Mathematical analysis of an age-structured HSV-2 model

Abstract

The stability analysis of an age-structured Herpes Simplex Virus type two is investigated. The classes of latent E are considered in the mathematical model. The threshold conditions for stability have been obtained. The model has both locally and globally asymptotically stable disease-free equilibrium point. Moreover, it is shown that the transformed model has a unique endemic equilibrium point whenever the reproduction number ${ℛ}_0>1$ . The endemic equilibrium of this model is shown to be locally-asymptotically stable. For the case where the effective contact rate and natural death rate are constants, it is shown that the model has a unique endemic equilibrium which is globally-asymptotically whenever the associated reproduction number exceeds unity. Furthermore, it is shown that adding the age-factor to the corresponding autonomous HSV2 model (considered in Podder and Gumel [23] for the case when quiescent infectious individuals can transmit infection at the same rate as the non-quiescent infectious individuals) does not alter the qualitative dynamics of the autonomous system (with respect to the elimination or persistence of the disease).