A unifying theory of aging and mortality

In this paper, we advance the network theory of aging and mortality by developing a causal mathematical model for the mortality rate. First, we show that in large networks, where health deficits accumulate at nodes representing health indicators, the modelling of network evolution with Poisson processes is universal and can be derived from fundamental principles. Second, with the help of two simplifying approximations, which we refer to as mean-field assumption and homogeneity assumption, we provide an analytical derivation of Gompertz law under generic and biologically relevant conditions. Third, we identify for which network parameters Gompertz law is accurate, express the parameters in Gompertz law as a function of the network parameters, and illustrate our computations with simulations and analytic approximations. Our paper is the first to offer a full mathematical explanation of Gompertz law and its limitations based on network theory.