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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".