In this work, quiescence is added to the Susceptible-Infectious-Recovered (SIR) model with demography. In order to investigate consequences of quiescence in the infection process in more depth, we use stochastic simulations on the stochastic version of model that we built. This method provides a more accurate picture of the dynamics of infectious diseases by taking into consideration the inherent randomness in the disease processes. We examine the effects of quiescence on the number of infected people using simulations. The results, presented in histograms depicting the distribution of infected individuals, reveal a notable trend: the mean number of infected individuals is higher when quiescence is incorporated into the dynamics. These finding emphasizes the dynamic influence of quiescence on infectious disease spread. The higher mean number of infections during periods of quiescence highlights the need for public health strategies that are flexible enough to focused interventions during these times to reduce the possibility of an increase in infections.

The present paper reviews evidence for ecological evolution of Montiaceae. Montiaceae (Portulacineae) comprise a family of ca. 275 species and ca. 25 subspecific taxa of flowering plants distributed mainly in extreme western America, with additional endemism elsewhere, including other continents and islands. They have diversified repeatedly across steep ecological gradients. Based on narrative analysis, I argue that phylogenetic transitions from annual to perennial life history have been more frequent than suggested by computational phylogenetic reconstructions. I suggest that a reported phylogenetic correlation between the evolution of life history and temperature niche is coincidental and not causal. I demonstrate how statistical phylogenetic comparative analysis (PhCA) missed evidence for marked moisture niche diversification among Montiaceae. I discount PhCA evidence for the relation between Montiaceae genome duplication and ecological diversification. Based on the present analysis of Montiaceae evolution, I criticize the premise of the prevalent statistical approach to PhCA, which tests Darwinian deterministic hypotheses against stochastic evolutionary null models. I discuss theoretical/empirical evidence that evolution is neither stochastic, nor Darwinistically-determined, but idiosyncratic. Idiosyncraticity describes the outcome of a stochastically perturbed nonlinear chaos-like process. The Principle of Evolutionary Idiosyncraticity (PEI) is based on the evolutionary theory of Natural Drift, which maintains that determinism in evolution is a property of the organism and not, as maintained by the theory of Natural Selection, its traits or its milieu. This determinism is characteristic of chaotic functions, which are absolutely determinate, generate self-similarity, but remain absolutely unpredictable. PEI explains precisely observations that evolution proceeds not linearly, but chaotically, producing both quasi-linear fractal-like patterns and non-linear jumps. PEI has ramifications for all areas of macroevolutionary research. In particular, it demonstrates both the fallacy and futility of the statistical PhCA approach that interprets evolutionary causes in terms of evolutionary correlations. However, statistical methods of PhCA can be applied heuristically and fruitfully to reveal idiosyncraticity and discover evolutionary novelty. This, in turn, is demonstrated by the emergence of statistical anomalies in evolutionary analyses of Montiaceae.