Age-structured Delayed SIPCV Epidemic Model of HPV and Cervical Cancer Cells Dynamics II. Convergence of Numerical Solution

Abstract

The numerical method for simulation of age-structured SIPCV epidemic model with age-structured sub-classes of susceptible, infectious, precancerous and cancer cells and unstructured population of human papilloma virus (HPV) dynamics with incubation period is developed. Convergence of the numerical approximations is studied both theoretically and numerically. We prove the stability and second rate of convergence of the approximate solutions to the exact solution of the SIPCV epidemic nonlinear system. The numerical experiments based on the grid refined method confirm and illustrate the second order of accuracy of the obtained numerical method and show the various dynamical regimes of population dynamics. Simulations for model parameters of the system reveal two unstable dynamical regimes of SIPCV population which correspond to the cancer tumor growth and formation of metastases in organism.