Development Of An Agent Based Model To Simulate The Immune System With IAV Infection And Integration Of A Regression Method To Estimate The Parameters

Seasonal and pandemic influenza A virus(IAV) continues to be a public health threat. To prevent the spread of virus and enhance people's immunity, scientists did a lot of research to study the immune principle of the virus. Especially, Agent based model(ABM) and differential equations(DE) are two commonly used methods for immune system simulation.Simulation methods need much shorter time in experiment and a higher efficiency in research process compared with biological experiment method. In the situation of responding to the influenza epidemic, ABM and DE have the ability to build a corresponding response model to help researchers find the infection mechanism quickly. Simulation methods have made a great contribution in immune system studying which avoiding the emergence of a wide spread pandemic. However, there are still shortcomings cannot be ignored for ABM and DE methods. For instance, it is difficult for ABM to estimate key parameters for the immune system model by incorporating experimental data, leading to a poor result in parameter estimation. Meanwhile, the ABM has high dependence on powerful computer hardware and software resources when it is faced a complex system like immune system. On the other hand, DE method is not able to descript the immune system model detailed enough in multi-dimensions though it is good at estimating parameters with excellent mathematical methods.To address these issues and integrate the advantages of these two commonly used models, a new effective method called integrated ABM regression model(IABMR) is created in this paper. Firstly, an agent based model were developed to describe the multi-scale immune system with various phenotypes and types of cells in a lung. Secondly, the key parameters were optimized using the particle swarm optimization algorithm(PSO) and Loess regression method. The detailed process of this study is explained in following content.In the modelling phase, we divided one kind of cell population into three different states, just as quiescence, proliferation and dead phenotypes, based on the cell biology and actual situations. There are not only the interaction between cells, but also between different phenotypes of the same kind of a cell. And then, we employed the advantages of ABM technology to build a multi-scaled immune system model in multi-level combined with the cell state transition diagrams and state transition equations in the situation of IAV attack.In the parameter estimation phase, a parameter vector space of four dimensions is generated as the input parameters of ABM by sparse grid. And then, we extract the input data and output data to train the Loess regression after running ABM model for many times until a Loess regression model is built. Loess regression is a nonparametric regression which can be fitted to the same data with many different times to explore the relationship data in a may be hidden in the data. Finally, we finish the parameter optimization of the immune system model by employing the particle swarm optimization algorithm and the Loess regression model.In the experimental results and analysis phase, we not only realized the whole algorithm of the IABMR method, but also completed some comparative experiments. Firstly, we made different configuration settings in vector space, repeat times, data noise and the number of sample time points to test the method itself. And then, the best optimal configuration of IAMBR could be found by computing the average relative errors of different settings. Fortunately, the result shows that IABMR method will perform better when it is set with a larger space, a smaller data noise and a sample with much more time points. Next, we compared IABMR with greedy algorithm and ODE model in parameter estimation and simulation aspects. The results indicate that IABMR not only has the potential to simulate the immune system at various scales, phenotypes and cell types, but can also accurately infer the key parameters like DE model.In a word, IABMR method developed an immune system model in multi-scaled and finished parameter estimation successfully by integrating agent based model, Loess regression and particle swarm optimization algorithm effectively. It can both describe the immune system model detailed in multi-dimensions and estimate the model parameters combined with the experimental data. The method developed in this paper not only improve the efficiency of scientific research but also has a very important significance in the study of infectious diseases.