Age-structured delayed SIPCV epidemic model of HPV and cervical cancer cells dynamics I. Numerical method

Abstract

The numerical method for simulation dynamics of nonlinear epidemic model of age-structured sub-populations of susceptible, infectious, precancerous and cancer cells and unstructured population of human papilloma virus (HPV) is developed (SIPCV model). Cell population dynamics is described by the initial-boundary value problem for the delayed semi-linear hyperbolic equations with age- and time-dependent coefficients and HPV dynamics is described by the initial problem for nonlinear delayed ODE. The model considers two time-delay parameters: the time between viral entry into a target susceptible cell and the production of new virus particles, and duration of the first stage of delayed immune response to HPV population growing. Using the method of characteristics and method of steps we obtain the exact solution of the SIPCV epidemic model in the form of explicit recurrent formulae. The numerical method designed for this solution and used the trapezoidal rule for integrals in recurrent formulae has a second order of accuracy. Numerical experiments with vanished mesh spacing illustrate the second order of accuracy of numerical solution with respect to the benchmark solution and show the dynamical regimes of cell-HPV population with the different phase portraits.

SVLIAR age-of-infection and -immunity structured epidemic model of COVID-19 dynamics

“…This study is focused on a qualitative analysis of transmission dynamics of the COVID-19 induced disease in sub-classes of susceptible, vaccinated, latent, infected, asymptomatic and recovered individuals of population. The mostly used methods of theoretical analysis of transmission dynamics of infectious diseases in epidemic models are based on the age-structured models of population dynamics [1][2][3][4][5][6][7][8] which relate the age-dependent demographic parameters of susceptible, infected, and recovered sub-classes of population with characteristics of infection-induced disease transmission. Be-cause such models use pretty complex and accurate mathematical methods for simulation, they help us understand better the features of mechanisms, risks, dynamics and mitigation of pandemic diseases.…”

“…Several concluding remarks are given in Section 6. The existence theorem, explicit recurrent formula for the solution of the agestructured SVLIAR model and numerical method with simulations (like in works [1,2]) are beyond the aim and scope of this paper due to the complexity of the model and will be the subject of our further study.…”