Related papers: Monotonic and nonmonotonic immune responses in vir…
Recently, Wang and Xu [ Appl. Math. Lett. 78 (2018) 105-111] studied thresholds and bi-stability in virus-immune dynamics. In this paper, we show there also exist backward bifurcation and saddle node bifurcation in this model. Our…
Viral infections trigger complex immune responses with heterogeneous outcomes shaped by nonlinear feedbacks. An ordinary differential equation model is developed to investigate immune response dynamics during viral infection, incorporating…
We investigate an epidemiological model that incorporates waning of immunity at the individual level and boosting of the immune system upon re-exposure to the pathogen. When immunity is fully restored upon boosting, the system can be…
In this paper we consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains wild-type virus and one mutant. A finite response time of the immune system was considered in order which leads…
It has been known for some time that human autoimmune diseases can be triggered by viral infections. Several possible mechanisms of interactions between a virus and immune system have been analysed, with a prevailing opinion being that the…
We performed a thorough sensitivity analysis of the herd immunity threshold for discrete-time SIR compartmental models with a static network structure. We find unexpectedly that these models violate classical intuition which holds that the…
We study convergence properties of competing epidemic models of the Susceptible-Infected-Susceptible (SIS) type. The SIS epidemic model has seen widespread popularity in modelling the spreading dynamics of contagions such as viruses,…
A model of nonlinear optical system surrounded by two loops of feedback is investigated. The cell with the vapor of rubidium - type atoms is taken in the capacity of nonlinear element. Two modes of near-resonant electromagnetic field…
Among various possible causes of autoimmune disease, an important role is played by infections that can result in a breakdown of immune tolerance, primarily through the mechanism of "molecular mimicry". In this paper we propose and analyse…
The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations…
We examine the properties of a recently proposed model for antigenic variation in malaria which incorporates multiple epitopes and both long-lasting and transient immune responses. We show that in the case of a vanishing decay rate for the…
This paper shows the global existence and boundedness of solutions of a reaction diffusion system modeling liver infections. The existence proof is presented step by step and the focus lies on the interpretation of intermediate results in…
This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the…
Tumor-immune interactions are shaped by both antigenic heterogeneity and stochastic perturbations in the tumor microenvironment, yet the mathematical mechanisms underlying immune phase transitions remain poorly understood. We propose a…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature…
SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure…
Infectious diseases often involve multiple strains that interact through the immune response generated after an infection. This study investigates the conditions under which a two-strain epidemic model with partial cross-immunity can lead…
Steady state nonmonotonic ("biphasic") dose responses are often observed in experimental biology, which raises the control-theoretic question of identifying which possible mechanisms might underlie such behaviors. It is well known that the…
A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune…