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
)

Arguments

wth

a data.frame of weather on a daily time-step containing data 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)
LAT	Optional latitude of weather observation, see LAT/LON Note
LON	Optional longitude of weather observation, see LAT/LON Note

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 and Table 1 of Savary et al. 2015.

onset

expected number of days until the onset of disease after emergence date (day, integer). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

duration

simulation duration i.e., growing season length (day, integer). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

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 5mm.

H0

initial number of plant's healthy sites (integer). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

I0

initial number of infective sites (integer). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

RcA

modifier for Rc (the basic infection rate corrected for removals) for crop age (numeric vector). Described in Table 1 of Savary et al. 2012 Table 1 of Savary et al. 2015.

RcT

modifier for Rc (the basic infection rate corrected for removals) for temperature (numeric vector). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

RcOpt

potential basic infection rate corrected for removals (numeric). Derived from Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

p

duration of latent period (day, integer). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

i

duration of infectious period (day, integer). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

Sx

maximum number of sites (integer). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

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 and Table 1 of Savary et al. 2015.

RRG

relative rate of growth (numeric). Described in Table 1 of Savary et al. 2012 and Table 1 of Savary et al. 2015.

Value

A data.table() 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

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.

LAT/LON

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: 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: 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: doi:10.1016/j.cropro.2011.11.009 .

See also

SEIR() is called by the following specific disease modelling functions:

• predict_bacterial_blight(),

• predict_brown_spot(),

• predict_leaf_blast(),

• predict_sheath_blight(),

• predict_tungro()

Author

Adam H. Sparks, adamhsparks@gmail.com

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")
)

# 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
))
#>      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 84935.3759 2397.238   1924.106 193.6346 51458.57203
#> 117:    117 2000-11-08 84982.0602 2096.164   2225.180 193.6346 52307.92579
#> 118:    118 2000-11-09 83854.0436 3266.923   2225.180 193.6346 53157.74639
#> 119:    119 2000-11-10 82652.3242 4142.047   2516.686 230.4750 54033.12717
#> 120:    120 2000-11-11 81282.3276 5044.983   2948.716 266.9368 54896.11230
#>       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 0.6723426
#>   2:    0.000    0.0000  64.93675   6.536400    0.000 0.00000000 0.6723426
#>   3:    0.000    0.0000  70.69703   7.120404    0.000 0.00000000 0.6723426
#>   4:    0.000    0.0000  76.96012   7.756170    0.000 0.00000000 0.6723426
#>   5:    0.000    0.0000  83.76837   8.448209    0.000 0.00000000 0.6723426
#>  ---                                                                      
#> 116:    0.000  301.0740 896.03812 849.353759 4514.978 0.04841477 0.6723426
#> 117: 1170.759    0.0000 892.56329 849.820602 4514.978 0.04838946 0.6723426
#> 118: 1203.470  328.3462 877.13163 875.380778 5685.738 0.06146995 0.6723426
#> 119: 1371.428  468.4924 864.41667 862.985132 6889.208 0.07455665 0.6723426
#> 120: 1601.380  583.8462 849.97224 855.605521 8260.636 0.08953915 0.6723426
#>          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