is only on the
mean stay in the compartments. The results give a considerable simplification
in the calculation of the basic reproduction number.
Citation: Christine K. Yang, Fred Brauer. Calculation of $R_0$ for age-of-infection models[J]. Mathematical Biosciences and Engineering, 2008, 5(3): 585-599. doi: 10.3934/mbe.2008.5.585
Abstract
We consider age-of-infection epidemic models to describe multiple-
stage epidemic models, including treatment. We derive an expression for the
basic reproduction number $R_0$ in terms of the distributions of periods of stay
in the various compartments. We find that, in the model without treatment,
$R_0$ depends only on the mean periods in compartments, and not on the form
of the distributions. In treatment models, $R_0$ depends on the form of the dis-
tributions of stay in infective compartments from which members are removed
for treatment, but the dependence for treatment compartments is only on the
mean stay in the compartments. The results give a considerable simplification
in the calculation of the basic reproduction number.