Open AccessA simple two-strain HSV epidemic model with palliative treatment
Author(s) -
Janet Kwakye,
AUTHOR_ID,
Jean M. Tchuenche,
AUTHOR_ID
Publication year - 2021
Publication title -
open journal of mathematical analysis
Language(s) - English
Resource type - Journals
eISSN - 2616-8111
pISSN - 2616-8103
DOI - 10.30538/psrp-oma2021.0093
Subject(s) - simplex , strain (injury) , ordinary differential equation , basic reproduction number , transmission (telecommunications) , herpes simplex virus , nonlinear system , virus strain , mathematics , combinatorics , reproduction , physics , virus , mathematical analysis , virology , biology , differential equation , computer science , genetics , quantum mechanics , demography , population , telecommunications , anatomy , sociology
A two-strain model of the transmission dynamics of herpes simplex virus (HSV) with treatment is formulated as a deterministic system of nonlinear ordinary differential equations. The model is then analyzed qualitatively, with numerical simulations provided to support the theoretical results. The basic reproduction number \(R_0\) is computed with \(R_0=\text{max}\lbrace R_1, R_2 \rbrace \) where \(R_1\) and \(R_2\) represent respectively the reproduction number for HSV1 and HSV2. We also compute the invasion reproductive numbers \(\tilde{R}_1\) for strain 1 when strain 2 is at endemic equilibrium and \(\tilde{R}_2\) for strain 2 when strain 1 is at endemic equilibrium. To determine the relative importance of model parameters to disease transmission, sensitivity analysis is carried out. The reproduction number is most sensitive respectively to the contact rates \(\beta_1\), \(\beta_2\) and the recruitment rate \(\pi\). Numerical simulations indicate the co-existence of the two strains, with HSV1, dominating but not driving out HSV2 whenever \(R_1 > R_2 > 1\) and vice versa.