# SIM-D: An Agent-Based Simulator for Modeling Contagion in Population
## 2 Disease Model Parameters  
In this section, the modeling parameters of a networked susceptible exposed infectious recovered (SEIR) diseases are discussed. This model can be used to describe SIR, SIS and SI disease models. The disease states in the SEIR model are used in describing the progression of disease in the individuals and its transmission in the population [13] as shown in Figure 1.  
The three most important parameters are transmissibility, infectious period and incubation period. The transmissibility (\(\rho\)) controls the diffusion intensity of the disease in population. It is the probability of transmission of disease from an infectious individual to a susceptible individual in one minute of contact [14].  
The incubation period (\(\Delta t_{E}\)), also known as the latent period, is the interval during which an infected individual cannot transmit the disease to other susceptible individuals. The infectious period (\(\Delta t_{I}\)) is the period during which an infected individual can transmit the disease to other susceptible individuals. Table 1 lists the dwell times in different disease states for typical influenza [15; 16].  
Based on the dwell times in exposed, infectious and recovered states, the diseases can be modelled using SIR, SIS and SI disease models as shown in Table 2. In SIR (susceptible\(\rightarrow\)exposed\(\rightarrow\)infectious\(\rightarrow\)recovered), a person after recovering stays in the recovered state forever. The individual develops immunity to that strain of the disease and will not become susceptible again [17]. Typical influenza is usually modelled using SIR [13]. In SIS (susceptible\(\rightarrow\)exposed\(\rightarrow\)infectious\(\rightarrow\)susceptible), a person after getting recovered becomes immediately susceptible to the disease again. The Measles, a well-known infectious disease, and most of the sexually transmitted diseases conform to SIS [18; 19]. In SIR (susceptible\(\rightarrow\)exposed\(\rightarrow\)infectious), a person after becoming infectious remains infectious forever. The human immunodeficiency virus (HIV/AIDS), usually transmitted through bodily fluids, is modelled using SI [20].  
The progression of disease within an agent is probabilistic and can be shown using a finite state machine as shown in Figure 2. The probability is dependent on whether the user is vaccinated or not. A person vaccinated against the disease is less likely to be infected compared to someone who is not vaccinated. The finite state machine (FSM) in Figure 2 shows the SIR model. For SI, the infectious period is changed to infinite. Moreover, for SIS, a transition is added from recovered to an uninfected state.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Disease State** & **Math Term** & **Typical Influenza Range (Days)** \\ \hline Exposed & \(\Delta t_{E}\) & 1–2 \\ Infectious & \(\Delta t_{I}\) & 3–7 \\ Recovered & \(\Delta t_{R}\) & \(\infty\)1  \\ \hline \hline \end{tabular}
\end{table}
Table 1: Typical influenza ranges for disease state parameters.  
Figure 1: The four states of a basic Susceptible-Exposed-Infectious-Recovered (SEIR) disease model. (\(\Delta t_{E}\)), (\(\Delta t_{I}\)), and (\(\Delta t_{R}\)) show the dwell times in exposed, infectious, and recovered states, respectively. The model can be used to describe (SIR), susceptible-infectious-susceptible (SIS) and susceptible-infectious (SI) disease models.  
Figure 2: A simple disease model that shows the progression of disease within an agent. Ovals represent disease states, while the lines represent the transition between states. The labels on lines show the probabilities of transitions.