American, German and British antecedents to Pearl and Reed's logistic curve

What Can We Learn from the Time Evolution of COVID-19 Epidemic in Slovenia?

A recent work indicates that temporarily splitting larger populations into smaller groups can efficiently mitigate the spread of SARS‐CoV‐2 virus. The fact that, soon afterward, the two million people Slovenia was the first European country proclaiming the end of COVID‐19 epidemic within national borders may be relevant from this perspective. Motivated by this evolution, in this paper the time dynamics of coronavirus cases in Slovenia is investigated with emphasis on how efficient various containment measures act to diminish the number of COVID‐19 infections. Noteworthily, the present analysis does not rely on any speculative theoretical assumption; it is solely based on raw epidemiological data. Out of the results presented here, the most important one is perhaps the finding that, while imposing drastic curfews and travel restrictions reduce the infection rate κ by a factor of four with respect to the unrestricted state, they only improve the κ‐value by ≈15% as compared to the much bearable state of social and economic life wherein wearing face masks and social distancing rules are enforced/followed. Significantly for behavioral and social science, our analysis may reveal an interesting self‐protection instinct of the population, which became manifest even before the official lockdown enforcement.

Suppression of Groups Intermingling as an Appealing Option for Flattening and Delaying the Epidemiological Curve While Allowing Economic and Social Life at a Bearable Level during the COVID-19 Pandemic

The COVID‐19 pandemic in a population modelled as a network wherein infection can propagate both via intra‐ and inter‐group interactions is simulated. The results emphasize the importance of diminishing the inter‐group infections in the effort of substantial flattening/delaying of the epi(demiologic) curve with concomitant mitigation of disastrous economy and social consequences. To exemplify, splitting a population into m (say, 5 or 10) noninteracting groups while keeping intra‐group interaction unchanged yields a stretched epidemiological curve having the maximum number of daily infections reduced and postponed in time by the same factor m (5 or 10). More generally, the study suggests a practical approach to fight against SARS‐ CoV‐ 2 virus spread based on population splitting into groups and minimizing intermingling between them. This strategy can be pursued by large‐scale infrastructure reorganization of activity at different levels in big logistic units (e.g., large productive networks, factories, enterprises, warehouses, schools, (seasonal) harvest work). Importantly, unlike total lockdown, the proposed approach prevents economic ruin and keeps social life at a more bearable level than distancing everyone from anyone. The declaration for the first time in Europe that COVID‐19 epidemic ended in the two‐million population Slovenia may be taken as support for the strategy proposed here.

An ecological framework for the analysis of prebiotic chemical reaction networks

It is becoming widely accepted that very early in life's origin, even before the emergence of genetic encoding, reaction networks of diverse small chemicals might have manifested key properties of life, namely self-propagation and adaptive evolution. To explore this possibility, we formalize the dynamics of chemical reaction networks within the framework of chemical ecosystem ecology. To capture the idea that life-like chemical systems are maintained out of equilibrium by fluxes of energy-rich food chemicals, we model chemical ecosystems in well-mixed compartments that are subject to constant dilution by a solution with a fixed concentration of input chemicals. Modelling all chemical reactions as fully reversible, we show that seeding an autocatalytic cycle with tiny amounts of one or more of its member chemicals results in logistic growth of all member chemicals in the cycle. This finding justifies drawing an instructive analogy between an autocatalytic cycle and a biological species. We extend this finding to show that pairs of autocatalytic cycles can exhibit competitive, predator-prey, or mutualistic associations just like biological species. Furthermore, when there is stochasticity in the environment, particularly in the seeding of autocatalytic cycles, chemical ecosystems can show complex dynamics that can resemble evolution. The evolutionary character is especially clear when the network architecture results in ecological precedence, which makes a system's trajectory historically contingent on the order in which cycles are seeded. For all its simplicity, the framework developed here helps explain the onset of adaptive evolution in prebiotic chemical reaction networks, and can shed light on the origin of key biological attributes such as thermodynamic irreversibility and genetic encoding.