diff --git a/vignettes/Xmod-SIS.Rmd b/vignettes/Xmod-SIS.Rmd index 36a7fa5..fc5fdd2 100644 --- a/vignettes/Xmod-SIS.Rmd +++ b/vignettes/Xmod-SIS.Rmd @@ -15,18 +15,27 @@ library(deSolve) suppressMessages(require(knitr)) ``` -# {.tabset} - -## $\odot$ 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: $$ \frac{dX}{dt} = h (H-X)-rX $$ +**Net Infectiousness** + True prevalence is: $$x = \frac{X}{H}.$$ @@ -34,20 +43,13 @@ $$x = \frac{X}{H}.$$ In our implementation, net infectiousness is linearly proportional to prevalence: $$c x.$$ -In this implementation, there is no immunity, but we assume a constant fraction of all infectious bites cause an infection. -**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. +*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. -## $\dagger$ -**References** +## References 1. Ross R. Report on the Prevention of Malaria in Mauritius. London: Waterlow; 1908. 2. Ross R. The Prevention of Malaria. 2nd ed. London: John Murray; 1911.