Generic 8: SIS - Reoccurring infections¶

This tutorial assumes that you have read Generic 7: SI - Lifelong infection and Generic 1: SIR - Simple single-node outbreak.

Similar to the SIRS model, the infected individuals return to the susceptible state. This model is appropriate for diseases that commonly have repeat infections, for example, the common cold (rhinoviruses), or sexually transmitted diseases like gonorrhea or chlamydia. For this model, we can analytically solve the ordinary differential equation (ODE) to understand the dynamics.

For simplicity, the following ODE model ignores the vital process (birth and death):

$\begin{aligned} \frac{dS}{dt} & = -\frac{\beta SI}{N} + \gamma I\\ \frac{dI}{dt} & = \frac{\beta SI}{N} - \gamma I\\ \end{aligned}$

At equilibrium, solving:

$\frac{dI}{dt} = \beta I \left(1-\frac{1}{N}\right) - \gamma I = 0$

There are two equilibrium states for the SIS model, the first is $I = 0$ (disease free state), and the second is:

$I = \frac{(\beta - \gamma)N}{\beta} = \left(1-\frac{\gamma}{\beta}\right)N$

For disease to spread, we need to have $dI/dt > 0$ . Therefore, similar to the previously described concept of the basic reproductive number, when $\beta/\gamma > 1$ , the disease will spread and approach the second steady state; otherwise, it will eventually reach the disease-free state.

Demographics inputs¶

This tutorial uses generic_scenarios_demographics file for demographics input. You can view the complete demographics file at <path_to_directory>RegressionScenariosInputFiles where <path_to_directory> is the location where EMOD source files were installed. For more information on demographics files, see Demographics parameters.

Key configuration parameters¶

The tutorial simulates a sexually-transmitted disease using the SIS model in a hypothetical closed community over a 10-year period. The infectious duration is 25 days, and the basic reproductive number is 1.2.

You can view the complete config.json in the <path_to_directory>RegressionScenariosGeneric08_SIS directory where <path_to_directory> is the location where EMOD source files were installed.

Population dynamics parameters¶

Set Enable_Vital_Dyanamics to 0. This will disable vital dynamics (birth and death) in the simulation. For more information, see Population dynamics parameters.

SIS model parameters¶

The generic simulation type uses an SEIR model by default. However, it can be modified to an SIS model with the following configurations: no incubation period and no immunity. For more information, see Incubation and Immunity parameters.

Set the following parameters:

Set Base_Incubation_Period to 0.

Set Incubation_Period_Distribution to “FIXED_DURATION.”

Set Enable_Immunity to 0.

Disease parameters¶

As demonstrated previously, the spread of disease in the SIS model depends on $\beta$ (set by base infectivity) and $\gamma$ which are set by duration of infection. For more information, see Infectivity and transmission parameters.

Set the following parameters:

Set Base_Infectivity to 0.048.

Set Base_Infectious_Period to 25.

Set Infectious_Period_Distribution to “EXPONENTIAL_DURATION.”

Simulation duration parameters¶

The simulation is run for 3 months with a 1-day time step. For more information, see Simulation setup parameters.

Set the following parameters:

Set Simulation_Timestep to 1.

Set Simulation_Duration to 3650.

Interventions¶

You can view the complete campaign.json in the <path_to_directory>RegressionScenariosGeneric08_SIS directory where <path_to_directory> is the location where EMOD source files were installed.

Initial outbreak¶

This simulation uses an OutbreakIndividual event at day 1 to provide the initial seeding. For more information, see OutbreakIndividual parameters.

{
    "Use_Defaults": 1,
    "Campaign_Name": "Initial Seeding",
    "Events": [{
        "Event_Coordinator_Config": {
            "Intervention_Config": {
                "Antigen": 0,
                "Genome": 0,
                "Outbreak_Source": "PrevalenceIncrease",
                "class": "OutbreakIndividual"
            },
            "Target_Demographic": "Everyone",
            "Demographic_Coverage": 0.0005,
            "class": "StandardInterventionDistributionEventCoordinator"
        },
        "Event_Name": "Outbreak",
        "Nodeset_Config": {
            "class": "NodeSetAll"
        },
        "Start_Day": 1,
        "class": "CampaignEvent"
    }]
}

Run the simulation¶

Run the simulation and generate graphs of the simulation output. For more information, see Run simulations.

Note

Because the EMOD model is stochastic, your graphs may appear slightly different from those given below.

Simulation output graphs¶

The following figure shows the growth of an outbreak over time that eventually approaches steady state. You can compare the fraction of infected people with the anticipated value based on the previous calculation. If we have a reproductive number of 1.2, the infected fraction at equilibrium will be 1 - (1/1.2) ~ 17%.

_images/Generic_SIS_output_plotInsetChart.png

Figure 1: Outbreak approaching steady-state

Exploring the model¶

You can change the Base_Infectivity value to alter the basic reproductive number (R₀ >1 and R₀<1) to observe the endemic state behavior.