Ponente
Descripción
The basic reproduction number ($R_0$) is the fundamental indicator used to assess the transmission potential of an infectious disease and the stability of the disease-free equilibrium in epidemiological and immunological models. However, computing $R_0$ using the Next-Generation Matrix method, $FV^{-1}$, is an algebraically demanding and error-prone process when performed manually, particularly for systems with multiple infected compartments or nonlinear structures. pyR0compute is a Python library that automates this computation through symbolic mathematics. Given a system of differential equations, together with its variables, parameters, and the indices of the infected compartments, the GeneralEpidemiologicalModel class symbolically constructs the matrices of new infections ($F$) and transitions ($V$), linearizes the system around the disease-free equilibrium, and computes $R_0$ as the spectral radius of the next-generation matrix $FV^{-1}$, eliminating the need for manual algebraic derivations. To apply the method, the model equations must be ordered such that the infected compartments appear first. The library is validated using several classical epidemiological models, including SIR, SEIR, and vector-borne disease transmission models, all implemented in Jupyter Notebook (or Google Colab), making the tool suitable for both teaching and applied research. This presentation introduces the mathematical foundation of the Next-Generation Matrix method, the architecture of the library, and its practical application to epidemiological and immunological models, with the aim of providing the mathematical immunology community with a reproducible, extensible, and open-source tool for epidemic threshold analysis.