Vaccination, asymptomatics and public health information in COVID-19

The dynamics of the COVID-19 pandemic are greatly influenced by vaccine quality, as well as by vaccination rates and the behaviour of infected individuals, both of which reflect public policy. We develop a model for the dynamics of relevant cohorts within a fixed population, taking extreme care to model the reduced social contact of infected individuals in a rigorous self-consistent manner. The basic reproduction number R0is then derived in terms of the parameters of the model. Analysis of R0 reveals two interesting possibilities, both of which are plausible based on known characteristics of COVID-19. Firstly, if the population in general moderates social contact, while infected individuals who display clinical symptoms tend not to isolate, then increased vaccination can drive the epidemic towards a disease-free equilibrium (DFE). However, if the reverse is true, then increased vaccination can destabilise the DFE and yield an endemic state. This surprising result is due to the fact that the vaccines are leaky, and can lead to an increase in asymptomatic individuals who unknowingly spread the disease. Therefore, this work shows that public policy regarding the monitoring and release of health information should be combined judiciously with vaccination policy to control COVID-19

A hierarchical cluster system based on Horton-Strahler rules for river networks

We consider a cluster system in which each cluster is characterized by two parameters: an \order" i; following Horton-Strahler's rules, and a \mass" j following the usual additive rule. Denoting by ci;j (t) the concen- tration of clusters of order i and mass j at time t; we derive a coagulation- like ordinary di erential system for the time dynamics of these clusters. Results about existence and the behaviour of solutions as t ! 1 are ob- tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1; where the functional Ni( ) measures the total amount of clusters of a given xed order i: Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that sug- gest the existence of self-similar solutions to these approximate equations and discuss its possible relevance for an interpretation of Horton's law of river number

On linear growth in COVID-19 cases

We present an elementary model of COVID-19 propagation that makes explicit the connection between testing strategies and rates of transmission and the linear growth in new cases observed in many parts of the world

Distributional fixed-point equations for island nucleation in one dimension : the inverse problem

The self-consistency of the distributional fixed-point equation (DFPE) approach to understanding the statistical properties of island nucleation and growth during submonolayer deposition is explored. We perform kinetic Monte Carlo simulations, in which point islands nucleate on a one-dimensional lattice during submonolyer deposition with critical island size $i$, and examine the evolution of the inter-island gaps as they are fragmented by new island nucleation. The DFPE couples the fragmentation probability distribution within the gaps to the consequent gap size distribution (GSD), and we find a good fit between the DFPE solutions and the observed GSDs for $i = 0, 1, 2, 3$. Furthermore, we develop numerical methods to address the inverse problem, namely the problem of obtaining the gap fragmentation probability from the observed GSD, and again find good self-consistency in the approach. This has consequences for its application to experimental situations where only the GSD is observed, and where the growth rules embodied in the fragmentation process must be deduced

Implications of TP53 allelic state for genome stability, clinical presentation and outcomes in myelodysplastic syndromes

Tumor protein p53 (TP53) is the most frequently mutated gene in cancer1,2. In patients with myelodysplastic syndromes (MDS), TP53 mutations are associated with high-risk disease3,4, rapid transformation to acute myeloid leukemia (AML)5, resistance to conventional therapies6–8 and dismal outcomes9. Consistent with the tumor-suppressive role of TP53, patients harbor both mono- and biallelic mutations10. However, the biological and clinical implications of TP53 allelic state have not been fully investigated in MDS or any other cancer type. We analyzed 3,324 patients with MDS for TP53 mutations and allelic imbalances and delineated two subsets of patients with distinct phenotypes and outcomes. One-third of TP53-mutated patients had monoallelic mutations whereas two-thirds had multiple hits (multi-hit) consistent with biallelic targeting. Established associations with complex karyotype, few co-occurring mutations, high-risk presentation and poor outcomes were specific to multi-hit patients only. TP53 multi-hit state predicted risk of death and leukemic transformation independently of the Revised International Prognostic Scoring System (IPSS-R)11. Surprisingly, monoallelic patients did not differ from TP53 wild-type patients in outcomes and response to therapy. This study shows that consideration of TP53 allelic state is critical for diagnostic and prognostic precision in MDS as well as in future correlative studies of treatment response

Stress-strain state in an elastic medium containing an inclusion of a new phase

The problem of elastic equilibrium of an isotropic solid phase with a melt is examined in connection with a study of problems of magma generation and volcanic earthquakes. For the case of a spherical inclusion and zero pressure at infinity the stress-strain state is calculated to terms of the second order of smallness (with respect to the relative difference of densities of the phases)

Bak-Sneppen-type models and rank-driven processes

The Bak-Sneppen model is a well-known stochastic model of evolution that exhibits self-organized criticality; only a few analytical results have been established for it so far. We report a surprising connection between Bak-Sneppen-type models and more tractable Markov processes that evolve without any reference to an underlying topology. Specifically, we show that in the case of a large number of species, the long time behavior of the fitness profile in the Bak-Sneppen model can be replicated by a model with a purely rank-based update rule whose asymptotics can be studied rigorously

Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a stable absolute minimum or only a minimizing sequence in which the term corresponding to the bulk energy is forced to zero by the production of a crack in the material