For this module, we will explore a fairly complex model that allows the study of different types of interventions. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.
This model is fairly big and has many parts that can be turned on or off depending on parameter settings. The model allows for 3 types of transmission: direct, through an environmental stage, and through a vector stage. The (human) host is modeled in some detail, the environment and vectors are modeled with 1 and 2 compartments. The following compartments are included:
The included processes/mechanisms are the following:
Note that we only track people that die due to the disease in our D compartment. All hosts dying due to other causes just “exit the system” and we don’t further keep track of them (though we could add another compartment to “collect” and track all individuals who died from non-disease-related causes.)
Also, note that we made several simplifications to keep the model from getting too complex. For instance, presymptomatic individuals do not shed into the environment, and only symptomatic hosts are assumed to be able to infect vectors. Further details relaxing these assumptions could, of course, be included, at the expense of a larger and more complex model.
The flow diagram and equations describe the model implemented in this app:
Flow diagram for this model.
\[\dot S = e_h - S (b_P P + b_A A + b_I I + b_E E + b_v I_v) + wR - n_h S \] \[\dot P = S (b_P P + b_A A + b_I I + b_E E + b_v I_v) - g_P P - n_h P\] \[\dot A = f g_P P - g_A A - n_h A\] \[\dot I = (1-f) g_P P - g_I I - n_h I \] \[\dot R = g_A A + (1-d) g_I I - wR - n_h R\] \[\dot D = d g_I I \] \[\dot E = p_I I + p_A A - c E \] \[\dot S_v = e_v - b_h I S_v - n_v S_v \] \[\dot I_v = b_h I S_v - n_v I_v \]
Births and natural deaths are not drawn to keep the diagram from getting too cluttered.
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).
Some of the simulations might take a few seconds to run. Be patient.
simulate_idcontrol_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.vignette('DSAIDE')
into the R console.Kirsch, Thomas D, Heidi Moseson, Moses Massaquoi, Tolbert G Nyenswah, Rachel Goodermote, Isabel Rodriguez-Barraquer, Justin Lessler, Derek A T Cumings, and David H Peters. 2017. “Impact of Interventions and the Incidence of Ebola Virus Disease in Liberia-Implications for Future Epidemics.” Health Policy and Planning 32 (2): 205–14. https://doi.org/10.1093/heapol/czw113.
Klepac, Petra, Sebastian Funk, T Deirdre Hollingsworth, C Jessica E Metcalf, and Katie Hampson. 2015. “Six Challenges in the Eradication of Infectious Diseases.” Epidemics 10 (March): 97–101. https://doi.org/10.1016/j.epidem.2014.12.001.
Klepac, Petra, C Jessica E Metcalf, Angela R McLean, and Katie Hampson. 2013. “Towards the Endgame and Beyond: Complexities and Challenges for the Elimination of Infectious Diseases.” Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 368 (1623): 20120137. https://doi.org/10.1098/rstb.2012.0137.
Tognotti, Eugenia. 2013. “Lessons from the History of Quarantine, from Plague to Influenza a.” Emerging Infectious Diseases 19 (2): 254–59. https://doi.org/10.3201/eid1902.120312.