Agent-Based Derivation of the SIR-Differential Equations

Due to exponentially increasing computational resources, individual-based models are getting more and more popular among epidemiologists. Inspired by SIR (Susceptible-Infected-Recovered) epidemics very complex and flexible models for diseases and vaccine strategies can be created accepting the risk, that maybe unexplained and unpredictable chaotic group-behavior could distort the results. Preventive theoretical analysis of these microscopic models is still very difficult. Based on the idea of diffusion approximation a technique is presented, how the mean value of a simple predefined agent-based SIR model can be calculated to asymptotically satisfy the classic SIR differential equations by Kermack and McKendrick. This technique can be generalized to contribute to the analysis of agent-based models and can help developing hybrid models.