A stage structured hybrid model for disease dynamics and complex systems modelling

Stochasticity and spatial distribution of the pathogen play a critical role in determining the outcome of an infection. 1 in a million immune system cells are specific to a particular pathogen. The serendipitous encounter of such a rare immune system cell with its fated antigen can determine the mortality of the infected animal. Moreover pathogens may remain initially localized in a small volume of tissue. Hence stochastic and spatial aspects play an important role in pathogenesis, especially early on in the infection. Current efforts at investigating the effect of stochasticity and space in modeling of host immune response and pathogens use agent based models (ABMs). However these are computationally expensive. Population level approaches like ordinary differential equations (ODEs) are computationally tractable. However they make simplifying assumptions that are unlikely to be true early on in the infection. We proposed a stage-structured hybrid model that aims to strike a balance between the detail of representation of an ABM and the computational tractability of an ODE model. It uses a spatially explicit ABM in the initial stage of infection, and a coarse-grained but computationally tractable ODE model in the latter stages of infection. Such an approach might hold promise in: 1) modeling of other pathogens where the initial stochasticity of the pathogen dictates the trajectory of pathogenesis, and 2) lead to insights into immune system inspired strategies and architectures for distributed systems of computers.