Search

• A deterministic model to study the dynamics of human immune response to Mycobacterium tuberculosis is proposed. • The host immune response is regulated by the interleukin-10 cytokine during disease progression. • Stability analysis of the model shows a possibility of dynamical stabilization of the disease-free steady state. • The occurrence of latent infection depends on the bacterial load for a reproduction number less than unity. • The time to switch from latent to active state is critically determined by the role of interferon gamma cytokine. The use of mathematical tools to study biological processes is of necessity in determining the effects of these biological processes occurring at different levels. In this paper, we study the immune system's response to infection with the bacteria Mycobacterium tuberculosis (the causative agent of tuberculosis). The response by the immune system is either global (lymph node, thymus, and blood) or local (at the site of infection). The response by the immune system against tuberculosis (TB) at the site of infection leads to the formation of spherical structures which comprised of cells, bacteria, and effector molecules known as granuloma. We developed a deterministic model capturing the dynamics of the immune system, macrophages, cytokines and bacteria. The hallmark of Mycobacterium tuberculosis (MTB) infection in the early stages requires a strong protective cell-mediated naive T cells differentiation which is characterised by antigen-specific interferon gamma (IFN- γ). The host immune response is believed to be regulated by the interleukin-10 cytokine by playing the critical role of orchestrating the T helper 1 and T helper 2 dominance during disease progression. The basic reproduction number is computed and a stability analysis of the equilibrium points is also performed. Through the computation of the reproduction number, we predict disease progression scenario including the latency state. The occurrence of latent infection is shown to depend on a number of effector function and the bacterial load for R 0 < 1. The model predicts that endemically there is no steady state behaviour; rather it depicts the existence of the MTB to be a continuous process progressing over a differing time period. Simulations of the model predict the time at which the activated macrophages overcome the infected macrophages (switching time) and observed that the activation rate (ω) correlates negatively with it. The efficacy of potential host-directed therapies was determined by the use of the model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of malicious object on the immune response of the computer network. Criteria for local stability, instability and global stability are obtained. It is shown that the immune response of the system decreases as the concentration of malicious objects increases, and certain criteria’s are obtained under which it settles down at its equilibrium level. This paper shows that the malicious objects have a grave effect on cyber defense mechanism. The paper has two parts – (i) in the first part a mathematical model is proposed in which dynamics of pathogen, immune response and relative characteristic of the damaged node in the network is investigated, (ii) in second part the effect of malicious object on the immune response of the network has been examined. Finally how and where to use this modeling is discussed. [Copyright &y& Elsevier]

In this paper, we establish and investigate an HIV infection model with treatments and delayed immune response and study its dynamical behaviors. By identifying a critical parameter, we show that if the effectiveness of RT inhibitor and protease inhibitor satisfy some conditions, the uninfected steady state is a unique equilibrium in the feasible region, and the point is globally asymptotically stable. However, if the treatment is not effective enough, then the equilibrium becomes unstable and HIV infection persists. In this case, the other two steady states can be either stable or unstable. By theoretical analyzing, we obtain the results that time delay can affect the stability of the immune-exhausted equilibrium and the infected equilibrium under some conditions. Finally, numerical simulations are carried out to illustrate the main mathematical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the combined effects of cytotoxic T lymphocyte (CTL) responses on the competition dynamics of two Simian immunodeficiency virus (SIV) strains model. One of strains concerns a relatively slowly replicating and mildly cytopathic virus in the early infection (SIVMneCL8), the other is faster replicating and more cytopathic virus at later stages of the infection (SIVMne170). It is shown that the global dynamics of the ordinary differential equations can be determined by several threshold parameters, and we prove the global stability of the equilibria by rigorous mathematical analysis. To account for a series of infection mechanism leading to viral production, we incorporate time delays in the infection term. Using the methods of constructing suitable Lyapunov functionals and LaSalle’s invariance principle, we obtain the sufficient conditions for the global attractiveness of infection-free equilibrium with both virus strains going extinct, single-infection equilibrium with one of two virus strains out-competing the other one and the two strains coexisting infection equilibrium. We establish that the intracellular delays can destabilize the single-infection equilibrium leading to Hopf bifurcation and periodic oscillations. We show that introduction of immune responses is responsible for the coexistence of two virus strains and the intracellular delays may alter the two-strain competition results. Numerical simulations are presented to illustrate the theoretical conclusions. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that the immune response plays an important role in eliminating or controlling the disease after human body is infected by virus. In this paper, we investigate the dynamical behavior of a viral infection model with retarded immune response. The effect of time delay on stability of the equilibria of the system has been studied and sufficient condition for local asymptotic stability of the infected equilibrium and global asymptotic stability of the infection-free equilibrium and the immune-exhausted equilibrium are given. By numerical simulating,we observe that the stationary solution becomes unstable at some critical immune response time, while the delay time and birth rate of susceptible host cells increase, and we also discover the occurrence of stable periodic solutions and chaotic dynamical behavior. The results can be used to explain the complexity of the immune state of patients. [Copyright &y& Elsevier]