Susceptible-Exposed-Infectious-Removed (SEIR) Model Framework

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

Usage

seir(
  wth,
  emergence,
  onset,
  duration,
  rhlim,
  rainlim,
  H0,
  I0,
  RcA,
  RcT,
  RcOpt,
  p,
  i,
  Sx,
  a,
  RRS,
  RRG,
  RcW,
  simple_wetness
)

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). Described in Table 1 of Savary et al. 2012.

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

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 (1 to duration) 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). Described in Table 1 of Savary et al. 2012.

i

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

RRG

relative rate of growth (numeric). Described in Table 1 of Savary et al. 2012.

RcW

an 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 (1 to 24) and the second the modifier (bounded by 0 and 1). Only used when simple_wetness == TRUE, if it is provided and simple_wetness == FALSE, these values will be ignored.

simple_wetness

Boolean value, if TRUE the function will use a simple calculation of leaf wetness based on the daily rhlim and rainlim values. If FALSE the function will use a more complex calculation of leaf wetness based on the wth data and will calculate the leaf wetness value for each hour of the day and use RcW to determine the effect of leaf wetness on the infection rate.

Value

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

simday: Zero indexed day of simulation that was run
dates: Date of simulation
sites: Total number of 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"
ratinf: Rate of infection
rtransfer: Rate of transfer from latent to infectious sites
rgrowth: Rate of growth of healthy sites
rsenesced: Rate of senescence of healthy sites
diseased: Number of diseased (latent + infectious + removed) sites on day "x"
intensity: Proportion of diseased (latent + infectious + removed) sites per total sites not including removed sites on day "x"
AUDPC: Area under the disease progress curve AUDPC for the simulation
lat: Latitude value if provided by the wth object
lon: Longitude value if provided by the wth object

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 TMAXcolumns in thewthobject to calculate the leaf wetness value for 24 hours of the day using therhlimandrainlimvalues and then usesRcWto calculate a value between 0 and 1 for the whole day. Whensimple_wetnessis set toTRUE, the function only sets the leaf wetness to 0 or 1 for the day based on the rhlimandrainlim` 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.

Examples

# get weather for IRRI Zeigler Experiment Station in wet season 2000
wth <- get_wth(
  lonlat = c(121.25562, 14.6774),
  dates = c("2000-06-30", "2000-12-31")
)
#> No encoding supplied: defaulting to UTF-8.
#> No encoding supplied: defaulting to UTF-8.

# provide suitable values for brown spot intensity
RcA <-
  cbind(
    c(0L, 20L, 40L, 60L, 80L, 100L, 120L),
    c(0.35, 0.35, 0.35, 0.47, 0.59, 0.71, 1.0)
  )
RcT <-
  cbind(
    c(15L, 20L, 25L, 30L, 35L, 40L),
    c(0, 0.06, 1.0, 0.85, 0.16, 0)
  )
emergence <- "2000-07-15"

(seir(
  wth = wth,
  emergence = emergence,
  onset = 20,
  duration = 120,
  rhlim = 90,
  rainlim = 5,
  RcA = RcA,
  RcT = RcT,
  RcOpt = 0.61,
  p = 6,
  i = 19,
  H0 = 600,
  I0 = 1,
  a = 1,
  Sx = 100000,
  RRS = 0.01,
  RRG = 0.1,
  simple_wetness = TRUE,
  RcW = NULL
))
#>      simday      dates      sites   latent infectious  removed    senesced
#>       <int>     <Date>      <num>    <num>      <num>    <num>       <num>
#>   1:      1 2000-07-15   600.0000    0.000      0.000   0.0000     0.00000
#>   2:      2 2000-07-16   653.6400    0.000      0.000   0.0000     6.00000
#>   3:      3 2000-07-17   712.0404    0.000      0.000   0.0000    12.53640
#>   4:      4 2000-07-18   775.6170    0.000      0.000   0.0000    19.65680
#>   5:      5 2000-07-19   844.8209    0.000      0.000   0.0000    27.41297
#>  ---                                                                      
#> 116:    116 2000-11-07 84936.1503 2396.758   1923.856 193.6086 51458.59847
#> 117:    117 2000-11-08 84982.8335 2095.723   2224.891 193.6086 52307.95998
#> 118:    118 2000-11-09 83854.9572 3266.341   2224.891 193.6086 53157.78831
#> 119:    119 2000-11-10 82653.3965 4141.364   2516.371 230.4324 54033.16175
#> 120:    120 2000-11-11 81283.5572 5044.205   2948.347 266.8889 54896.15221
#>       rateinf rtransfer   rgrowth  rsenesced diseased  intensity     AUDPC
#>         <num>     <num>     <num>      <num>    <num>      <num>     <num>
#>   1:    0.000    0.0000  59.64000   6.000000    0.000 0.00000000 0.6722434
#>   2:    0.000    0.0000  64.93675   6.536400    0.000 0.00000000 0.6722434
#>   3:    0.000    0.0000  70.69703   7.120404    0.000 0.00000000 0.6722434
#>   4:    0.000    0.0000  76.96012   7.756170    0.000 0.00000000 0.6722434
#>   5:    0.000    0.0000  83.76837   8.448209    0.000 0.00000000 0.6722434
#>  ---                                                                      
#> 116:    0.000  301.0350 896.04470 849.361503 4514.223 0.04840657 0.6722434
#> 117: 1170.618    0.0000 892.56992 849.828335 4514.223 0.04838127 0.6722434
#> 118: 1203.327  328.3038 877.13981 875.373444 5684.841 0.06146017 0.6722434
#> 119: 1371.274  468.4328 864.42524 862.990455 6888.168 0.07454541 0.6722434
#> 120: 1601.204  583.5952 849.98224 855.611813 8259.442 0.08952622 0.6722434
#>          lat      lon
#>        <num>    <num>
#>   1: 14.6774 121.2556
#>   2: 14.6774 121.2556
#>   3: 14.6774 121.2556
#>   4: 14.6774 121.2556
#>   5: 14.6774 121.2556
#>  ---                 
#> 116: 14.6774 121.2556
#> 117: 14.6774 121.2556
#> 118: 14.6774 121.2556
#> 119: 14.6774 121.2556
#> 120: 14.6774 121.2556