2.2. Transmission Rate Functions

Each agent is either a regular agent or a super-spreader, and the proportion of super-spreaders in the total population (N agents) is determined by the parameter λ. Agents in the E or I status can infect other S agents within a distance r0 with the transmission probability function of β(r). Here, the distance between two agents located at (x1,y1) and (x2,y2) is calculated as r=(x2−x1)2+(y2−y1)2. We define two types of transmission rate functions for regular-spreaders and super-spreaders. Here, super-spreaders are assumed to have either a higher transmission probability or larger number of contacts than regular spreaders (three different models for super-spreaders will be described below).

Let us define transmission rate functions for regular-spreaders and super-spreaders. The transmission rate function is defined as a function of the distance between exposed (or infected) and susceptible individuals.

Regular-spreader:

Here, β(r) is a decreasing function of the distance r within an effective contact radius r0, and α is the exponent of the given function of distance r with α>1. Please note that this model is referred as to the no super-spreader model No-SS when there is no super-spreader agent (λ=0).

Super-Spreader Model 1:

Our first super-spreader model (SSM1) assumes that super-spreaders have a higher transmission probability (or higher infectivity) than regular spreaders within the effective contact radius r0. Please note that β1(r) is a constant function remaining at a value of β0 for 0≤r≤r0.

Super-Spreader Model 2:

The second super-spreader model (SSM2) assumes that super-spreaders have more links (or a larger number of contacts) than regular spreaders and is modeled by a longer effective contact radius with rn=6r0.

Super-Spreader Model 3:

Lastly, we propose a hybrid model (SSM3) for super-spreaders by considering a combined transmission probability of SSM1 and SSM2 since super-spreaders have both a higher transmission probability and a larger number of contacts [1].