Age-Structured SILV Epidemic Model on HPV and Cellular Dynamics with Implicit Impact of Vaccination

Abstrak

The implicit impact of vaccination on susceptible cells (epithelial layer) is studied on the basis of stability analysis of age-structured epidemic model of susceptible cells, infected cells and cells of lesion tissue (dysplasia and cancer), human papillomavirus (HPV). The efficacy of the vaccine indirectly influences the coefficients of the system, thereby determining the types of dynamical regime of the HPV and cellular population. The model possesses unique disease-free (DFE) and unique endemic equilibria (EE) (Theorem 1). The asymptotically stable DFE is associated with the resilience of epithelial layer of vaccinated organism to HPV infection while the asymptotically stable EE is associated with the resilience of the lesion tissue of epithelial layer to treatment. The analysis of the model reveals independent factors affecting the stability/instability of DFE and EE (Theorems 2, 3): (i) cell death rate and proliferation rate, (ii) HPV infection rate, budding number of HPV virions, apoptosis rate of infected cells and HPV death rate (parameters of the implicit influence of vaccine efficacy), and (iii) DFE value of epithelial tissue size (environmental capacity of HPV depending on the initial size of the epithelial layer). Thus, HPV vaccine efficacy should be sufficiently high to guarantee the asymptotic stability of DFE with the epithelial tissue of large possible size, which can be taken into account when studying the efficacy of new vaccines in control groups in clinical trials.