Frank Namugera | Searcharxiv

arXiv2026

The truncation property and continuity for the long-range contact process on $\mathbb{Z}^d$

We consider a general class of contact processes on $\mathbb{Z}^d$ with potentially long-range interactions. By adapting well established renormalization arguments to the long-range setting we extend by now classical results for finite-range processes to this more general setting. Particularly, we provide general conditions on the decay of the interactions under which a supercritical process remains supercritical after truncation of the interaction parameter at a sufficiently large distance. Further, for the family of parameters satisfying this latter truncation property, we conclude that the probability of the process to never recover is continuous.

math.PR↗

arXiv2025

Discrete-Time Two-Strain Epidemic Dynamics on Complex Networks

We investigate a discrete-time two-strain symbiotic epidemic model on complex networks with both random and long-range interactions. Our analysis examines how the co-infection recovery rate ($μ$), the long-range decay exponent ($α$), and the scale-free connectivity exponent ($γ$) shape epidemic persistence under cooperative dynamics. Comparison with a two-strain competition model shows how these parameters control strain dominance, coexistence, or extinction. The results demonstrate that contagion dynamics are strongly affected by environmental randomness and long-range couplings. In facultative symbiosis, the co-infection recovery rate undergoes a clear phase transition, separating persistence from extinction. In the competitive setting, regimes with $α< 2$ and $γ< 3$ markedly lower the epidemic threshold, allowing persistence even at small contagion rates ($σ$). Statistical analysis further reveals that $γ$ and $α$ exert pronounced, nonlinear, and time-dependent effects on strain survival.

physics.soc-ph↗