[SS26] Emerging challenges in Mathematical Epidemiology

[SS26-02] Analysis of a diffusive SIS model with nonlocal infection

*Dhiraj Kumar Das¹, S. Ghorai², Malay Banerjee² (1. Birla Institute of Technology and Science, Pilani (India), 2. Indian Institute of Technology, Kanpur (India))

Keywords:

Nonlocal infection,Spatiotemporal epidemic model,Turing instability,Transient dynamics

The study of spatio-temporal distribution of susceptible and infected over a region is a prominent focus of epidemiology. The force of infection is typically distance dependent, in particular the distance between the susceptible and infected. Such distanced transmission of the causative agent is called `nonlocal infection', which is primarily modeled with a kernel function K, whose support determines the range of the nonlocal infection area. In our current study, a susceptible–infected–susceptible-type epidemic model with nonlinear disease incidence rate is extended to incorporate the nonlocal infection. Complete bifurcation characteristics of the corresponding temporal model include the saddle-node, subcritical Hopf, and homoclinic bifurcations. A wide variety of spatio-temporal patterns, including stationary, quasi-periodic, periodic, and chaotic patterns, are observed. Qualitative changes in these spatio-temporal distribution between the local and nonlocal models have been identified. It is observed that the nonlocal disease transmission expands the parametric domain (referred to as Hopf and stable domains) on which the system possesses oscillatory and spatially homogeneous solutions. As a result, the spatially heterogeneous stationary solutions (referred to as Turing patterns) of the local system turn into either irregular oscillatory solutions or spatially homogeneous solutions whenever the nonlocal extent of the disease transmission gradually increases. Also, the increased range of nonlocal infections reduces the number of stationary patches.