Spatiotemporal Dynamics of a Generalized Viral Infection Model with Distributed Delays and CTL Immune Response

Infection propagation in a tissue with resident macrophages

The progression of viral infection within the human body is governed by a complex interplay between the pathogen and the immune response. The initial phase of the innate immune response is driven by inflammatory cytokines and interferons produced by infected target cells and tissue-resident macrophages. These inflammatory cytokines not only amplify the immune response but also initiate programmed cell death, which helps slow the spread of the infection. The propagation of the infection within tissues can be modeled as a reaction-diffusion wave, where the speed of this wave is linked to the virus virulence, and the overall viral load determines its infectivity. In this study, we demonstrate that inflammation reduces both the speed and viral load of the infection wave, and we establish the conditions necessary to halt the spread of the infection. Depending on the relative strength of the infection and the immune response, there are three possible outcomes of infection progression. If the virus replication number is sufficiently low, the infection does not develop. For intermediate values of this parameter, the infection spreads within the affected tissue at a decreasing speed and amplitude before ultimately being eliminated. However, if the virus replication number is high, the infection propagates as a reaction-diffusion wave with a constant speed and amplitude. These findings are derived using analytical methods and are corroborated by numerical simulations. Additionally, we explore viral diffusion, comparing the conventional parabolic diffusion model with the hyperbolic diffusion model, which is introduced to address the limitation of infinite propagation speed. Our results show that while the viral load remains the same across both models, the wave speed in the hyperbolic model is smaller and approaches that of the parabolic model as the relaxation time decreases.

Stability of a diffusive-delayed HCV infection model with general cell-to-cell incidence function incorporating immune response and cell proliferation

In this work, we analyse the dynamics of a five-dimensional hepatitis C virus infection mathematical model including the spatial mobility of hepatitis C virus particles, the transmission of hepatitis C virus infection by mitosis process of infected hepatocytes with logistic growth, time delays, antibody response and cytotoxic T lymphocyte (CTL) immune response with general incidence functions for both modes of infection transmission, namely virus-to-cell as well as cell-to-cell. Firstly, we prove rigorously the existence, the uniqueness, the positivity and the boundedness of the solution of the initial value and boundary problem associated with the new constructed model. Secondly, we found that the basic reproductive number is the sum of the basic reproduction number determined by cell-free virus infection, determined by cell-to-cell infection and determined by proliferation of infected cells. It is proved the existence of five spatially homogeneous equilibria known as infection-free, immune-free, antibody response, CTL response and antibody and CTL responses. By using the linearization methods, the local stability of the latter is established under some rigorous conditions. Finally, we proved the existence of periodic solutions by highlighting the occurrence of a Hopf bifurcation for a certain threshold value of one delay.

A modular framework for multiscale, multicellular, spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues and its application to drug therapy timing and effectiveness

Simulations of tissue-specific effects of primary acute viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding of infection mechanisms, and parallel development of components by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage, specifically designed to be modular and extensible to support continuous updating and parallel development. The base simulation of a simplified patch of epithelial tissue and immune response exhibits distinct patterns of infection dynamics from widespread infection, to recurrence, to clearance. Slower viral internalization and faster immune-cell recruitment slow infection and promote containment. Because antiviral drugs can have side effects and show reduced clinical effectiveness when given later during infection, we studied the effects on progression of treatment potency and time-of-first treatment after infection. In simulations, even a low potency therapy with a drug which reduces the replication rate of viral RNA greatly decreases the total tissue damage and virus burden when given near the beginning of infection. Many combinations of dosage and treatment time lead to stochastic outcomes, with some simulation replicas showing clearance or control (treatment success), while others show rapid infection of all epithelial cells (treatment failure). Thus, while a high potency therapy usually is less effective when given later, treatments at late times are occasionally effective. We illustrate how to extend the platform to model specific virus types (e.g., hepatitis C) and add additional cellular mechanisms (tissue recovery and variable cell susceptibility to infection), using our software modules and publicly-available software repository.

A modular framework for multiscale, multicellular, spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues and its application to drug therapy timing and effectiveness: A multiscale model of viral infection in epithelial tissues

Simulations of tissue-specific effects of primary acute viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding of infection mechanisms, and parallel development of components by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage, specifically designed to be modular and extensible to support continuous updating and parallel development. The base simulation of a simplified patch of epithelial tissue and immune response exhibits distinct patterns of infection dynamics from widespread infection, to recurrence, to clearance. Slower viral internalization and faster immune-cell recruitment slow infection and promote containment. Because antiviral drugs can have side effects and show reduced clinical effectiveness when given later during infection, we studied the effects on progression of treatment potency and time-of-first treatment after infection. In simulations, even a low potency therapy with a drug which reduces the replication rate of viral RNA greatly decreases the total tissue damage and virus burden when given near the beginning of infection. Many combinations of dosage and treatment time lead to stochastic outcomes, with some simulation replicas showing clearance or control (treatment success), while others show rapid infection of all epithelial cells (treatment failure). Thus, while a high potency therapy usually is less effective when given later, treatments at late times are occasionally effective. We illustrate how to extend the platform to model specific virus types (e.g., hepatitis C) and add additional cellular mechanisms (tissue recovery and variable cell susceptibility to infection), using our software modules and publicly-available software repository.

Nonlinear character analysis for bistability in virus–immune dynamics

Structured abstract

Aim: The nonlinear characters of two linearly stable equilibrium states (virus and immune) for a theoretical virus-immune model are analyzed. Methods: Conditional nonlinear optimal perturbation (CNOP), Lyapunov method and linear singular vector method. Results & conclusion: Two linearly stable equilibrium states (immune-free and immune) with linear methods are nonlinearly unstable using the CNOP method. When the CNOP-type of initial perturbation is used in the model, the immune-free (immune) equilibrium state will be made into the immune (immune-free) equilibrium state. Through computing the variations of nonlinear terms of the model, the nonlinear effect of immune proliferation plays an important role in abrupt changes of the immune-free equilibrium state compared with the linear term. For the immune equilibrium state, the nonlinear effect of viral replication is also an important factor.