Delay equation formulation for an epidemic model with waning immunity: an application to mycoplasma pneumoniae

摘要: Abstract We formulate a general epidemic model with two arbitrary probability distributions for describing durations of infectivity and immunity. The is given as coupled system delay differential equation renewal dynamical variables: susceptible population the force infection. It shown that there exists unique endemic equilibrium if basic reproduction number greater than one. Assuming fixed duration immunity we show becomes unstable via Hopf bifurcation. briefly discuss periodic outbreak mycoplasma pneumoniae may be interpreted result instability equilibrium.