Stability analysis of a multistage compartmental model of infection

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This paper explores the dynamics of a multistage SIRS model. Using the Lyapunov method as our primary tool, we first revisit the stability analysis of the disease-free and endemic equilibria of a single-stage SIRS model. We then extend the techniques employed in this analysis to enable a similar stability analysis of multistage infection models. In particular, we propose a systematic approach to construct Lyapunov functions for multistage models using symbolic computation in MATLAB. We find that the structure of the constructed Lyapunov functions is closely related to the subsystems or pathways through which the disease progresses. The complete stability analysis for two- and three-stage infection models is presented, and we show that the equilibria are globally asymptotically stable when several parameter constraints are satisfied. Some of these mathematical constraints also provide meaningful epidemiological interpretations.