Stability of Epidemic Models over Directed Graphs: A Positive Systems\n Approach
Bibliographic record
Abstract
We study the stability properties of a susceptible-infected-susceptible (SIS)\ndiffusion model, so-called the $n$-intertwined Markov model, over arbitrary\ndirected network topologies. As in the majority of the work on infection spread\ndynamics, this model exhibits a threshold phenomenon. When the curing rates in\nthe network are high, the disease-free state is the unique equilibrium over the\nnetwork. Otherwise, an endemic equilibrium state emerges, where some infection\nremains within the network. Using notions from positive systems theory, {we\nprovide novel proofs for the global asymptotic stability of the equilibrium\npoints in both cases over strongly connected networks based on the value of the\nbasic reproduction number, a fundamental quantity in the study of epidemics.}\nWhen the network topology is weakly connected, we provide conditions for the\nexistence, uniqueness, and global asymptotic stability of an endemic state, and\nwe study the stability of the disease-free state. Finally, we demonstrate that\nthe $n$-intertwined Markov model can be viewed as a best-response dynamical\nsystem of a concave game among the nodes. This characterization allows us to\ncast new infection spread dynamics; additionally, we provide a sufficient\ncondition for the global convergence to the disease-free state, which can be\nchecked in a distributed fashion. Several simulations demonstrate our results.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".