Optimal control strategy for abnormal innate immune response

A data-driven model of the role of energy in sepsis

Exposure to pathogens elicits a complex immune response involving multiple interdependent pathways. This response may mitigate detrimental effects and restore health but, if imbalanced, can lead to negative outcomes including sepsis. This complexity and need for balance pose a challenge for clinicians and have attracted attention from modelers seeking to apply computational tools to guide therapeutic approaches. In this work, we address a shortcoming of such past efforts by incorporating the dynamics of energy production and consumption into a computational model of the acute immune response. With this addition, we performed fits of model dynamics to data obtained from non-human primates exposed to Escherichia coli. Our analysis identifies parameters that may be crucial in determining survival outcomes and also highlights energy-related factors that modulate the immune response across baseline and altered glucose conditions.

Optimal Allocation of Vaccine and Antiviral Drugs for Influenza Containment over Delayed Multiscale Epidemic Model considering Time-Dependent Transmission Rate

In this study, two types of epidemiological models called "within host" and "between hosts" have been studied. The within-host model represents the innate immune response, and the between-hosts model signifies the SEIR (susceptible, exposed, infected, and recovered) epidemic model. The major contribution of this paper is to break the chain of infectious disease transmission by reducing the number of susceptible and infected people via transferring them to the recovered people group with vaccination and antiviral treatment, respectively. Both transfers are considered with time delay. In the first step, optimal control theory is applied to calculate the optimal final time to control the disease within a host's body with a cost function. To this end, the vaccination that represents the effort that converts healthy cells into resistant-to-infection cells in the susceptible individual's body is used as the first control input to vaccinate the susceptible individual against the disease. Moreover, the next control input (antiviral treatment) is applied to eradicate the concentrations of the virus and convert healthy cells into resistant-to-infection cells simultaneously in the infected person's body to treat the infected individual. The calculated optimal time in the first step is considered as the delay of vaccination and antiviral treatment in the SEIR dynamic model. Using Pontryagin's maximum principle in the second step, an optimal control strategy is also applied to an SEIR mathematical model with a nonlinear transmission rate and time delay, which is computed as optimal time in the first step. Numerical results are consistent with the analytical ones and corroborate our theoretical results.

A novel control set-valued approach with application to epidemic models

This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations that model the temporal evolution of disease spread. The set of initial data, from which the number of infected people decrease to zero, is generated by a new type of Lyapunov functions defined in the sense of viability theory. The associated controls are provided via selections of adequately designed feedback map. The existence of such selections is improved by using Micheal selection theorem. Finally, an application to the SIRS epidemic model, with numerical simulations, is given to show the efficiency of our approach. To the best of our knowledge, our work is the first one that used a set-valued approach based on the viability theory to deal with an epidemic control problem.

Mathematical modeling of energy consumption in the acute inflammatory response

When a pathogen invades the body, an acute inflammatory response is activated to eliminate the intruder. In some patients, runaway activation of the immune system may lead to collateral tissue damage and, in the extreme, organ failure and death. Experimental studies have found an association between severe infections and depletion in levels of adenosine triphosphate (ATP), increase in nitric oxide production, and accumulation of lactate, suggesting that tissue energetics is compromised. In this work we present a differential equations model that incorporates the dynamics of ATP, nitric oxide, and lactate accompanying an acute inflammatory response and employ this model to explore their roles in shaping this response. The bifurcation diagram of the model system with respect to the pathogen growth rate reveals three equilibrium states characterizing the health, aseptic and septic conditions. We explore the domains of attraction of these states to inform the instantiation of heterogeneous virtual patient populations utilized in a survival analysis. We then apply the model to study alterations in the inflammatory response and survival outcomes in metabolically altered conditions such as hypoglycemia, hyperglycemia, and hypoxia.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Negative feedback contributes to the stochastic expression of the interferon-β gene in virus-triggered type I interferon signaling pathways

Type I interferon (IFN) signaling pathways play an essential role in the defense against early viral infections; however, the diverse and intricate molecular mechanisms of virus-triggered type I IFN responses are still poorly understood. In this study, we analyzed and compared two classes of models i.e., deterministic ordinary differential equations (ODEs) and stochastic models to elucidate the dynamics and stochasticity of type I IFN signaling pathways. Bifurcation analysis based on an ODE model reveals that the system exhibits a bistable switch and a one-way switch at high or low levels when the strengths of the negative and positive feedbacks are tuned. Furthermore, we compared the stochastic simulation results under the Master and Langevin equations. Both of the stochastic equations generate the bistable switch phenomenon, and the distance between two stable states are smaller than normal under the simulation of the Langevin equation. The quantitative computations also show that a moderate ratio between positive and negative feedback strengths is required to ensure a reliable switch between the different IFN concentrations that regulate the immune response. Moreover, we propose a multi-state stochastic model based on the above deterministic model to describe the multi-cellular system coupled with the diffusion of IFNs. The perturbation and inhibition analysis showed that the positive feedback, as well as noises, has little effect on the stochastic expression of IFNs, but the negative feedback of ISG56 on the activation of IRF7 has a great influence on IFN stochastic expression. Together, these results reveal that positive feedback stabilizes IFN gene expression, and negative feedback may be the main contribution to the stochastic expression of the IFN gene in the virus-triggered type I IFN response. These findings will provide new insight into the molecular mechanisms of virus-triggered type I IFN signaling pathways.