A general theory for infectious disease dynamics

Abstract

We present a general theory of infection spreading. It directly follows from conservation laws once known the probability density functions of latent times. The theory can deal with any distribution of compartments latent times. Real probability density function can be then employed, thus overcoming the limitations of standard SIR, SEIR and other similar models that implicitly make use of exponential or exponential-related distributions. SIR and SEIR-type models are, in fact, a subclass of the theory here presented. We show that beside the infection rate, the probability density functions of latent times in the exposed and infectious compartments govern the dynamics of infection spreading. We study the stability of such dynamical system and provide the general solution of the linearized equations in terms of the characteristic functions of latent times probability density functions. We exploit the theory to simulate the spreading of COVID-19 infection in Italy during the first 120 days.