Abstract
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.
Highlights
Herpes simplex virus (HSV) is one of the most highly widespread sexually transmitted infections [1]
The two strains of the disease are, HSV1 mostly known as cold sores and HSV2 known as genital herpes
Numerical simulations indicate that the two HSV strains co-exist, with HSV1 dominating but not driving out HSV2 whenever R1 > R2 > 1 and vice versa
Summary
Herpes simplex virus (HSV) is one of the most highly widespread sexually transmitted infections [1]. In order to mitigate the spread and global socio-economic burden, mathematical modeling is an important tool that can provide insight into the long-term dynamics of a disease. It helps to simplify complex disease systems and has been a catalyst for decision making. There are type-specific serology testing in the absence of symptoms which helps to determine the particular strain of the virus [15], and palliative treatment is administered to infected individuals to help get rid of the sores, reduce the risk of transmission as well as minimize the number and intensity of within host outbreaks.
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