Cognitive diffusion of susceptibles driven by new infection cases in SIS epidemic models: frequency-dependent incidence

Coloured Epidemic Models: Functional Law of Large Numbers and Propagation of Chaos

In this paper, we study a stochastic Susceptible-Infected-Removed (SIR) model where the infection and the recovery rates depend on individual covariates for susceptibility and infectiousness of the infector and the infectee. Such models allow explicit nonlinearity in the incidence term. They are also important from a p...

From Individual-Based Stochastic Epidemics to Heterogeneous SIR Equations

A stochastic framework for a broad class of heterogeneous SIR epidemic models with persistent individual heterogeneity that provides a unified probabilistic foundation for deterministic epidemic models with persistent individual heterogeneity is developed.

On the dynamics of a diffusive SEIRS epidemic model

Thresholds for Stochastic SIRS with Switching Exponents.

The derivation of the rigorous sufficient conditions that characterize both the extinction and the long-term persistence of disease dynamics are derived, including a threshold parameter Λ, expressed in terms of the switching exponents ρξ(t) and ζξ(t), from a nonlinear stochastic SIRS epidemic model evolving in a random...

Epidemic dynamics as a Wasserstein gradient flow on viral load distributions

Classical epidemic models assume that infected individuals are homogeneous, reducing disease progression to a single aggregate variable. This hides the role of within‑host variability, in particular differences in viral load that directly influence both infectivity and recovery. We propose a geometric perspective in wh...

Threshold dynamics of a time-periodic nonlocal dispersal SIS epidemic model with saturated incidence function and Neumann boundary conditions

In this paper, we consider a time-periodic nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with saturated incidence and Neumann boundary conditions in a spatiotemporally heterogeneous environment. First, we define the basic reproduction number for the model, which depends on dispersal rates, to...