Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · q-bio/0510005

Pair Approximation Models for Disease Spread

Jerome Benoit·Ana Nunes·Margarida Telo da Gama
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider a Susceptible-Infective-Recovered (SIR) model, where the mechanism for the renewal of susceptibles is demographic, on a ring with next nearest neighbour interactions, and a family of correlated pair approximations (CPA), parametrized by a measure of the relative contributions of loops and open triplets of the sites involved in the infection process. We have found that the phase diagram of the CPA, at fixed coordination number, changes qualitatively as the relative weight of the loops increases, from the phase diagram of the uncorrelated pair approximation to phase diagrams typical of one-dimensional systems. In addition, we have performed computer simulations of the same model and shown that while the CPA with a constant correlation parameter cannot describe the global behaviour of the model, a reasonable description of the endemic equilibria as well as of the phase diagram may be obtained by allowing the parameter to depend on the demographic rate.

Explore related subjects

q-bio.PE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jerome Benoit, Ana Nunes, Margarida Telo da Gama. 2013-05-31. Pair Approximation Models for Disease Spread. https://doi.org/10.1140/epjb%2Fe2006-00096-x

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A greedy nearest-neighbor approach to quantify site revisitation: comparing two sympatric raven species

A central challenge in movement ecology is to describe ecologically meaningful residence sites from raw tracking data due to heterogeneous sampling frequency and uncertain site boundaries. Here, we develop a greedy nearest-neighbor clustering approach with local reassignment and polygon-based site construction that generates timestamped sequences of site visits for each tracked individual, and apply it to nine years of GPS data from two sympatric raven species in the Dead Sea region---the Fan-tailed Raven (\emph{Corvus rhipidurus}) and the Brown-necked Raven (\emph{C. ruficollis}). Using the resulting visitation sequences, we quantify recursion patterns using the non-Markovian individual mobility model (IMM), which captures the balance between novel-site discovery $β$ and preferential return $α$. The inferred dynamics are consistent with IMM predictions and reveal clear interspecific differences: Brown-necked Ravens continue to discover new sites at a higher rate (lower $β$), whereas Fan-tailed Ravens show a steeper concentration of visits among top-ranked sites. Entropy analyses further separate the species, with Brown-necked Ravens exhibiting higher site entropy and higher conditional entropy of site-to-site transitions. Together, these results provide a robust framework for describing interspecific differences in movement strategies that can be used to infer memory from GPS data and suggest distinct space-use strategies in two closely related sympatric species.

q-bio.PE↗
arXiv2026

Pathways of early evolution from the perspectives of a riboreplisome -- the ultimate RNA machine of life

Translation of the genetic code into proteins is universal across life, with ribosomes serving as the ancient molecular machines enabling this information transformation. We propose that early replication and protein biosynthesis were inseparable functions performed by a single ancient RNA molecule: the riboreplisome. This hypothesis addresses fundamental challenges facing RNA world, protein world, and RNA-protein co-evolution theories -- particularly the problem of non-Darwinian starting points and the interdependence of replication and translation machineries. We present a 12-step evolutionary pathway from simple RNA replicase to proto-ribosome, supported by quantitative modelling demonstrating that only two steps require non-Darwinian transitions while the remaining ten proceed through standard selection. The single-molecule riboreplisome architecture provides an approximately 6-fold evolutionary advantage over multi-component "RNA soup" scenarios, principally by maintaining genetic linkage and retaining catalytic products close to the replicating genome (resisting diffusion loss); structural resistance to parasitic "cheater" molecules follows as a corollary. The riboreplisome framework explains the origins of ribosomal, transfer, and messenger RNA as derivatives of a single ancestral molecule, while providing a driving force for cellular compartmentalisation. Although the original riboreplisome is likely lost to deep time, molecular remnants may persist in extant biological RNA. Identification or reconstruction of riboreplisome-like molecules could advance both origin-of-life research and synthetic biology applications.

q-bio.PE↗
arXiv2026

Predator self limitation controls pattern formation in a predator prey system with additional food: a Turing Hopf analysis

Supplying a released predator with additional, non reproducing food is a standard lever in augmentative biological control, with a known drawback with nothing limiting the predators own numbers, the extra food lets its population grow without bound. Competition among the predators supplies the missing brake. Howthis self limitation reshapes the spatial arrangement of the two species has not been asked. We address it with a reaction diffusion model of a logistically growing prey and a predator feeding through a Holling type II response that also draws on additional food , the predators competing among themselves at strength. In the well mixed setting we locate the Hopf bifurcation of the coexistence state exactly and show the cycle born there is stable, so weak competition gives boom bust oscillations, not runaway growth. Allowing movement, we obtain the diffusion driven Turing threshold at which the uniform state breaks into stationary patches of high and low density, and find the uniform oscillation stable as it appears. With prey mobility and competition strength as control parameters, the pattern forming and oscillatory instabilities meet at a single point, where we compute the dynamics. Simulations confirm the sequence weak competition gives a wholefield oscillation, stronger competition with faster prey spread gives fixed patterns, and near the crossover the two combine into patterns that pulse in time. Predator self competition therefore sets the spatial structure of the community, which is what matters when additional food is used to steer a control agent in the field.

q-bio.PE↗