Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence

Abstract

In this paper, a discrete-time model has been proposed by applying nonstandard finite difference (NSFD) scheme to solve a delayed viral infection model with immune response and general nonlinear incidence. It is shown that the discrete model has equilibria which are exactly the same as those of the original continuous model. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria of the discrete model is fully determined by the basic reproduction number of the virus and immune response, R 0 and R 1 , with no restriction on the time step size, which implies that the NSFD scheme preserves the qualitative dynamics of the corresponding continuous model.

Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

“…The model proposed and studied here generalizes some existence results in the literatures. 10,18,19 We have obtained two threshold values, ℜ 0 and ℜ 1 , which determine the existence of the equilibria of the model. Moreover, by constructing Lyapunov functionals, we have proved that the global stabilities of the equilibria of the model are completely determined by the two threshold values.…”

“…However, these two features an have important impact on analyzing the virus infection and describing the dynamics of the virus population in vivo (see eg, previous works [11][12][13] ). Thus, to take such two features into consideration for a more real system, many literatures have been proposed and analyzed (see eg, previous works [14][15][16][17][18][19] and references cited in). Recently, Manna 19 studied the following model by taking CTL immune response and intracellular delays into account in model (1) ⎧…”

“…Recently, nonlinear incidence form has been taken into consideration in viral infection models as kH (V). 6,18 Of course, several other incidence forms have been included in viral infection models (see previous studies 7,16,17 and references therein). In addition, notice that the death rates of the five compartments and the production rate of viruses presented in model (2) are given by linear functions; moreover, the activation rate of CTLs and the removal rate of the infection hepatocytes by CTLs are given by specific forms.…”

Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

“…One particular numerical method that we are interested in is by using NSFD schemes to guarantee some properties of the continuous mathematical model. Some previous works using this methodology have been developed for linear and nonlinear delay differential equations [103][104][105][106][107].…”

Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

“…Numerical modeling involves the study of methods to find approximate solutions to differential equations. In recent times, numerical solutions of delay differential equations are of great import due to the versatility of the modeling processes in different fields [42][43][44][45][46][47][48]. Various physical systems involving delay differential equations possesses the physical phenomenon like population sizes, concentration, density and pressure etc.…”