Susceptible-Exposed-Infectious-Removed (SEIR) Model Framework with Lesion Expansion

This function is originally used by specific disease models in ‘EPIRICE’ and ‘EPIWHEAT’ to model disease intensity of several rice diseases and two wheat diseases respectively. Given proper values it can be used with other pathosystems as well.

Usage

epicrop_sim(
  wth,
  emergence,
  onset,
  duration,
  rhlim = 90,
  rainlim = 5,
  H0,
  I0,
  RcA,
  RcT,
  RcOpt,
  p,
  i,
  Sx,
  a = 1,
  RRS,
  RRG,
  RcW = NULL,
  RRLEX = 0,
  simple_wetness = TRUE,
  age_driver = "day",
  thermal_time = list(base_temp = 0, gdd_to_maturity = 1100),
  steps_per_day = 1L
)

Arguments

wth

a data.frame of class epicrop.wth from either get_wth() or format_wth() containing weather on a daily time-step with the following field names:

Field Name	Value
YYYYMMDD	Date as Year Month Day (ISO8601)
DOY	Consecutive day of year, commonly called "Julian date"
TEMP	Mean daily temperature (°C)
RHUM	Mean daily relative humidity (%)
RAIN	Mean daily rainfall (mm)
TMIN	Optional Minimum daily temperature (°C), see TMIN/TMAX Details
TMAX	Optional Maximum daily temperature (°C), see TMIN/TMAX Details
LAT	Optional latitude of weather observation, see LAT/LON Details
LON	Optional longitude of weather observation, see LAT/LON Details

emergence

Expected date of plant emergence (or transplanting for rice) entered in YYYY-MM-DD format (character).

onset

expected number of days until the onset of disease after emergence date (day, integer). Described in Table 1 of Savary et al. 2012.

duration

simulation duration i. e., growing season length (day, integer). Described in Table 1 of Savary _et al. _ 2012.

rhlim

relative humidity value threshold to decide whether leaves are wet or not (numeric). Described in Table 1 of Savary et al. 2012. Savary et al. 2012 used 90.

rainlim

rainfall amount (mm) threshold to decide whether leaves are wet or not (numeric). Described in Table 1 of Savary et al. 2012. Savary et al. 2012 used 5.

H0

initial number of plant's healthy sites (integer). Described in Table 1 of Savary et al. 2012.

I0

initial number of infective sites (scalar integer) OR a list with:

mode: "impulse", "uniform", "triangle", or "series"
I0: Total inoculum amount
start_offset: Day to start inoculation (defaults to onset)
duration: Number of days over which to distribute inoculum
series: Custom daily inoculum vector (for mode = "series") Described in Table 1 of Savary et al. 2012. I0 is injected as new infections (become infectious after p days).

RcA

modifier for Rc (the basic infection rate corrected for removals) for crop age as a numeric two-column matrix with the first column being the crop age in days (0 to duration-1) or DVS (0 to 2) and the second being the modifier (bounded by 0 and 1). Described in Tables 1 and 2 of Savary et al. 2012.

RcT

modifier for Rc (the basic infection rate corrected for removals) for temperature as a numeric two-column matrix with the first column being temperature in °C and the second the modifier (bounded by 0 and 1). Described in Tables 1 and 2 of Savary et al. 2012.

RcOpt

potential basic infection rate corrected for removals (numeric). Described in Table 1 of Savary et al. 2012. This value can be modified to reflect crop cultivar resistance ratings as well, see Kim _et al. _ 2015 for more details.

p

duration of latent period (day, integer or function of temperature). Described in Table 1 of Savary et al. 2012.

i

duration of infectious period (day, integer or function of temperature). Described in Table 1 of Savary et al. 2012.

Sx

maximum number of sites (integer). Described in Table 1 of Savary et al. 2012.

a

aggregation coefficient, values are from 1 to >1 (numeric or function of DVS). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015. See further details in a - Aggregation section.

RRS

relative rate of physiological senescence (numeric, vector, or function of DVS). Described in Table 1 of Savary et al. 2012.

RRG

relative rate of growth (numeric, vector, or function of time). Described in Table 1 of Savary et al. 2012.

RcW

Optional modifier for Rc to calculate leaf wetness effect from 1 if wet to 0 if dry. This is a numeric two-column matrix with the first column being hours (0 to 24) and the second the modifier (bounded by 0 and 1). Used when simple_wetness = FALSE (hourly/derived wetness). If NULL (default), a linear relationship is used where 0 hours wet = 0 and 24 hours wet = 1. Ignored if simple_wetness = TRUE.

RRLEX

Rate of lesion expansion (scalar, vector, or function). Allows healthy sites to be directly converted to infectious sites without passing through latent stage. Set to 0 (default) for standard SEIR behavior.

simple_wetness

Logical. If TRUE (default), uses binary wetness calculation (0 or 1) based on rhlim and rainlim thresholds. If FALSE, uses hourly wetness duration calculation (requires TMIN, TMAX, LAT, DOY in wth) and applies RcW curve.

age_driver

Character. Use "day" (default, 0-indexed days from emergence) or "dvs" (development stage 0-2) for age-based modifiers in RcA. When "dvs", thermal_time parameter is required.

thermal_time

List with base_temp (°C) and gdd_to_maturity (°C·days). Only required when age_driver = "dvs". Determines how growing degree days are accumulated and converted to development stage (DVS).

steps_per_day

Integer. Number of sub-daily time steps for numerical integration. Default is 1 (daily steps). Values of 2, 4, or 8 can improve accuracy for stiff systems at cost of computation time. Should be a power of 2.

Value

A data.table::data.table() object containing the following columns:

simday: Day of simulation (1-indexed, where 1 is the emergence date)
dates: Date of simulation (Date class)
sites: Total number of healthy sites present on day "x"
latent: Number of latent sites present on day "x"
infectious: Number of infectious sites present on day "x"
removed: Number of removed sites present on day "x"
senesced: Number of senesced sites present on day "x"
rateinf: Rate of infection (new infections on day "x")
rlex: Rate of lesion expansion (healthy sites converted to infectious via direct expansion on day "x")
rtransfer: Rate of transfer from latent to infectious sites on day "x"
rremoved: Rate of removal from infectious to removed sites on day "x"
rgrowth: Rate of growth of healthy sites on day "x"
rsenesced: Rate of senescence of healthy sites on day "x"
diseased: Number of diseased (latent + infectious + removed) sites on day "x"
intensity: Proportion of diseased sites (latent + infectious) per total living sites (excludes removed and senesced) on day "x"
lat: Latitude value if provided by the wth object
lon: Longitude value if provided by the wth object

The returned object also has an attribute AUDPC (accessed via attr(result, "AUDPC")) containing the area under the disease progress curve for the entire simulation, calculated using the trapezoidal rule.

Output Structure

The output is organized into three categories:

State Variables (stocks at end of each day):

sites, latent, infectious, removed, senesced

Flow Variables (rates/changes during each day):

rateinf, rlex, rtransfer, rremoved, rgrowth, rsenesced

Derived Variables (calculated from states):

diseased, intensity

Mass Balance: At any day: sites + latent + infectious + removed + senesced should equal initial sites (H0) plus cumulative growth minus cumulative senescence (accounting for numerical precision).

a – Aggregation Details

When a is set to 1 the assumption is that that there is no disease aggregation with new infections occurring at random among the healthy sites. When a is greater than 1 there is aggregation in the disease occurrence, the pathogen is unable to access the entire population of healthy sites, which results in disease aggregation. Refer to Savary et al. (2012) for greater detail.

TMIN/TMAX Details

If simple_wetness is set to FALSE, the function will use the TMIN and TMAX columns in the wth object to calculate the leaf wetness value for 24 hours of the day using the rhlim and rainlim values and then uses RcW to calculate a value between 0 and 1 for the whole day. When simple_wetness is set to TRUE, the function only sets the leaf wetness to 0 or 1 for the day based on the rhlim and rainlim values.

LAT/LON Details

If the wth object provides LAT and LON columns, these will be included in the output for mapping purposes. Both values must be present. These columns are provided by default when using get_wth().

References

Sparks, A. H., P. D. Esker, M. Bates, W. Dall' Acqua, Z. Guo, V. Segovia, S.D. Silwal, S. Tolos, and K. A. Garrett, 2008. Ecology and Epidemiology in R: Disease Progress over Time. The Plant Health Instructor. doi:10.1094/PHI-A-2008-0129-02 .

Madden, L. V., G. Hughes, and F. van den Bosch. 2007. The Study of Plant Disease Epidemics. American Phytopathological Society, St. Paul, MN. doi:10.1094/9780890545058 .

Savary, S., Nelson, A., Willocquet, L., Pangga, I., and Aunario, J. Modeling and mapping potential epidemics of rice diseases globally. Crop Protection, Volume 34, 2012, Pages 6-17, ISSN 0261-2194 doi:10.1016/j.cropro.2011.11.009 .

Author

Adam H. Sparks, adamhsparks@gmail.com from original by Robert J. Hijmans, Rene Pangga and Jorrel Aunario.