# Load the requisite packages:
library(malariasimulation)
# Set colour palette:
cols <- c("#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")This vignette describes the unique features of the P. vivax model.
To select the P. vivax model, use the parasite
argument in the get_parameters() function:
Then we can run the simulation as normal:
Our default P. vivax parameters are sourced from a version
of the analysis in White et al. 2018 (doi: 10.1038/s41467-018-05860-8),
where model parameters were fitted to data from Papua New Guinea. The
chosen parameter set fixes b = 0.25 and
sigma_squared = 1.67 (for consistency with the P.
falciparum model). The default parameters for both parasite species
can be found in data/raw/parasite_parameters.csv, while
parameters common to both models are given in
R/parameters.R under get_parameters().
Values for the model fitting posterior distribution can be selected
using the set_parameter_draw() function as found in the Parameter
Variation vignette.
The P. falciparum model has five human disease compartments: susceptible (S), clinical disease (D), asymptomatic infection (A), sub-patent infection (U), and treated (Tr). Asymptomatic infections may or may not be detectable by light-microscopy.
The P. vivax model follows a similar structure to the P. falciparum model, and also has five human disease compartments. However, the human disease states modeled explicitly focus on parasite density and detectability, such that we have: susceptible (S), clinical disease (D), light-microscopy detectable infection (A), PCR detectable infection (U), and treated (Tr).
The rate of infection for an individual who has been bitten increases with the number of bites they have received in the P. vivax model. In contrast, the rate of infection in the P. falciparum model is independent of the number of bites an individual has received.
Newly infected individuals in the P. falciparum model can move into either the clinically diseased or asymptomatic infection compartment. In addition to these compartments, the P. vivax model allows infection to the PCR-detectable compartment (U), where the assignment of light-miscroscopy detectable infections and PCR-detectable infections is mediated by anti-parasite immunity.
The P. falciparum model tracks four kinds of immunity: immunity to blood stage infection (IB), clinical disease (acquired and maternal, ICA and ICM), to severe disease (acquired and maternal, IVA and IVM), and to detectability (ID).
The P. vivax model tracks two kinds of immunity: immunity to clinical infection (acquired and maternal, ICA and ICM) and anti-parasite immunity (acquired and maternal, IAA and IAM). We do not track immunity to blood stage infections, severe immunity or immunity to detectability.
Anti-parasite immunity has effects in two places. The first is in the
separation of PCR-detectable infections from LM-detectable infections
(where greater immunity reduces the change of an infection with higher
parasitaemia). The second is in the calculation of a PCR-detectable
infection (where greater immunity results in a shorter duration before
recovery). The P. falciparum model does not model infections to
the sub-patent compartment (U) and has a constant sub-patent infection
duration (du = 110).
While the P. falciparum model calculates the onward
infectivity of asymptomatic infections (ca) using the age
and detectability immunity of each individual, the P. vivax
model uses a constant onwards infectivity for LM-detectable infections
(ca = 0.1).
The P. vivax model tracks the number of hypnozoite batches
of each individual which then contribute to the rate of new infections.
Acquisition of new batches come from bite infections, which are mediated
by liver-stage drug prophylaxis, and are capped (where
kmax = 10 by default). All individuals can acquire new
hypnozoite batches via bites, even when these do not result in new
blood-stage infection (as in the clinically diseased and treated).
Hypnozoite batches are lost probabilistically where an individual’s
number of batches determines the loss rate of a single batch.
Successful liver-stage drug treatment results in the clearing of all hypnozoite batches of an individual.
While P. falciparum drugs have four parameters (efficacy, relative reduction in onwards infectivity, and two prophylaxis parameters: shape and scale), the P. vivax drug parameters may have four (if the drug only targets the blood stage infection) or seven parameters (if the drug also targets hypnozoites). These three additional parameters are drug efficacy on hypnozoite clearance and two hypnozoite prophylaxis parameters: shape and scale. The hypnozoite prophylaxis functions the same way as standard prophlylaxis to infection, but reduced the probability that a bite infection results in the formation of a new hypnozoite batch.
The malariaEquilibriumVivax package has been designed to calculate
the equilibrium solution for the P. vivax model. This
equilibrium is calculated by assigning an initial EIR value via the
set_equilibrium function, as in the P. falciparum
model. Based on the age and heterogeneity group of an individual, it
assigns a human disease state, clinical and anti-parasite immunities and
number of hypnozoite batches.
White, M. T., Walker, P., Karl, S., Hetzel, M. W., Freeman, T., Waltmann, A., Laman, M., Robinson, L. J., Ghani, A., & Mueller, I. (2018). Mathematical modelling of the impact of expanding levels of malaria control interventions on Plasmodium vivax. Nature Communications, 9(1), 1–10. https://doi.org/10.1038/s41467-018-05860-8