| Title: |
Stability Analysis of Biological Systems Under Threshold Conditions. |
| Authors: |
Mahbuba, Jannat E; Wang, Xiang-Sheng |
| Source: |
Symmetry (20738994); Aug2025, Vol. 17 Issue 8, p1193, 14p |
| Subject Terms: |
BASIC reproduction number; BIOLOGICAL systems; CRITICAL point theory; STABLE equilibrium (Physics); STABILITY criterion; NONLINEAR systems; MATHEMATICAL models; STABILITY theory |
| Abstract: |
In biological models exhibiting symmetric interactions within each compartmental group, threshold dynamics are typically governed by a key parameter known as the basic reproduction number R 0 . The stability of an equilibrium often hinges on whether R 0 is greater than or less than one. However, general results for stability at the critical threshold—when R 0 equals one—remain scarce. In this paper, we establish two theorems to analyze the stability of both trivial and boundary equilibria under this threshold condition. Our results provide explicit expressions for the threshold parameters in terms of partial derivatives of the nonlinear reaction function, making them readily applicable to a wide range of biological systems. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |