Package 'bioinactivation'

Title: Mathematical Modelling of (Dynamic) Microbial Inactivation
Description: Functions for modelling microbial inactivation under isothermal or dynamic conditions. The calculations are based on several mathematical models broadly used by the scientific community and industry. Functions enable to make predictions for cases where the kinetic parameters are known. It also implements functions for parameter estimation for isothermal and dynamic conditions. The model fitting capabilities include an Adaptive Monte Carlo method for a Bayesian approach to parameter estimation.
Authors: Alberto Garre [aut, cre], Pablo S. Fernandez [aut], Jose A. Egea [aut]
Maintainer: Alberto Garre <[email protected]>
License: GPL-3
Version: 1.3.0.9999
Built: 2024-10-27 05:05:25 UTC
Source: https://github.com/albgarre/bioinactivation

Help Index

Isothermal Arrhenius model

Description

Returns the predicted logarithmic reduction in microbial count according to Arrhenius model for the time, temperature and model parameters given.

Usage

Arrhenius_iso(time, temp, k_ref, temp_ref, Ea)

Arguments

time

numeric indicating the time at which the prediction is taken.
temp

numeric indicating the temperature of the treatment.
k_ref

numeric indicating the inactivation rate at the reference temperature.
temp_ref

numeric indicating the reference temperature.
Ea

numeric indicating the activation energy.

Value

A numeric with the predicted logarithmic reduction (log10(N/N0)log10(N/N0)).

Isothermal Bigelow's Model

Description

Returns the predicted logarithmic reduction in microbial count according to Bigelow's model for the time, temperature and model parameters given.

Usage

Bigelow_iso(time, temp, z, D_R, temp_ref)

Arguments

time

numeric indicating the time at which the prediction is taken.
temp

numeric indicating the temperature of the treatment.
z

numeric defining the z-value.
D_R

numeric defining the D-value at the reference temperature.
temp_ref

numeric defining the reference temperature.

Value

A numeric with the predicted logarithmic reduction (log10(N/N0)log10(N/N0)).

Continuum Interpolation of Discrete Temperatures Values

Description

Builds an interpolator of the temperature at each time and its first derivative. First derivatives are approximated using forward finite differences (approxfun). It is assumed that temperature is 0 and constant outside the time interval provided.

Usage

build_temperature_interpolator(temperature_data)

Arguments

temperature_data

data frame with the values of the temperatures at each value of time. It need to have 2 columns, named time and temperature.

Value

a list with with two elements:

  • temp, the interpolator of the temperature and

  • dtemp, the interpolator of its first derivative

See Also

approxfun

Correctness Check of Model Parameters

Description

Makes 3 checks of compatibility between the input parameters for the adjustment and the DOF of the inactivation model selected.

  • Check of equal length of model DOF and input DOF. Raises a warning if failed.

  • Check that every single one of the input DOF is a model DOF. Raises a warning if failed.

  • Check that every single one of the model DOF are defined as an input DOF.

Usage

check_model_params(
  simulation_model,
  known_params,
  starting_points,
  adjust_vars
)

Arguments

simulation_model

character with a valid model key.
known_params

named vector or list with the dof of the model known.
starting_points

named vector or list with the dof of the model to be adjusted.
adjust_vars

logical specifying whether the model variables need to be included in the check (not used for isothermal fit)

First derivative of the Arrhenius model

Description

Calculates the first derivative of the Arrhenius model with log-linear inactivation for dynamic problems at a given time for the model parameters provided and the environmental conditions given.

Usage

dArrhenius_model(t, x, parms, temp_profile)

Arguments

t

numeric vector indicating the time of the experiment.
x

list with the value of N at t.
parms

parameters for the secondary model. No explicit check of their validity is performed.
temp_profile

a function that provides the temperature at a given time.

Details

This function is compatible with the function predict_inactivation.

Value

The value of the first derivative of NN at time t as a list.

Model Equation

dNdt=−k∗N\frac{dN}{dt} = - k * N

Model parameters

  • temp_ref: Reference temperature for the calculation,

  • k_ref: inactivation rate at the ref. temp.

  • Ea: Activation energy.

See Also

predict_inactivation

First Derivate of the Linear Bigelow Model

Description

Calculates the first derivative of the linearized version of Bigelow's model for dynamic problems at a given time for the model parameters provided and the environmental conditions given.

Usage

dBigelow_model(t, x, parms, temp_profile)

Arguments

t

numeric vector indicating the time of the experiment.
x

list with the value of N at t.
parms

parameters for the secondary model. No explicit check of their validity is performed.
temp_profile

a function that provides the temperature at a given time.

Details

The model is developed from the isothermal Bigelow's model assuming during the derivation process that DTD_T is time independenent.

This function is compatible with the function predict_inactivation.

Value

The value of the first derivative of NN at time t as a list.

Model Equation

dNdt=−Nln(10)DT(T)\frac{dN}{dt} = - N \frac {\mathrm{ln}(10)}{D_T(T)}

Model parameters

  • temp_ref: Reference temperature for the calculation,

  • D_R: D-value at the reference temperature,

  • z: z value.

See Also

predict_inactivation

First Derivate of Geeraerd's Model

Description

Calculates the first derivative of the Geeraerd's model at a given time for the model parameters provided and the environmental conditions given.

Usage

dGeeraerd_model(t, x, parms, temp_profile)

Arguments

t

numeric vector indicating the time of the experiment.
x

list with the values of the variables at time tt.
parms

parameters for the secondary model. No explicit check of their validity is performed (see section Model Parameters).
temp_profile

a function that provides the temperature at a given time.

Details

This function is compatible with the function predict_inactivation.

Value

A list with the value of the first derivatives of N and C_c at time t.

Model Equation

dNdt=−N⋅kmax⋅α⋅γ\frac{dN}{dt} = -N \cdot k_{max} \cdot \alpha \cdot \gamma

dCcdt=−Cc⋅kmax\frac{dC_c}{dt} = - C_c \cdot k_{max}

α=11+Cc\alpha = \frac {1}{1+C_c}

γ=1−NresN\gamma = 1 - \frac{N_{res}}{N}

kmax=1DTk_{max} = \frac{1}{D_T}

log10DT=log10DR+TR−Tzlog_{10}D_T = log_{10}D_R + \frac{T_R-T}{z}

Model Parameters

  • temp_ref: Reference temperature for the calculation,

  • D_R: D-value at the reference temperature,

  • z: z value,

  • N_min: Minimum value of N (defines the tail).

Notes

To define the Geeraerd model without tail, assign N_min = 0. For the model without shoulder, assign C_0 = 0

See Also

predict_inactivation

First Derivate of the Weibull-Mafart Model

Description

Calculates the first derivative of Weibull-Mafart model at a given time for the model parameters provided and the environmental conditions given.

Usage

dMafart_model(t, x, parms, temp_profile)

Arguments

t

numeric vector indicating the time of the experiment.
x

list with the value of N at t.
parms

parameters for the secondary model. No explicit check of their validity is performed (see section Model Parameters).
temp_profile

a function that provides the temperature at a given time.

Details

The model is developed from the isothermal Weibull-Mafart model without taking into account in the derivation the time dependence of δT\delta_T for non-isothermal temperature profiles.

This function is compatible with the function predict_inactivation.

Value

The value of the first derivative of N at time t as a list.

Model Equation

dNdt=−N⋅p⋅(1/δ)p⋅tp−1\frac{dN}{dt} = -N \cdot p \cdot (1/\delta)^p \cdot t^{p-1}

δ(T)=δref⋅10−(T−Tref)/z\delta(T) = \delta_{ref} \cdot 10^{- (T-T_ref)/z}

Model Parameters

  • temp_ref: Reference temperature for the calculation.

  • delta_ref: Value of the scale factor at the reference temperature.

  • z: z-value.

  • p: shape factor of the Weibull distribution.

Note

For t=0, dN = 0 unless n=1. Hence, a small shift needs to be introduced to t.

See Also

predict_inactivation

First Derivate of the Metselaar Model

Description

Calculates the first derivative of Metselaar model at a given time for the model parameters provided and the environmental conditions given.

Usage

dMetselaar_model(t, x, parms, temp_profile)

Arguments

t

numeric vector indicating the time of the experiment.
x

list with the value of N at t.
parms

parameters for the secondary model. No explicit check of their validity is performed (see section Model Parameters).
temp_profile

a function that provides the temperature at a given time.

Details

The model is developed from the isothermal Metselaar model without taking into account in the derivation the time dependence of δT\delta_T for non-isothermal temperature profiles.

This function is compatible with the function predict_inactivation.

Value

The value of the first derivative of N at time t as a list.

Model Equation

dNdt=−N⋅p⋅(1/D)p⋅(t/Delta)p−1\frac{dN}{dt} = -N \cdot p \cdot (1/D)^p \cdot (t/Delta)^{p-1}

D(T)=Dref⋅10−(T−Tref)/zD(T) = D_{ref} \cdot 10^{- (T-T_ref)/z}

Model Parameters

  • temp_ref: Reference temperature for the calculation.

  • D_R: D-value at the reference temperature.

  • z: z-value.

  • p: shape factor of the Weibull distribution.

  • Delta: Scaling parameter

Note

For t=0, dN = 0 unless n=1. Hence, a small shift needs to be introduced to t.

See Also

predict_inactivation

First Derivate of the Weibull-Peleg Model

Description

Calculates the first derivative of Weibull-Peleg model at a given time for the model parameters provided and the environmental conditions given.

Usage

dPeleg_model(t, x, parms, temp_profile)

Arguments

t

numeric vector indicating the time of the experiment.
x

list with the value of logS at t.
parms

parameters for the secondary model. No explicit check of their validity is performed (see section Model Parameters).
temp_profile

a function that provides the temperature at a given time.

Details

The model is developed from the isothermal Weibull model without taking into account in the derivation the time dependence of bb for non-isothermal temperature profiles.

This function is compatible with the function predict_inactivation.

Value

The value of the first derivative of logS at time t as a list.

Model Equation

d(log10(S))dt=−b(T)⋅n⋅(−log10(S)/b(T))(n−1)/n)\frac{d(\mathrm{log}_{10}(S))}{dt}=-b(T) \cdot n \cdot (- log10(S)/b(T))^{(n-1)/n)}

b(T)=ln(1+exp(kb∗(T−Tcrit)))b(T) = \mathrm{ln}(1 + exp( k_b*(T - T_{crit}) ))

Model Parameters

  • temp_crit: Temperature below which there is inactivation.

  • k_b: slope of the b ~ temp line for temperatures above the critical one.

  • n: shape factor of the Weibull distribution.

Note

For logS=0, dlogS = 0 unless n=1. Hence, a small shift needs to be introduced to logS.

See Also

predict_inactivation

Example Dynamic Inactivation of a Microorganis

Description

Example of experimental data of the dynamic inactivation process of a microorganism.

Usage

data(dynamic_inactivation)

Format

A data frame with 19 rows and 2 variables.

Details

  • time: Time in minutes of the measurement.

  • N: Number of microorganism.

  • temperature: Observed temperature.

Fitting of Dynamic Inactivation Models

Description

Fits the parameters of an inactivation model to experimental data. The function modFit of the package FME is used for the adjustment.

Usage

fit_dynamic_inactivation(
  experiment_data,
  simulation_model,
  temp_profile,
  starting_points,
  upper_bounds,
  lower_bounds,
  known_params,
  ...,
  minimize_log = TRUE,
  tol0 = 1e-05
)

Arguments

experiment_data

data frame with the experimental data to be adjusted. It must have a column named “time” and another one named “N”.
simulation_model

character identifying the model to be used.
temp_profile

data frame with discrete values of the temperature for each time. It must have one column named time and another named temperature providing discrete values of the temperature at time points.
starting_points

starting values of the parameters for the adjustment.
upper_bounds

named numerical vector defining the upper bounds of the parameters for the adjustment.
lower_bounds

named numerical vector defining the lower bounds of the parameters for the adjustment.
known_params

named numerical vector with the fixed (i.e., not adjustable) model parameters.
...

further arguments passed to modFit
minimize_log

logical. If TRUE, the adjustment is based on the minimization of the error of the logarithmic count. TRUE by default.
tol0

numeric. Observations at time 0 make Weibull-based models singular. The time for observatins taken at time 0 are changed for this value.

Value

A list of class FitInactivation with the following items:

  • fit_results: a list of class modFit with the info of the adjustment.

  • best_prediction: a list of class SimulInactivation with prediction made by the adjusted model.

  • data: a data frame with the data used for the fitting.

See Also

modFit

Examples

## EXAMPLE 1 ------

data(dynamic_inactivation)  # The example data set is used.

get_model_data()  # Retrieve the valid model keys.

simulation_model <- "Peleg"  # Peleg's model will be used

model_data <- get_model_data(simulation_model)
model_data$parameters  # Set the model parameters

dummy_temp <- data.frame(time = c(0, 1.25, 2.25, 4.6),
                         temperature = c(70, 105, 105, 70))  # Dummy temp. profile

## Set known parameters and initial points/bounds for unknown ones

known_params = c(temp_crit = 100)

starting_points <- c(n = 1, k_b = 0.25, N0 = 1e+05)
upper_bounds <- c(n = 2, k_b = 1, N0 = Inf)
lower_bounds <- c(n = 0, k_b = 0, N0 = 1e4)

dynamic_fit <- fit_dynamic_inactivation(dynamic_inactivation, simulation_model,
                                        dummy_temp, starting_points,
                                        upper_bounds, lower_bounds,
                                        known_params)

plot(dynamic_fit)
goodness_of_fit(dynamic_fit)

## END EXAMPLE 1 -----

Fitting of dynamic inactivation with MCMC

Description

Fits the parameters of an inactivation model to experimental using the Markov Chain Monte Carlo fitting algorithm implemented in the function modMCMC of the package FME.

Usage

fit_inactivation_MCMC(
  experiment_data,
  simulation_model,
  temp_profile,
  starting_points,
  upper_bounds,
  lower_bounds,
  known_params,
  ...,
  minimize_log = TRUE,
  tol0 = 1e-05
)

Arguments

experiment_data

data frame with the experimental data to be adjusted. It must have a column named “time” and another one named “N”.
simulation_model

character identifying the model to be used.
temp_profile

data frame with discrete values of the temperature for each time. It must have one column named time and another named temperature providing discrete values of the temperature at time points.
starting_points

starting values of the parameters for the adjustment.
upper_bounds

named numerical vector defining the upper bounds of the parameters for the adjustment.
lower_bounds

named numerical vector defining the lower bounds of the parameters for the adjustment.
known_params

named numerical vector with the fixed (i.e., not adjustable) model parameters.
...

other arguments for modMCMC.
minimize_log

logical. If TRUE, the adjustment is based on the minimization of the error of the logarithmic count.
tol0

numeric. Observations at time 0 make Weibull-based models singular. The time for observatins taken at time 0 are changed for this value.

Value

A list of class FitInactivationMCMC with the following items:

  • modMCMC: a list of class modMCMC with the information of the adjustment process.

  • best_prediction: a list of class SimulInactivation with the prediction generated by the best predictor.

  • data: a data frame with the data used for the fitting.

Examples

## EXAMPLE 1 ------
data(dynamic_inactivation)  # The example data set is used.

get_model_data()  # Retrieve the valid model keys.

simulation_model <- "Peleg"  # Peleg's model will be used

model_data <- get_model_data(simulation_model)
model_data$parameters  # Set the model parameters

dummy_temp <- data.frame(time = c(0, 1.25, 2.25, 4.6),
                         temperature = c(70, 105, 105, 70))  # Dummy temp. profile

## Set known parameters and initial points/bounds for unknown ones

known_params = c(temp_crit = 100)

starting_points <- c(n = 1, k_b = 0.25, N0 = 1e+05)
upper_bounds <- c(n = 2, k_b = 1, N0 = 1e6)
lower_bounds <- c(n = 0.5, k_b = 0.1, N0 = 1e4)

MCMC_fit <- fit_inactivation_MCMC(dynamic_inactivation, simulation_model,
                                     dummy_temp, starting_points,
                                     upper_bounds, lower_bounds,
                                     known_params,
                                     niter = 100)
                                     # It is recommended to increase niter

plot(MCMC_fit)
goodness_of_fit(MCMC_fit)

## END EXAMPLE 1 -----

Fit of Isothermal Experiments

Description

Fits the parameters of the model chosen to a set of isothermal experiments using nonlinear regression through the function nls.

Usage

fit_isothermal_inactivation(
  model_name,
  death_data,
  starting_point,
  known_params,
  adjust_log = TRUE
)

Arguments

model_name

character specyfing the model to adjust.
death_data

data frame with the experiment data where each row is one observation. It must have the following columns:

  • log_diff: Number of logarithmic reductions at each data point.

  • temp: Temperature of the data point.

  • time: Time of the data point.

starting_point

List with the initial values of the parameters for the adjustment.
known_params

List of the parameters of the model known.
adjust_log

logical. If TRUE, the adjustment is based on the minimization of the error of the logarithmic microbial count. If FALSE, it is based on the minimization of the error of the microbial count. TRUE by default.

Value

An instance of class IsoFitInactivation with the results. This list has four entries:

  • nls: The object of class nls with the results of the adjustment.

  • parameters: a list with the values of the model parameters, both fixed and adjusted.

  • model: a string with the key identifying the model used.

  • data: the inactivation data used for the fit.

See Also

nls

Examples

## EXAMPLE 1 -----------

data("isothermal_inactivation")  # data set used for the example.

get_isothermal_model_data()  # retrieve valid model keys.
model_name <- "Bigelow"  # Bigelow's model will be used for the adjustment.

model_data <- get_isothermal_model_data(model_name)
model_data$params  # Get the parameters of the model

## Define the input arguments

known_params = list(temp_ref = 100)
starting_point <- c(z = 10,D_R = 1)

## Call the fitting function
iso_fit <- fit_isothermal_inactivation(model_name,
                                       isothermal_inactivation, starting_point,
                                       known_params)

## Output of the results

plot(iso_fit, make_gg = TRUE)
goodness_of_fit(iso_fit)

## END EXAMPLE 1 --------

Isothermal Model Data

Description

Provides information of the models implemented for fitting of isothermal data. This models are valid only for isothermal adjustment with the function fit_isothermal_inactivation. To make predictions with the function predict_inactivation or adjust dynamic experiments with fit_dynamic_inactivation, use get_model_data.

Usage

get_isothermal_model_data(model_name = "valids")

Arguments

model_name

Optional string with the key of the model to use.

Value

If model_name is missing, a list of the valid model keys. If model_name is not a valid key, NULL is returned. Otherwise, a list with the parameters of the model selected and its formula for the nonlinear adjustment.

Mapping of Simulation Model Functions

Description

Provides information about the function for dynamic predictions associated to a valid simulation_model key. If simulation_model is missing or NULL, a character vector of valid model keys is provided. This function is designed as an assistant for using the functions predict_inactivation and fit_dynamic_inactivation. For the adjustment of isothermal experiments with the function fit_isothermal_inactivation, use the function get_isothermal_model_data.

Usage

get_model_data(simulation_model = NULL)

Arguments

simulation_model

(optional) character with a valid model key or NULL.

Value

If simulation_model is NULL or missing, a character vector of possible names. Otherwise, a list including information of the relevant function:

  • ode: Pointer to the function defining the model ode.

  • cost: Pointer to the function calculating the error of the approximation.

  • dtemp: logical defining whether the function requires the definition of the first derivative of temperature.

  • variables: a character vector defining which entry variables are needed by the model.

  • variables_priv: for internal use only.

  • parameters: character vector with the parameters needed by the model.

See Also

predict_inactivation, fit_dynamic_inactivation

Error of the Prediction of Microbial Inactivation

Description

Calculates the error of the prediction of microbial inactivation for the chosen inactivation model and the given parameters with respect to the experimental data provided. This function is compatible with the function fit_dynamic_inactivation.

Usage

get_prediction_cost(
  data_for_fit,
  temp_profile,
  simulation_model,
  P,
  known_params
)

Arguments

data_for_fit

A data frame with the experimental data to fit. It must contain a column named “time” and another one named “N”.
temp_profile

data.frame defining the temperature profile. It must have a column named “time” and another named “temperature”.
simulation_model

character key defining the inactivation model.
P

list with the unknown parameters of the model to be adjusted.
known_params

list with the parameters of the model fixed (i.e., not adjusted)

Value

An instance of modCost with the error of the prediction.

See Also

modCost, fit_dynamic_inactivation

Goodness of fit for Dynamic fits

Description

Goodness of fit for Dynamic fits

Usage

goodness_dyna(object)

Arguments

object

An instance of FitInactivation

Goodness of fit for Isothermal fits

Description

Goodness of fit for Isothermal fits

Usage

goodness_iso(object)

Arguments

object

An object of class IsoFitInactivation.

Goodness of fit for MCMC fits

Description

Goodness of fit for MCMC fits

Usage

goodness_MCMC(object)

Arguments

object

An instance of FitInactivationMCMC

Goodness of fit for microbial inactivation models

Description

Generates a table with several statistical indexes describing the quality of the model fit:

  • ME: Mean Error.

  • RMSE: Root Mean Squared Error.

  • loglik: log-likelihood.

  • AIC: Akaike Information Criterion.

  • AICc: Akaike Information Criterion with correction for finite sample size.

  • BIC: Bayesian Infromation Criterion.

  • Af: Accuracy factor.

  • Bf: Bias factor.

Usage

goodness_of_fit(object)

Arguments

object

A model fit generated by bioinactivation

Test of FitInactivation object

Description

Tests if an object is of class FitInactivation.

Usage

is.FitInactivation(x)

Arguments

x

object to be checked.

Value

A logic specifying whether x is of class FitInactivation

Test of FitInactivationMCMC object

Description

Tests if an object is of class FitInactivationMCMC.

Usage

is.FitInactivationMCMC(x)

Arguments

x

object to be checked.

Value

A logic specifying whether x is of class FitInactivationMCMC

Test of IsoFitInactivation object

Description

Tests if an object is of class IsoFitInactivation.

Usage

is.IsoFitInactivation(x)

Arguments

x

object to be checked.

Value

A logic specifying whether x is of class IsoFitInactivation

Test of PredInactivationMCMC object

Description

Tests if an object is of class PredInactivationMCMC.

Usage

is.PredInactivationMCMC(x)

Arguments

x

object to be checked.

Value

A logic specifying whether x is of class PredInactivationMCMC

Test of SimulInactivation object

Description

Tests if an object is of class SimulInactivation.

Usage

is.SimulInactivation(x)

Arguments

x

object to be checked.

Value

A logic specifying whether x is of class SimulInactivation

Example Isothermal Inactivation of a Microorganis

Description

Example of experimental data for an isothermal process of a microorganism.

Usage

data(isothermal_inactivation)

Format

A data frame with 36 rows and 3 variables.

Details

  • time: Time in minutes of the measurement.

  • temp: Temperature at which the experiment was made.

  • log_diff: Logarithmic difference.

Example Dynamic Inactivation of a Laterosporus

Description

Example of experimental data of the dynamic inactivation process of Laterosporus

Usage

data(laterosporus_dyna)

Format

A data frame with 20 rows and 3 variables.

Details

  • time: Time in minutes of the measurement.

  • temp: observed temperature.

  • logN: recorded number of microorganism.

Example Isothermal Inactivation of a Laterosporus

Description

Example of experimental data for an isothermal process of Laterosporus.

Usage

data(laterosporus_iso)

Format

A data frame with 52 rows and 3 variables.

Details

  • time: Time in minutes of the measurement.

  • temp: Temperature at which the experiment was made.

  • log_diff: Logarithmic difference.

Isothermal Metselaar model

Description

Returns the predicted logarithmic reduction in microbial count according to Metselaars's model for the time, temperature and model parameters given.

Usage

Metselaar_iso(time, temp, D_R, z, p, Delta, temp_ref)

Arguments

time

numeric indicating the time at which the prediction is taken.
temp

numeric indicating the temperature of the treatment.
D_R

numeric defining the delta-value at the reference temperature.
z

numeric defining the z-value.
p

numeric defining shape factor of the Weibull distribution.
Delta

numeric reparametrization factor
temp_ref

numeric indicating the reference temperature.

Value

A numeric with the predicted logarithmic reduction (log10(N/N0)log10(N/N0)).

Plot of FitInactivation Object

Description

Plots a comparison between the experimental data provided and the prediction produced by the model parameters adjusted for an instance of FitInactivation.

Usage

## S3 method for class 'FitInactivation'
plot(
  x,
  y = NULL,
  ...,
  make_gg = TRUE,
  plot_temp = FALSE,
  label_y1 = "logN",
  label_y2 = "Temperature",
  ylims = NULL
)

Arguments

x

the object of class FitInactivation to plot.
y

ignored
...

additional arguments passed to plot.
make_gg

logical. If TRUE, the plot is created using ggplot2. Otherwise, the plot is crated with base R. TRUE by default.
plot_temp

logical. Whether the temperature profile will be added to the plot. FALSE by default.
label_y1

Label of the principal y-axis.
label_y2

Label of the secondary y-axis.
ylims

Numeric vector of length 2 with the Limits of the y-axis. NULL by default (0, max_count).

Value

If make_gg = FALSE, the plot is created. Otherwise, an an instance of ggplot is generated, printed and returned.

Plot of FitInactivationMCMC Object

Description

Plots a comparison between the experimental data provided and the prediction produced by the model parameters adjusted for an instance of FitInactivationMCMC.

Usage

## S3 method for class 'FitInactivationMCMC'
plot(
  x,
  y = NULL,
  ...,
  make_gg = TRUE,
  plot_temp = FALSE,
  label_y1 = "logN",
  label_y2 = "Temperature",
  ylims = NULL
)

Arguments

x

the object of class FitInactivation to plot.
y

ignored
...

additional arguments passed to plot.
make_gg

logical. If TRUE, the plot is created using ggplot2. Otherwise, the plot is crated with base R. TRUE by default.
plot_temp

logical. Whether the temperature profile will be added to the plot. FALSE by default.
label_y1

Label of the principal y-axis.
label_y2

Label of the secondary y-axis.
ylims

Numeric vector of length 2 with the Limits of the y-axis. NULL by default (0, max_count).

Value

If make_gg = FALSE, the plot is created. Otherwise, an an instance of ggplot is generated, printed and returned.

Plot of IsoFitInactivation Object

Description

For each one of the temperatures studied, plots a comparison between the predicted result and the experimental one for an instance of IsoFitInactivation.

Usage

## S3 method for class 'IsoFitInactivation'
plot(x, y = NULL, ..., make_gg = FALSE)

Arguments

x

the object of class IsoFitInactivation to plot.
y

ignored
...

additional arguments passed to plot.
make_gg

logical. If TRUE, the plot is created using ggplot2. Otherwise, the plot is crated with base R. FALSE by default.

Plot of PredInactivationMCMC Object

Description

Plots the prediction interval generated by predict_inactivation_MCMC.

Usage

## S3 method for class 'PredInactivationMCMC'
plot(x, y = NULL, ..., make_gg = TRUE)

Arguments

x

the object of class PredInactivationMCMC to plot.
y

ignored
...

additional arguments passed to plot.
make_gg

logical. If TRUE, the plot is created using ggplot2. Otherwise, the plot is crated with base R. TRUE by default.

Details

The plot generated in ggplot (default) generates a dashed line with the mean of the MC simulations. Moreover, a ribbon with the 2 first quantiles (i.e. columns 3 and 4) is generated.

The plot generated with base R (make_gg = FALSE) generates a solid line wth the mean of the MC simulations. Each one of the other quantiles included in the data frame are added with different

Value

If make_gg = FALSE, the plot is created. Otherwise, an an instance of ggplot is generated, printed and returned.

Plot of SimulInactivation Object

Description

Plots the predicted evolution of the logarithmic count with time for an instance of SimulInactivation.

Usage

## S3 method for class 'SimulInactivation'
plot(
  x,
  y = NULL,
  ...,
  make_gg = TRUE,
  plot_temp = FALSE,
  label_y1 = "logN",
  label_y2 = "Temperature",
  ylims = NULL
)

Arguments

x

The object of class SimulInactivation to plot.
y

ignored
...

additional arguments passed to plot.
make_gg

logical. If TRUE, the plot is created using ggplot2. Otherwise, the plot is crated with base R. TRUE by default.
plot_temp

logical. Whether the temperature profile will be added to the plot. FALSE by default.
label_y1

Label of the principal y-axis.
label_y2

Label of the secondary y-axis.
ylims

Numeric vector of length 2 with the Limits of the y-axis. NULL by default (0, max_count).

Value

If make_gg = FALSE, the plot is created. Otherwise, an an instance of ggplot is generated, printed and returned.

Prediction of Dynamic Inactivation

Description

Predicts the inactivation of a microorganism under isothermal or non-isothermal temperature conditions. The thermal resistence of the microorganism are defined with the input arguments.

Usage

predict_inactivation(
  simulation_model,
  times,
  parms,
  temp_profile,
  ...,
  tol0 = 1e-05
)

Arguments

simulation_model

character identifying the model to be used.
times

numeric vector of output times.
parms

list of parameters defining the parameters of the model.
temp_profile

data frame with discrete values of the temperature for each time. It must have one column named time and another named temperature providing discrete values of the temperature at time points.
...

Additional arguments passed to ode.
tol0

numeric. Observations at time 0 make Weibull-based models singular. The time for observatins taken at time 0 are changed for this value. By default ('tol0 = 1e-5')

Details

The value of the temperature is calculated at each value of time by linear interpolation of the values provided by the input argument temp_profile. The function ode of the package deSolve is used for the resolution of the differential equation.

Value

A list of class SimulInactivation with the results. It has the following entries:

  • model: character defining the model use for the prediction.

  • model_parameters: named numeric vector with the values of the model parameters used.

  • temp_approximations: function used for the interpolation of the temperature. For a numeric value of time given, returns the value of the temperature and its first derivative.

  • simulation: A data frame with the results calculated. Its first column contains the times at which the solution has been calculated. The following columns the values of the variables of the model. The three last columns provide the values of logN, S and logS.

See Also

ode, get_model_data

Examples

## EXAMPLE 1 -----------

## Retrieve the model keys available for dynamic models.
get_model_data()

## Set the input arguments
example_model <- "Geeraerd"  # Geeraerd's model will be used
times <- seq(0, 5, length=100)  # values of time for output

model_data <- get_model_data(example_model)  # Retrive the data of the model used
print(model_data$parameters)
print(model_data$variables)
model_parms <- c(D_R = 1,
                 z = 10,
                 N_min = 100,
                 temp_ref = 100,
                 N0 = 100000,
                 C_c0 = 1000
                 )

## Define the temperature profile for the prediction
temperature_profile <- data.frame(time = c(0, 1.25, 2.25, 4.6),
                                  temperature = c(70, 105, 105, 70))

## Call the prediction function
prediction_results <- predict_inactivation(example_model, times,
                                           model_parms, temperature_profile)

## Show the results
head(prediction_results$simulation)
plot(prediction_results)
time_to_logreduction(1.5, prediction_results)

## END EXAMPLE 1 -----------

Dynamic Prediction Intervals from a Monte Carlo Adjustment

Description

Given a model adjustment of a dynamic microbial inactivation process performed using any of the functions in bioinactivation calculates probability intervals at each time point using a Monte Carlo method.

Usage

predict_inactivation_MCMC(
  fit_object,
  temp_profile,
  n_simulations = 100,
  times = NULL,
  quantiles = c(2.5, 97.5),
  additional_pars = NULL
)

Arguments

fit_object

An object of classes FitInactivationMCMC, IsoFitInactivation or FitInactivation.
temp_profile

data frame with discrete values of the temperature for each time. It must have one column named time and another named temperature providing discrete values of the temperature at time points.
n_simulations

a numeric indicating how many Monte Carlo simulations to perform. 100 by default.
times

numeric vector specifying the time points when results are desired. If NULL, the times in MCMC_fit$best_prediction are used. NULL by default.
quantiles

numeric vector indicating the quantiles to calculate in percentage. By default, it is set to c(2.5, 97.5) which generates a prediction interval with confidence 0.95. If NULL, the quantiles are not calculated and all the simulations are returned.
additional_pars

Additional parameters not included in the adjustment (e.g. the initial number of microorganism in an isothermal fit).

Value

A data frame of class PredInactivationMCMC. On its first column, time at which the calculation has been made is indicated. If quantiles = NULL, the following columns contain the results of each simulation. Otherwise, the second and third columns provide the mean and median of the simulations at the given time point. Following columns contain the quantiles of the results.

Random sample of the parameters of a FitInactivation object

Description

Function to be called by predict_inactivation_MCMC. Produces a random sample of the parameters adjusted from dynamic experiments with non linear regression.

Usage

sample_dynaFit(dynamic_fit, times, n_simulations)

Arguments

dynamic_fit

An object of class FitInactivationMCMC as generated by fit_inactivation_MCMC.
times

numeric vector specifying the time points when results are desired. If NULL, the times in MCMC_fit$best_prediction are used.
n_simulations

a numeric indicating how many Monte Carlo simulations to perform.

Details

It is assumed that the parameters follow a Multivariate Normal distribution with the mean the parameters estimated by modFit. The unscaled covariance matrix returned by modFit is used.

The function produces a random sample using the function mvrnorm.

Value

Returns a list with 4 components.

  • par_sample: data frame with the parameter sample.

  • simulation_model: model key for the simulation

  • known_pars: parameters of the model known

  • times: points where the calculation is made.

Random sample of the parameters of a IsoFitInactivation object

Description

Function to be called by predict_inactivation_MCMC. Produces a random sample of the parameters adjusted from isothermal experiments.

Usage

sample_IsoFit(iso_fit, times, n_simulations)

Arguments

iso_fit

An object of class FitInactivationMCMC as generated by fit_inactivation_MCMC.
times

numeric vector specifying the time points when results are desired. If NULL, an equispaced interval between 0 and the maximum time of the observations with length 50 is used.
n_simulations

a numeric indicating how many Monte Carlo simulations to perform.

Details

It is assumed that the parameters follow a Multivariate Normal distribution with the mean and covariance matrix estimated by the adjustment. The function produces a random sample using the function mvrnorm.

Value

Returns a list with 4 components.

  • par_sample: data frame with the parameter sample.

  • simulation_model: model key for the simulation

  • known_pars: parameters of the model known

  • times: points where the calculation is made.

See Also

mvrnorm

Random sample of the parameters of a FitInactivationMCMC object

Description

Function to be called by predict_inactivation_MCMC. Produces a random sample of the parameters calculated on the iterations of the Monte Carlo simulation.

Usage

sample_MCMCfit(MCMC_fit, times, n_simulations)

Arguments

MCMC_fit

An object of class FitInactivationMCMC as generated by fit_inactivation_MCMC.
times

numeric vector specifying the time points when results are desired. If NULL, the times in MCMC_fit$best_prediction are used.
n_simulations

a numeric indicating how many Monte Carlo simulations to perform.

Value

Returns a list with 4 components.

  • par_sample: data frame with the parameter sample.

  • simulation_model: model key for the simulation

  • known_pars: parameters of the model known

  • times: points where the calculation is made.

Summary of a FitInactivation object

Description

Summary of a FitInactivation object

Usage

## S3 method for class 'FitInactivation'
summary(object, ...)

Arguments

object

Instance of Fit Inactivation
...

ignored

Summary of a FitInactivationMCMC object

Description

Summary of a FitInactivationMCMC object

Usage

## S3 method for class 'FitInactivationMCMC'
summary(object, ...)

Arguments

object

Instance of FitInactivationMCMC
...

ignored

Summary of a IsoFitInactivation object

Description

Summary of a IsoFitInactivation object

Usage

## S3 method for class 'IsoFitInactivation'
summary(object, ...)

Arguments

object

Instance of IsoFitInactivation
...

ignored

Time to reach X log reductions

Description

Calculates the treatment time required to reach a given number of log reductions.

Usage

time_to_logreduction(n_logs, my_prediction)

Arguments

n_logs

Numeric of length one indicating the number of log recutions
my_prediction

An object of class SimulInactivation

Details

The treatement time is calculated by linear interpolation betweent the two points of the simulation whose logS is closer to n_logs

Isothermal Weibull-Mafart Model

Description

Returns the predicted logarithmic reduction in microbial count according to Weibull-Mafarts's model for the time, temperature and model parameters given.

Usage

WeibullMafart_iso(time, temp, delta_ref, z, p, temp_ref)

Arguments

time

numeric indicating the time at which the prediction is taken.
temp

numeric indicating the temperature of the treatment.
delta_ref

numeric defining the delta-value at the reference temperature.
z

numeric defining the z-value.
p

numeric defining shape factor of the Weibull distribution.
temp_ref

numeric indicating the reference temperature.

Value

A numeric with the predicted logarithmic reduction (log10(N/N0)log10(N/N0)).

Isothermal Weibull-Peleg Model

Description

Returns the predicted logarithmic reduction in microbial count according to Weibull-Peleg's model for the time, temperature and model parameters given.

Usage

WeibullPeleg_iso(time, temp, n, k_b, temp_crit)

Arguments

time

numeric indicating the time at which the prediction is taken.
temp

numeric indicating the temperature of the treatment.
n

numeric defining shape factor of the Weibull distribution.
k_b

numeric indicating the slope of the b~temp line.
temp_crit

numeric with the value of the critical temperature.

Value

A numeric with the predicted logarithmic reduction (log10(N/N0)log10(N/N0)).