# Infectious disease surveillance

## Overview

This app teaches the topic of Infectious disease surveillance and demonstrates the effect of the type and extent of surveillance on the dynamics of an infectious disease in a population, including the course and outcome of an epidemic. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

### Learning Objectives

- Understand the influence of infectious disease surveillance on the dynamics of an infectious disease in a population by comparing disease dynamics with and without surveillance.

- Understand the effect of the extent of surveillance and under-reporting/incomplete surveillance on the course and outcome of the epidemic. The effect of the extent of surveillance on the number of susceptibles left at the end of the simulation and the total number of deaths that occurred will be explored. In addition, users will explore which surveillance parameters prevent the occurrence of an outbreak.

- Understand influence of the type of surveillance (e.g., one that detects presymptomatic, asymptomatic or symptomatic infections or pairwise combinations of the three or all) on disease dynamics. The effect of the type of surveillance will be explored in the case where individuals in the different stages of infection (presymptomatic, asymptomatic or symptomatic) transmit or don’t.

## The Model

### Model Overview

For this compartmental model, we track the following compartments/stages:

- S - susceptible, uninfected individuals
- P - presymptomatic individuals who are infected and do not yet show symptoms. Those individuals can potentially be infectious.
- A - asymptomatic, infected individuals. Those individuals can potentially be infectious.
- I - individuals who are infected and show symptoms. Those individuals are likely infectious, but the model allows to adjust this, including no infectiousness.
- R - Observed/removed individuals. Those individuals have been observed/detected by the surveillance system and have been removed from the transmission cycle.
- D - Individuals who die from disease. Only symptomatic individuals are assumed to die from disease.

The model can be extended to include a reported compartment. This compartment would represent for example the US Centers for Disease Control and Prevention (CDC) to which health systems report the observed cases of disease at some rate(s).

In addition to specifying the compartments of a model, we need to specify the dynamics determining the changes for each compartment. In general, more compartments leads to more processes and more parameters governing these processes.

For this model, we include the following processes:

- Susceptible individuals (S) can become infected by presymptomatic (P), asymptomatic (A) or symptomatic (I) hosts. The rates at which infections from the different types of infected individuals (P, A and I) occur are governed by 3 parameters, bP, bA, and bI. In other words, those bi parameters determine how infectious an individual in stages P, A and I is.
- All infected individuals first enter the presymptomatic stage. They remain there for some time (determined by rate gP, the inverse of which is the average time spent in the presymptomatic stage i.e., the latent period). A fraction f of presymptomatic hosts move into the asymptomatic category, and the rest become symptomatic infected hosts.
- Asymptomatic infected hosts are removed by surveillance after some time (specified by the rate rA).
- Similarly, infected symptomatic hosts and presymptomatic hosts leave that stage at rate rI and rP respectively.
- Removed individuals recover from the infection and are initially immune to reinfection. They can loose their immunity at rate w and return to the susceptible compartment.
- New susceptibles enter the system/model at a fixed rate m. From each compartment (apart from the observed/removed compartment), hosts “leave” after some time (i.e. they die) at rate n. The inverse of this rate is the average lifespan of a host. In addition, infected symptomatic individuals can die due to the disease at rate d.

### Model Implementation

The flow diagram and the set of ordinary differential equations (ODE) which are used to implement this model are as follows:

Flow diagram for this model.

\[\dot S = m - S(b_P P + b_A A + b_I I) + wR - nS\] \[\dot P = S (b_P P + b_A A + b_I I) - P(g_P + r_P + n) \] \[\dot A = f g_P P - A(r_A + n) \] \[\dot I = (1-f) g_P P - I (r_I + n + d) \] \[\dot R = r_PP + r_A A + r_I I - wR \] \[\dot D = dD\]

## What to do

The tasks below are described in a way that assumes everything is in units of months (rate parameters, therefore, have units of inverse months). If any quantity is not given in those units, you need to convert it first (e.g. if it says a year, you need to convert it to 12 months).

### Task 1

This will be our ‘base case’–we’ll have no surveillance going on, so that you have a comparison point for when we later include some surveillance. Set the model parameters such that they correspond to the following setting: A population size, S, of 1000, 1 initially infected presymptomatic host, P, simulation duration tmax = 50 years. Be sure to convert the units to months. Assume that only symptomatic individuals transmit, at rate bI = 0.002. Assume that gP = 5 (the inverse of this parameter is the average duration of the presymptomatic period). Assume that 20% of the infections are asymptomatic–accordingly set f = 0.2. Assume that immunity wanes at a rate w = 1/100. Set the natural death rate, n, to a value that corresponds to an average lifespan of 41 years. Recall that the unit of n needs to be in 1/months. You need to convert lifespan to months, then take the inverse to get the death rate. Round to the first significant digit (i.e. 0.00X). Set the birth rate to m = 5 per month and the death rate d = 0.5. Also assume that no surveillance is done. Accordingly set the surveillance parameters rP, rA and rI to zero. With parameters set to correspond to the scenario just described, run the simulation and ensure that you observe oscillations/cycles (i.e. repeated outbreaks). In the diagram for the model, make note of which arrows are present and which are not when you plug in these parameters (for example, the arrows pointing to the ‘R’ compartment would disappear). Because there is no mechanism for recovery or removal, you should see the number of deaths steadily increase. Additionally, you should see the number of susceptibles oscillate due to the nonzero birth rate parameter.

Record

- The number of susceptibles left, Sf

- The final value of the disease induced deaths, Df

### Task 2

Surveillance ensures that diseased individuals are removed from the transmission cycle before they contribute to the next generation of cases. Previously, we assumed that there was no surveillance. Now, assume that there exists a surveillance system that detects only symptomatic infections. Set the rate of surveillance of symptomatic hosts, rI to 0.5. Leave the rest of the settings as in task 1, and run the simulation. Compare this result with the result observed in task 1 so as to understand the effect of surveillance on the course of the epidemic. Pay attention to the y-axis! You should see changes in the number of deaths over time, in the number of susceptibles over time, and of course in the number of removed over time. Why might the number of deaths change as it did?

Record

- The number of susceptibles left, Sf

- The final value of the disease induced deaths, Df

### Task 3

Now, let’s see what happens when we change values of rI. First, plot a graph of Sf as a function of rI to determine the effect of the extent of surveillance on the number of susceptibles left at the end of the simulation. Then, plot a graph of Df as a function of rI to determine the effect of the extent of surveillance on the total number of deaths that occurred. You can make this plot either by hand or in R. If you plot by hand, you’ll want to plot a rough trend line. If you want to plot in R, see the DSAIDE Package Tutorial, under the ‘Level 2’ heading, for an example of how to write the code.

Record

- Do you see an increasing trend between rI and the number of susceptibles left at the end Sf? (Yes/No)

- The number of deaths at the end drops to 0 once rI passes 1 (Yes/No)

### Task 4

Previously, although we had 20% of our infections as asymptomatic, they weren’t actually transmitting (recall, bA was set to be 0). Now, let’s consider the scenario where they do transmit the infection–and let’s see what happens with and without surveillance. Start with the settings in task 2. Consider the case where asymptomatic individuals transmit, and they do so at a rate similar to that of symptomatic hosts (bA = 0.002) but no surveillance for them is done (rA = 0). Run the simulation. Compare Sf with that in task 2. Note–the only thing we’ve changed is the number of susceptibles becoming infected (because now they can get infected by both infected symptomatic and infected asymptomatic individuals). What happens to the susceptible population?

Record

- The number of susceptibles left, Sf

- The final value of the disease induced deaths, Df

### Task 5

Then consider the case where a new surveillance system detects asymptomatic cases at the same rate as that of symptomatic cases, i.e., rA = 0.5 in addition to surveillance of symptomatic cases. Also in this case, assume that asymptomatic cases still transmit at a rate similar to that of symptomatic hosts, i.e., bA = 0.002. Run the simulation and compare this result with that in task 4 part 1. Notice now what happens to the susceptible population. A couple other compartments should also change!

Record

- The number of susceptibles left, Sf

- The final value of the disease induced deaths, Df

### Task 6

Finally, consider the case where asymptomatic individuals don’t transmit but they’re still detected by the surveillance system, i.e., set bA = 0 but keep rA = 0.5. Run the simulation and compare your result with that in task 4 part 1 and part 2.

Record

- The number of susceptibles left, Sf

- The final value of the disease induced deaths, Df

### Task 7

For some infectious diseases, such as tuberculosis (TB), it is possible to control the epidemic by identifying latently infected individuals i.e., while individuals are at the presymptomatic stage. These can be given Preventive Therapy so as to reduce the number of individuals transitioning to infectiousness. Consider the case where surveillance is done for asymptomatic, symptomatic and presymptomatic individuals at the same rate (i.e., 0.5). Also assume that asymptomatic individuals don’t transmit, as the case is with TB. Leave the other settings as in task 1. Run the simulation and compare the value of Sf in this simulation with those in the other tasks.

Record

- The number of susceptibles left, Sf

- The final value of the disease induced deaths, Df

### Task 8

Play with the rates of disease detection ( rP , rI, and rA) and explore their effect on the disease dynamics. Specifically, consider the case where the rate of detection of asymptomatic and presymptomatic hosts is lower than the rate of detection of symptomatic hosts, which is usually the case. Set rI = 1, rA = 0.5 and rP = 0.5 and leave other settings as in task 7.

Record

- The number of susceptibles left, Sf

- The final value of the disease induced deaths, Df

## Further Information

- This app (and all others) are structured such that the Shiny part (the graphical interface you see and the server-side function that goes with it) calls an underlying R script (or several) which runs the simulation for the model of interest and returns the results.
- For this app, the underlying function(s) running the simulation are called `simulate_idsurveillance_ode`. You can call them directly, without going through the shiny app. Use the `help()` command for more information on how to use the functions directly. If you go that route, you need to use the results returned from this function and produce useful output (such as a plot) yourself.
- You can also download all simulator functions and modify them for your own purposes. Of course to modify these functions, you’ll need to do some coding.
- For examples on using the simulators directly and how to modify them, read the package vignette by typing `vignette('DSAIDE')` into the R console.
- For some more information on the topics discussed here, see e.g. (Brabazon et al. 2015; Kazerooni et al. 2018; Jelastopulu, Merekoulias, and Alexopoulos 2010)

### References

Brabazon, E. D., A. Sheridan, P. Finnegan, M. W. Carton, and D. Bedford. 2015. “Under-Reporting of Notifiable Infectious Disease Hospitalizations: Significant Improvements in the Irish Context.” Epidemiology and Infection 143 (6): 1166–74. https://doi.org/10.1017/S0950268814001733.
Jelastopulu, E., G. Merekoulias, and E. C. Alexopoulos. 2010. “Underreporting of Communicable Diseases in the Prefecture of Achaia, Western Greece, 1999-2004 - Missed Opportunities for Early Intervention.” Eurosurveillance 15 (21): 1999–2004. https://doi.org/10.2807/ese.15.21.19579-en.
Kazerooni, P. A., M. Fararouei, M. Nejat, M. Akbarpoor, and Z. Sedaghat. 2018. “Under-Ascertainment, Under-Reporting and Timeliness of Iranian Communicable Disease Surveillance System for Zoonotic Diseases.” Public Health 154: 130–35. https://doi.org/10.1016/j.puhe.2017.10.029.