A mathematical model for the immune system response to bacterial infections is proposed. The formalism is based on modeling the chemokine-determined transmigration of leukocytes from a venule through the venule walls and the subsequent in-tissue migration and engulfment of the pathogens that are responsible for the infection. The model is based on basic principles, such as Poiseuille blood flow through the venule, fundamental solutions of the diffusion-reaction equation for the concentration field of pathogen-released chemokines, linear chemotaxis of the leukocytes, random walk of pathogens, and stochastic processes for the death and division of pathogens. Thereby, a computationally tractable and, as far as we know, original framework has been obtained, which is used to incorporate the interaction of a substantial number of leukocytes and thereby to unravel the significance of biological processes and parameters regarding the immune system response. The developed model provides a neat way for visualization of the biophysical mechanism of the immune system response. The simulations indicate a weak correlation between the immune system response in terms of bacterial clearing time and the leukocyte stiffness, and a significant decrease in the clearing time with increasing in-blood leukocyte density, decreasing pathogen motility, and increasing venule wall transmissivity. Finally, the increase in the pathogen death rate and decrease in pathogen motility induce a decrease in the clearing time of the infection. The adjustment of the latter two quantities mimic the administration of antibiotics.
- Immune system
- Stochastic modeling