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We formulate a compartmental model of the murine lymphatic system with the transfer rate parameters derived from the data on the geometric characteristics of the lymphatic system (LS) graph structure and the Hagen–Poiseuille-based values of the lymph flows through the system components, i.e., vertices and edges. It is supplemented by the physics-based model of lymph node draining-related function which considers a paradigmatic view of its geometry with one- and three-afferent lymphatic vessels and one efferent vessel, and the lymph flow described by the Darcy–Starling equations. We discuss further modelling work needed to gain a predictive understanding of the LS function in response to various perturbations including infections and therapeutic treatments. [ABSTRACT FROM AUTHOR]

Optimal disturbances of the periodic solution of the hepatitis B dynamics model corresponding to the chronic recurrent form of the disease are found. The dependence of the optimal disturbance on the phase of periodic solution is analyzed. Four phases of the solution are considered, they correspond to clinically different periods of development of the immune response and severity of the disease, namely, activation of antiviral immune reactions, attenuation of reactions, peak and minimum viral load. The possibility of using optimal disturbances to exit the domain of attraction of the considered periodic solution using minimal impact is studied. The components of disturbances that may underlie the phenomenon of spontaneous recovery from chronic hepatitis B observed in clinical practice are identified. [ABSTRACT FROM AUTHOR]

SARS-CoV-2 still presents a global threat to human health due to the continued emergence of new strains and waning immunity among vaccinated populations. Therefore, it is still relevant to investigate potential therapeutics, such as therapeutic interfering particles (TIPs). Mathematical and computational modeling are valuable tools to study viral infection dynamics for predictive analysis. Here, we expand on the previous work on SARS-CoV-2 intra-cellular replication dynamics to include defective interfering particles (DIPs) as potential therapeutic agents. We formulate a deterministic model that describes the replication of wild-type (WT) SARS-CoV-2 virus in the presence of DIPs. Sensitivity analysis of parameters to several model outputs is employed to inform us on those parameters to be carefully calibrated from experimental data. We then study the effects of co-infection on WT replication and how DIP dose perturbs the release of WT viral particles. Furthermore, we provide a stochastic formulation of the model that is compared to the deterministic one. These models could be further developed into population-level models or used to guide the development and dose of TIPs. [ABSTRACT FROM AUTHOR]

Optimal disturbances of a number of typical stationary solutions of the hepatitis B virus infection dynamics model have been found. Specifically optimal disturbances have been found for stationary solutions corresponding to various forms of the chronic course of the disease, including those corresponding to the regime of low-level virus persistence. The influence of small optimal disturbances of individual groups of variables on the stationary solution is studied. The possibility of transition from stable stationary solutions corresponding to chronic forms of hepatitis B to stable stationary solutions corresponding to the state of functional recovery or a healthy organism using optimal disturbances is studied. Optimal disturbances in this study were constructed on the basis of generalized therapeutic drugs characterized by one-compartment and two-compartment pharmacokinetics. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to modeling the repertoire of the immune system and its adaptation in response to the evolutionary dynamics of pathogens associated with their genetic variability. It is based on application of a dynamic programming-based framework to model the antigen-driven immune repertoire synthesis. The processes of formation of new receptor specificity of lymphocytes (the growth of their affinity during maturation) are described by an ordinary differential equation (ODE) with a piecewise-constant right-hand side. Optimal control synthesis is based on the solution of the Hamilton–Jacobi–Bellman equation implementing the dynamic programming approach for controlling Gaussian random processes generated by a stochastic differential equation (SDE) with the noise in the form of the Wiener process. The proposed description of the clonal repertoire of the immune system allows us to introduce an integral characteristic of the immune repertoire completeness or the integrative fitness of the whole immune system. The quantitative index for characterizing the immune system fitness is analytically derived using the Feynman–Kac–Kolmogorov equation. [ABSTRACT FROM AUTHOR]

Mathematical models with time delays are widely used to analyze the mechanisms of the immune response to virus infections and predict various therapeutic effects. Using the lymphocytic choriomeningitis virus infection model as an example, this work describes an original computational technology for searching the bistable regimes of such models. This technology includes numerical methods for finding all possible steady states at fixed values of parameters, for tracing these states along the parameters and for analyzing their stability. [ABSTRACT FROM AUTHOR]

In this study, we discuss critical issues in modelling the structure and function of lymph nodes (LNs), with emphasis on how LN physiology is related to its multi-scale structural organization. In addition to macroscopic domains such as B-cell follicles and the T cell zone, there are vascular networks which play a key role in the delivery of information to the inner parts of the LN, i.e., the conduit and blood microvascular networks. We propose object-oriented computational algorithms to model the 3D geometry of the fibroblastic reticular cell (FRC) network and the microvasculature. Assuming that a conduit cylinder is densely packed with collagen fibers, the computational flow study predicted that the diffusion should be a dominating process in mass transport than convective flow. The geometry models are used to analyze the lymph flow properties through the conduit network in unperturbed- and damaged states of the LN. The analysis predicts that elimination of up to 60%-90% of edges is required to stop the lymph flux. This result suggests a high degree of functional robustness of the network. [ABSTRACT FROM AUTHOR]