Optimal Control Strategy for Abnormal Innate Immune Response

Innate immune response plays an important role in control and clearance of pathogens following viral infection. However, in the majority of virus-infected individuals, the response is insufficient because viruses are known to use different evasion strategies to escape immune response. In this study, we use optimal control theory to investigate how to control the innate immune response. We present an optimal control model based on an ordinary-differential-equation system from a previous study, which investigated the dynamics and regulation of virus-triggered innate immune signaling pathways, and we prove the existence of a solution to the optimal control problem involving antiviral treatment or/and interferon therapy. We conduct numerical experiments to investigate the treatment effects of different control strategies through varying the cost function and control efficiency. The results show that a separate treatment, that is, only inhibiting viral replication (u1(t)) or enhancing interferon activity (u2(t)), has more advantages for controlling viral infection than a mixed treatment, that is, controlling both (u1(t)) and (u2(t)) simultaneously, including the smallest cost and operability. These findings would provide new insight for developing effective strategies for treatment of viral infectious diseases

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

Nonlinear Control and Estimation of an Infammatory Immune Response

The immune response is a complex mechanism that can be triggered by biological or physical stresses on the organism. However an excessive and dys-regulated inflammatory response may lead to sepsis, a critical state, promoting tissue damage, organ dysfunction or even death.The main objective in this dissertation is to derive a strategy consisting of manipulating pro and anti-inflammatory mediators in order to direct the state of a virtual patient to a healthy equilibrium, after some disturbance from health due to infection. Two key challenges need to be addressed in solving such a problem: estimating the unmeasurable states of the inflammatory model as well as the model\u27s unknown rate parameters; and second, determining an appropriate strategy to effectively control the response.We initially study the nonlinear controllability, observability and identifiability of the inflammatory immune model. Then, we address the first challenge by comparing the performance of various nonlinear filters for state estimation in the presence of noise and incomplete information. For parameter estimation, a recently introduced approximate Markov chain Monte Carlo approach known as the Particle Metropolis- Hastings method is used. To control the highly nonlinear model, various model-based optimization approaches were investigated in which the control strategy is derived in terms of pro-inflammatory and anti-inflammatory response doses. Due to parameter variability and the difficult practical task of obtaining accurate state and parameter estimates in real time, a new model-free control methodology and its intelligent controllers is explored. The method does not rely on any precise modeling and the identification of each parameter of the inflammatory immune model is no longer needed for control design. The various methods are compared for performance to adequately control the responses in a diverse patient population as well as the clinical feasibility of the derived control protocol from the approach used

Mathematical modeling of energy consumption in the acute inflammatory response during sepsis

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. We present a computational model consisting of ordinary differential equations to explore the dynamics of the acute inflammatory response against infections caused when a pathogen makes its way into a host. This model incorporates energy production along with the energy requirements that arise when fighting such an infection. In particular, we investigate the role of energetics during infection and explore the relation between overproduction of nitric oxide (NO), lactate, altered adenosine triphosphate (ATP) levels, and sepsis. Finally, a data-driven approach is used to extend our model as an effort to better understand the role of energy in sepsis. This extended model is calibrated by fitting animal data from a study done in thirty-two baboons that were induced into sepsis after infusing E. coli intravenously. Using Bayesian analysis, we quantify uncertainty in model parameters and with them we investigate differences across different populations, including survivors and non-survivors