ramp.xds includes computational
support for qualitative analysis of dynamical systems describing malaria
and other mosquito-transmitted pathogens. This vignette provides an
overview.
ramp.xds includes algorithms to
compute:
steady states and stable orbits;
next generation matrices and \(R_0\) / threshold or quasi-threshold criteria;
analysis of connectivity;
scaling relationships.
Through qualitative analysis, we seek to develop an understanding of these models, to become better at judging whether they are fit for purpose, and to make it easier to compare and benchmark different models.
The algorithms are used in the related sites:
Adaptive Malaria Control, including a discussion of robust analytics for malaria policy (RAMP).
Steady States & Stable Orbits
Most autonomous systems describing malaria have a trivial steady
state (no malaria) and a non-trivial, globally attractive steady state
describing endemic malaria. Each one of the modules includes functions
to compute its steady state as a function of one or more inputs. Steady
states for the whole system are computed by calling
xds_steady. The function burnin accomplishes
essentially the same thing, but it also copies the final state to the
initial state.
Stable orbits are computed for malaria in systems with seasonal canonical forcing from a trivial module. After a long burnin, the orbits from the last full year are stored. The orbits are used to compute the average annual values of key metrics.
Thresholds & Connectivity
ramp.xds takes a computational approach
to computing thresholds using a next generation matrix approach
for autonomous systems, and a next generation matrix function approach
for non-autonomous systems. See Thresholds
Using these same next generation approaches, we compute various measures of connectivity: tracing transmission back through one full parasite generation, and it outputs a matrix describing parasite movement among patches. See Connectivity
Scaling Relationships
Scaling relationships look at relationships among various malaria metrics across the spectrum of malaria transmission intensity. The scaling functions create a mesh over the mean forcing parameter for a model and compute stable orbits for every value of that mesh. The mean annual values and the orbits are stored for analysis. See Scaling Relationships