The SIS model, as it is now called, is a simple compartmental model,
first introduced by Ross. It is included in exDE as a base
model.
Parameters
\(r\) is the rate infections clear
\(b\) is the fraction of bites by infective mosquitoes that transmit parasites and cause an infection.
\(c\) is the fraction of bites on an infectious human that would infect a mosquito.
Dynamics
The model defined herein is defined in two parts. To model exposure and infection (i.e. the conversion of eir into foi), we assume that the fraction of infective bites that cause an infection is \(b\). The dynamics are given by:
\[ \frac{dI}{dt} = h (H-I)-rI \]
Terms
Net Infectiousness
True prevalence is:
\[x = \frac{X}{H}.\]
In our implementation, net infectiousness (NI) is linearly proportional to prevalence:
\[c x.\]
Human Transmitting Capacity
After exposure, a human would remain infected for \(1/r\) days, transmitting with probability \(c\) so:
\[c/r\]
Exposure and Infection
In this model family, there is no immunity. The model assumes that a constant fraction of all infectious bites, \(b\), cause an infection.
References
- Ross R. Report on the Prevention of Malaria in Mauritius. London: Waterlow; 1908.
- Ross R. The Prevention of Malaria. 2nd ed. London: John Murray; 1911.
- Smith DL, Battle KE, Hay SI, Barker CM, Scott TW, McKenzie FE. Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathog. 2012;8: e1002588. doi:10.1371/journal.ppat.1002588