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Infection Dynamics

Dynamics of MoI, AoI, and the AoY

zda()
Compute infection density in a cohort of humans, \(z_\tau(\alpha, a |h)\)
truePR()
Compute the true PR in a cohort as a function of age and exposure

Multiplicity of Infection (MoI)

Methods to compute the MoI

meanMoI()
The mean MoI in a host cohort of age \(a\)
dMoIda()
Derivatives for the queuing model \(M/M/\infty\)
solveMMinfty()
Solve the queuing model \(M/M/\infty\)
MoIDistPlot()
Plot the output of solveMMinfty

Age of Infection (AoI)

Methods to compute the AoI density and distribution functions, random numbers, and moments

dAoI()
Compute the density function for AoI
pAoI()
Compute the distribution function for AoI
rAoI()
Random numbers for the AoI
momentAoI()
Compute the moments for the AoI density function for a cohort of age a

Age of the Youngest Infection (AoY)

Methods to compute the AoY density and distribution functions, random numbers, and moments

dAoY()
The density function for the age of the youngest infection (AoY)
pAoY()
The distribution function for the age of the youngest infection (AoY)
pAoY_long()
Alternative method for computing the distribution function for the age of the youngest infection (AoY)
rAoY()
The random generation function for the age of the youngest infection (AoY)
momentAoY()
Compute the moments for the AoY density function for a cohort of age a

Age of the Youngest of N Infections (AoYN)

Methods to compute the AoYN density and distribution functions & random numbers

dAoYN()
The youngest of N infections, density function
pAoYN()
The youngest of N infections, distribution function
rAoYN()
The youngest of N infections, random numbers

Hybrid Models

Methods to solve hybrid models

dmda()
Compute the derivatives for MoI using a hybrid model
solve_dm()
Solve the hybrid model for the MoI
dpda()
Compute the derivatives for MoI and true PR
solve_dpda()
Solve a system of differential equations to compute the true PR and the MoI
dAoIda()
Compute the derivatives of the AoI moments dynamically
solve_dAoI()
Solve the system of differential equations to compute the moments of the AoI over time.
dAoYda()
Compute the derivatives of the approximate moments of the AoY dynamically
solve_dAoYda()
Solve the system of differential equations to compute the approximate moments of the AoY over time.

Parasite Densities

Expected densities by AoI

F_mu(alpha)

Expected log10 parasites (mu) from the AoI (alpha)

Fmu()
Compute mean, expected parasite densities mu as a function of the age of infection alpha
sFmu()
Compute mean, expected parasite densities mu for multiple values of the age of infection alpha
Fmu(<W>)
Compute expected log10 parasite densities, mu, as a function of the age of infection alpha
par_Fmu_W()
Set up parameters for Fmu.W
Fmu(<base>)
Compute expected log10 parasite densities, mu, as a function of the age of infection alpha
par_Fmu_base()
Set up parameters for Fmu.base
Fmu(<chronic>)
Compute expected log10 parasite densities, mu, as a function of the age of infection alpha
par_Fmu_chronic()
Set up parameters for Fmu.chronic

P(mu)

log10 parasites distributions from mu

d_Omega()
The density function for parasite densities in a simple malaria infection
p_Omega()
The density function for parasite densities as a function of the mean
q_Omega()
The quantile function for parasite densities in a simple malaria infection
r_Omega()
Random generation of parasite densities from a simple malaria infection
par_Omega_beta()
The quantile function for parasite densities in a simple malaria infection

P(mu)

log10 parasites distributions from mu

d_Omega(<beta>)
Modified beta distribution, density function
dbeta1()
Density function for the beta distribution, an alternative parameterization
p_Omega(<beta>)
Modified beta distribution, distribution function
pbeta1()
Disribution function for the beta distribution, an alternative parameterization
q_Omega(<beta>)
Modified beta distribution, distribution function
qbeta1()
The quantile function for the beta distribution, an alternative parameterization
r_Omega(<beta>)
Modified beta distribution, random numbers
rbeta1()
The random generation function for the beta distribution, an alternative parameterization Title
sigma_mu()
A function to compute the variance of the beta distrution as a function of the mean.
sigma_mu(<abc>)
A function that returns constrained values of the variance for the beta distrution as a function of the mean.
par_sigma_abc()
Parameters to configure sigma_mu.abc

P(alpha)

log10 parasites from AoI (alpha)

d_alpha2density()
The density function for parasite densities in a simple malaria infection of age alpha
p_alpha2density()
The distribution function for parasite densities in a simple malaria infection of age alpha
q_alpha2density()
The quantile function for parasite densities in a simple malaria infection of age alpha
r_alpha2density()
The distribution function for parasite densities in a simple malaria infection of age alpha

P(a)

Parasite density distributions by host cohort age

d_clone_density()
Compute \(P_\tau(a |h)\)
moments_clone_density()
Compute the moments of P_density

Complex Infections

Expected densities by AoI

parasite_density()
Compute \(B_\tau(a | h)\)
d_parasite_density()
Compute the distribution function for \(B_\tau(a)\)
p_parasite_density()
Call parasite_density and return the density vector
r_parasite_density()
Random generation for parasite densities in a host cohort
moments_parasite_density()
Compute the moments of P_density
rRda()
Random generation for M parasite densities in a host cohort with MoI

Convolutions

Other

dDensityPaConvolve2()
The density function for the sum of two infections
cdfConvolve2()
The density function for the sum of two infections
cdfConvolve2a()
The density function for the sum of two infections, method b
cdfConvolve2b()
The density function for the sum of two infections, method a

Sampling

Generic Functions

Parasite positivity

d_detect()
The probability of detecting parasites
d_counts()
The PDF for counting \(x\) parasites
p_counts()
The CDF for counting \(x\) parasites
d_nz_counts_log()
The PDF for non-zero counts, \(\log_{10}\) transformed
p_nz_counts_log()
The CDF for non-zero counts, \(\log_{10}\) transformed
d_nz_counts_log_binned()
The binned PDF for non-zero counts, \(\log_{10}\) transformed
p_nz_counts_log_binned()
The binned PDF for non-zero counts, \(\log_{10}\) transformed

Poisson Sampling

par_pois()
Parameters for Poisson sampling
d_detect(<pois>)
Detection of infection given parasitemia
p_counts(<pois>)
Detection of infection given parasitemia
d_counts(<pois>)
Detection of infection given parasitemia

Negative Binomial Sampling

par_nb()
Parameters for negative binomial sampling
d_detect(<nb>)
Detection of infection given parasitemia
p_counts(<nb>)
Detection of infection given parasitemia
d_counts(<nb>)
Negative binomial PDF for raw parasite counts

Parasite Detection and Counts

Observed Prevalence

Detection and observed prevalence

d_detect_mesh() d_detect_mesh()
Detection of infection given parasitemia
d_clone_detect()
Detection of infection given parasitemia
d_parasite_detect_moi() d_parasite_detect_moi()
Detection of infection given parasitemia
d_parasite_detect() d_parasite_detect()
Detection of infection given parasitemia
FQ()
The proportion of zero counts in

Observed MoI

Number of Clones Counted

d_moi_count() d_moi_count()
Detection of infection given parasitemia

Counts

Parasite counts

d_clone_counts()
Compute the density of parasite counts for simple infections
p_clone_counts()
Compute the distribution of parasite counts for simple infections
mean_clone_counts()
Compute the mean parasite counts in simple infections
d_parasite_counts()
Compute the density of parasite counts in complex infections
p_parasite_counts()
Compute the distribution of parasite counts in complex infections
mean_parasite_counts()
Compute the mean parasite counts in complex infections

Force of Infection

Methods to set up FoI trace functions

FoI()
Force of Infection, \(h_\tau(a)\)

FoI by Age

Specialized methods modify the FoI by Age

ageFoI()
Functions to modify the FoI by age
ageFoI(<flat>)
A function that does not modify the FoI by age
par_flatAge()
Make a parameter list to dispatch ageFoI.flat
ageFoI(<type2>)
A function that does not modify the FoI by age
par_type2Age()
Make a parameter list to dispatch ageFoI.type2

FoI by Season

Specialized methods set the seasonal FoI

seasonalFoI()
Add a seasonal pattern to the FoI trace function
seasonalFoI(<exp>)
A generalized sinusoidal seasonal pattern, exponentiated
par_expSeason()
Return a list to dispatch seasonalFoI.exp
seasonalFoI(<flat>)
The "no seasonality" function
par_flatSeason()
Return a list that dispatches seasonalFoI.flat
seasonalFoI(<sin>)
A generalized sinusoidal seasonal pattern
par_sinSeason()
Return a list to configure and dispatch seasonalFoI.sin

Specialized methods to set trends in the FoI

trendFoI()
Add a trend to the FoI trace function
trendFoI(<flat>)
The "no trend" function
par_flatTrend()
Return a list that dispatches trendFoI.flat

Utilities

Other

nzPois()
Compute N non-zero values from a Poisson distribution with a given MoI

Immune Tracking Variables

Expected densities by AoI

Wda()
Compute immune tracking variables as a function of host age and exposure
Wda(<none>)
Compute immune tracking variables as a function of host age and exposure
par_Wda_none()
Make a parameter set for Wda.none
Wda(<delta>)
Compute immune tracking variables as a function of host age and exposure
par_Wda_delta()
Make a parameter set for Wda.none

Red Blood Cells

Other

log10RBC()
Compute log10 of the red blood cell population
log10RBC(<static>)
Compute log10 of the red blood cell population
par_lRBC_static()
Set up parameters for log10RBC.static