Analysis of an age-dependent SIS epidemic model with vertical transmission and proportionate mixing assumption

An SIS epidemic model of a vertically as well as horizontally transmitted disease is investigated when the fertility, mortality, and recovery rates depend on age and the force of infection is of proportionate mixing assumption type. We determine the steady states and obtain an explicitly computable threshold condition, and then we perform stability analysis. We also study the time dependent solution of the model and determine the large time behavior of the solution.