Mathematical analysis of an age-structured HSV-2 model

Article type: Research Article

Authors: Safi, Mohammad A.^{a; *} | DarAssi, Mahmoud H.^b

Affiliations: [a] Department of Mathematics, The Hashemite University, Zarqa, Jordan | [b] Princess Sumaya University for Technology, Amman, Jordan

Correspondence: [*] Corresponding author: Mohammad A. Safi, Department of Mathematics, The Hashemite University, Zarqa, Jordan. E-mail: [email protected].

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 ℛ0>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).

Keywords: Age-structure, HSV-2, equilibria, stability Mathematics Subject Classification (2010): Primary: 92B05, 92C60; Secondary: 92D30.

DOI: 10.3233/JCM-181111

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 19, no. 3, pp. 841-856, 2019