Modelling of COVID-19 distribution in Nigeria

Load library and the data

The data is scrapped from the website of the Nigerian Centre for Disease Control (NCDC) i.e (NCDC 2020). The scrapping was done with some bits of tricks. Please see my post on that. The BREAKS were established from the visual inspection of the data (see (Nmadu, Yisa, and Mohammed 2009))

library(tidyverse)
library(splines)
library(Metrics)
library(scales)
library(readxl)
library(patchwork)
library(Dyn4cast)

BREAKS <- c(70, 131, 173, 228, 274, 326)

z.s           <- readRDS("data/zs.RDS")
cumper        <- readRDS("data/cumper.RDS")
niz           <- readRDS("data/niz.RDS")
States_county <- read_excel("data/States.xlsx")

Like mentioned earlier, some tricks were used to obtain the daily data from the website of NCDC. The NCDC uploads the cumulative data on daily basis, so each day, the data were scrapped and then the daily incidence were recorded. For example, below is the data scrapped from the website on March 15, 2021.

Deaths <- readr::read_csv("data/today.csv")
names(Deaths) <- c("Region", "Confirmed", "Active", "Recovered", "Deaths")
DDmap <- Deaths
Deaths
## # A tibble: 37 × 5
##    Region      Confirmed Active Recovered Deaths
##    <chr>           <dbl>  <dbl>     <dbl>  <dbl>
##  1 Abia             1629     44      1564     21
##  2 Adamawa           942    641       270     31
##  3 Akwa Ibom        1707    483      1210     14
##  4 Anambra          1909     64      1826     19
##  5 Bauchi           1482    198      1267     17
##  6 Bayelsa           828     37       765     26
##  7 Benue            1188    575       591     22
##  8 Borno            1321     83      1200     38
##  9 Cross River       344     14       313     17
## 10 Delta            2593    780      1744     69
## # … with 27 more rows

Creating date items

The dates are created starting with the day COVID-19 was first recorded in Nigeria, which is February 29, 2020. The sequence of dates were created fron the day to the last day the dataset was uploaded, which is March 15, 2021. In addition, sequence of dates were created from March 16, 2021 to march the number of days the virus have been recorded in Nigeria.

ss <- seq(1:length(cumper$DailyCase))
Dss <- seq(as.Date("2020-02-29"), by = "day", length.out = length(cumper$DailyCase))
Dsf <- seq(as.Date(Dss[length(Dss)] + lubridate::days(1)),
           by = "day", length.out = length(cumper$DailyCase))
day01 <- format(Dss[1], format = "%B %d, %Y")
daylast <- format(Dss[length(Dss)], format = "%B %d, %Y")
casesstarts <- paste("Starting from", day01, "to", daylast,
                     collapse=" ")
lastdayfo <- format(Dsf[length(Dsf)], format = "%B %d, %Y")

Modelling and forecasting of COVID-19 caes

The incidence of the virus was model using five machine learning algorithms which are:

Splines model without Knots

Smooth spline

Splines model with Knots (or breaks)

Quadratic Polynomial

ARIMA

Then using the ensemble technology, another set of four machine learning models were estimated as follows:

Essembled based on summed weight

Essembled based on weight of fit

Essembled based on weight

Essembled with equal weight

The esemble technology is an attempt to combine models into one especially were the individual models are weak (Mahoney 2021).

fit0  <- lm(Case ~ bs(Day, knots = NULL), data = niz)
fit   <- lm(Case ~ bs(Day, knots = BREAKS), data = niz)
fit1  <- smooth.spline(niz$Day, niz$Case)
fita  <- forecast::auto.arima(niz$Case)
fitpi <- lm(Case ~ Day + I(Day^2), data = niz)

kk  <- forecast::forecast(fitted.values(fit), 
                           h = length(Dsf))
 kk0 <- forecast::forecast(fitted.values(fit0),
                           h = length(Dsf))
 kk1 <- forecast::forecast(fitted.values(fit1),
                           h = length(Dsf))
 kk10 <- forecast::forecast(fitted.values(fitpi),
                            h = length(Dsf))
 kk2 <- forecast::forecast(forecast::auto.arima(z.s$Case), h = length(Dsf))
 
 kk30 <- (fitted.values(fit) + fitted.values(fit0) +
              fitted.values(fit1) + fitted.values(fitpi) +
            fita[["fitted"]])/5
 kk31 <- forecast::forecast(kk30, h = length(Dsf))
 
 kk40 <- lm(niz[,2]~fitted.values(fit)*fitted.values(fit0)*
              fitted.values(fit1)*fitted.values(fitpi)*
              fita[["fitted"]])
 kk41 <- forecast::forecast(fitted.values(kk40),
                            h = length(Dsf))
 kk60 <- lm(niz[,2]~fitted.values(fit)+fitted.values(fit0)+
              fitted.values(fit1)+fitted.values(fitpi)+
              fita[["fitted"]])
 kk61 <- forecast::forecast(fitted.values(kk60),
                            h = length(Dsf))
 
 KK <- as.data.frame(cbind("Date" = Dsf,"Day" = ss, "Without Knots" = kk[["mean"]], "Smooth spline" = kk0[["mean"]],  "With Knots" = kk1[["mean"]], "Polynomial" = kk10[["mean"]], "Lower ARIMA" = kk2[["lower"]], "Upper ARIMA" = 
                             kk2[["upper"]]))

 KK <- KK[,-c(7,9)]
names(KK) <- c("Date", "Day", "Without Knots", "Smooth spline", "With Knots", "Polynomial", "Lower ARIMA", "Upper ARIMA") 

WK   <- sum(KK$`Without Knots`)
WKs  <- sum(KK$`With Knots`)   
SMsp <- sum(KK$`Smooth spline`)
LA   <- sum(KK$`Lower ARIMA`)  
UA   <- sum(KK$`Upper ARIMA`)  
POL  <- sum(KK$Polynomial)

RMSE <- c("Without knots" = rmse(niz[,2],
                                 fitted.values(fit)),
"Smooth Spline" = rmse(niz[,2], fitted.values(fit0)),
"With knots" = rmse(niz[,2], fitted.values(fit1)),
"Polynomial" = rmse(niz[,2], fitted.values(fitpi)),
"Lower ARIMA" = rmse(niz[,2], fita[["fitted"]]),
"Upper ARIMA" = rmse(niz[,2], fita[["fitted"]]))

#RMSE <- 1/RMSE
RMSE_weight <- as.list(RMSE / sum(RMSE))

KK$Date <- as.Date(KK$Date, origin = as.Date("1970-01-01"))

DDf <- c("Without knots", "Smooth Spline", 
          "With knots", "Quadratic Polynomial",
         "Lower ARIMA", "Upper ARIMA",
         "Essembled with equal weight",
         "Essembled based on weight",
         "Essembled based on summed weight",
         "Essembled based on weight of fit" )

KK$`Essembled with equal weight` <- kk31[["mean"]]
KK$`Essembled based on weight` <- kk41[["mean"]]
KK$`Essembled based on summed weight` <- kk61[["mean"]]
ESS  <- sum(KK$`Essembled with equal weight`)
ESM  <- sum(KK$`Essembled based on weight`)
ESMS  <- sum(KK$`Essembled based on summed weight`)
P_weight <-
  (fitted.values(fit) * RMSE_weight$`Without knots`) + (fitted.values(fit0) *
                                                          RMSE_weight$`Smooth Spline`) +
  (fitted.values(fit1) * RMSE_weight$`With knots`) + (fitted.values(fitpi) *
                                                        RMSE_weight$Polynomial) + (fita[["fitted"]] * RMSE_weight$`Lower ARIMA`)
kk51 <- forecast::forecast(P_weight, h = length(Dsf))
KK$`Essembled based on weight of fit` <-
  kk51[["mean"]]
ESF  <- sum(KK$`Essembled based on weight of fit`)
RMSE$`Essembled with equal weight` <- rmse(niz[,2], kk30)
RMSE$`Essembled based on weight` <- rmse(niz[,2], fitted.values(kk40))
RMSE$`Essembled based on summed weight` <- rmse(niz[,2], fitted.values(kk60))
RMSE$`Essembled based on weight of fit` <- rmse(niz[,2], P_weight)
Forcasts <- colSums(KK[,-c(1,2)])

RMSE_f <- as.data.frame(cbind("Model" = DDf,
                              "Confirmed cases" =
                                comma(round(Forcasts, 0))))

Deaths$County <- States_county$County
Deaths <- Deaths[order(-Deaths$Deaths),]
Deaths$Region <- factor(Deaths$Region, levels = Deaths$Region)
Deaths$Ratio <- Deaths$Deaths/Deaths$Confirmed*100
Deaths <- Deaths[order(-Deaths$Ratio),]
Deaths$Region <- factor(Deaths$Region, levels = Deaths$Region)

Deaths$RecRatio <- Deaths$Recovered/Deaths$Confirmed*100
Deaths <- Deaths[order(-Deaths$RecRatio),]
Deaths$Region <- factor(Deaths$Region, levels = Deaths$Region)
PerDeath <- round(sum((Deaths$Deaths)/
                     sum(Deaths$Confirmed)*100), 2)
PerRec <- round(sum((Deaths$Recovered)/
                     sum(Deaths$Confirmed)*100), 2)

RMSE_f$Recoveries <- comma(round(Forcasts * PerRec/100, 0))
RMSE_f$Fatalities <- round(Forcasts * PerDeath/100, 0)
RMSE_f$RMSE <- RMSE
RMSE_f <- RMSE_f[order(-RMSE_f$Fatalities),]
RMSE_f$Model <- factor(RMSE_f$Model, levels = RMSE_f$Model)
RMSE_f$Fatalities <- comma(RMSE_f$Fatalities)
RMSE_fk <- knitr::kable(RMSE_f, row.names = FALSE, "html")

The report

It is now 381 days since the first COVID-19 case was reported in Nigeria. As at March 15, 2021 the confirmed cases are 163,646 with 2,016 (1.25%, 100) fatalities, however, 145,752 (90.59%, 100) have recovered.

Based on equal days forecast, by March 31, 2022, Nigeria’s aggregate confirmed COVID-19 cases are forecast to be:

kableExtra::kable_styling(RMSE_fk, "striped")
ModelConfirmed casesRecoveriesFatalitiesRMSE
Smooth Spline889,385805,69411,117371.3422
Upper ARIMA805,328729,54710,067209.3347
Quadratic Polynomial598,274541,9777,478373.6787
Essembled based on summed weight-70,387-63,763-880185.4474
Essembled based on weight of fit-94,320-85,444-1,179283.632
Essembled based on weight-182,959-165,743-2,287179.7495
Essembled with equal weight-426,038-385,948-5,325232.0987
Lower ARIMA-626,365-567,424-7,830209.3347
Without knots-815,453-738,719-10,193199.6519
With knots-1,114,856-1,009,948-13,936187.3864

Take a further look at some of the visuals

plot(z.s[,1], z.s[,2], main = " ", col = "red", type = "l", lwd = 2, xlab = casesstarts, ylab = "COVID-19 confirmed cases")
grid(10,20,lty=1,lwd=1)
abline(v = BREAKS, lwd = 2, lty = 2, col = "black")
#lines(density(z.s$Case), lwd = 2, type = "l", col = "blue", bw = 69.22)
lines(fitted.values(smooth.spline(z.s[,1],z.s[,2])), type = "l", 
      col = "blue", lwd = 2)
DDf <- c("Observed", "Cut points", "Smooth spline") #, "Density")
legend("topleft", 
       inset = c(0, 0),  bty = "n", x.intersp = 0.5,
       xjust = 0, yjust = 0,
       legend = DDf, col = c("red", "black", "blue"),
       lwd = 2, cex = 0.75, xpd = TRUE, horiz = FALSE)

The above plot shows that as at March 15, 2021; Nigeria has gone through two waves and there were more cases of COVID-19 in the second wave.

plot(cumper$Per, main = " ",
     xlab = casesstarts, ylab = "Per Cent",
     ylim = c(-50,100),
     type = "l", lwd = 2, col="forestgreen")
grid(10,20,lty=1,lwd=1)
lines(cumper$Per, lty=1,lwd=2, col= "forestgreen")
lines(cumper$PerCum, lty=1,lwd=2, col= "orangered")
lines(log(cumper$DailyCase), lty=1,lwd=2, col= "magenta")
lines(cumper$LPer, lty=1,lwd=2, col= "brown")
lines(cumper$LPerCum, lty=1,lwd=2, col= "blue")
legend("topright", 
       inset = c(0, 0, 0, 0),  bty = "n", x.intersp = 0.5,
       xjust = 0, yjust = 0,
       "topright", col = c("forestgreen", "orangered", "magenta", "brown", "blue"),
       c("Per cent of total cases","Percent of cummulative cases", 
         "Daily cases, log transformed", 
         "Difference from previsous rate",
         "Difference from previous cummulative rate"),
       lwd = 2, cex = 0.75, xpd = TRUE, horiz = FALSE)

The above two visuals show the log transformation of the distribution and the difference from previous day. The plots were mage with plot and ggplot functions respectively.

The plot on the right is the cumulative cases of COVID-19 recorded in Nigeria while on the left is the forecast using spline and polynomial models. The forecast is based on equal duation of the lenght of the data.

References

Mahoney, Mike. 2021. “Model Averaging Methods: How and Why to Build Ensemble Models.” 2021. https://www.mm218.dev/posts/2021/01/model-averaging/.
NCDC. 2020. “NCDC Coronavirus COVID-19 Microsite.” Abuja, Nigeria: The Nigerian Centre for Disease Control. 2020. https://covid19.ncdc.gov.ng/.
Nmadu, Job, Ezekiel Yisa, and Usman Mohammed. 2009. “Spline Functions: Assessing Their Forecasting Consistency with Changes in the Type of Model and Choice of Joint Points.” Trends in Agricultural Economics 2 (1): 17–27. https://doi.org/10.3923/tae.2009.17.27.
Job Nmadu
Professor of Agricultural Economics and Dean, School of Agriculture and Agricultural Technology

Research interests are economic efficiencies of small scale farming and welfare effects of agricultural interventions.

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