I exhibit an SEIR (Susceptible Exposed Infectious Recovered) model below for illustrating the spread of Monkeypox infection among high-risk populations, using the presenting parameter derived from the paper presented by Lin et al (2023). Given the reproduction number R0 is 3.22, Sigma (infection period): 1/8.23 – 4, and Gamma (rate of progression from infection to recovery); therefore, the Beta variable is known as 0.9172577.

Although mpox has developed to become an epidemic in Indonesia in 2023, this model figures the initial spread of the disease progressing for 60 days ahead, assuming that there was 1 case in 100 high-risk groups.

https://snipboard.io/TvqSQi.jpg

R-code:

#Beta parameter given the reproduction number

R0 <- 3.88 #Reproduction number in a high-risk group

sigma <- 1/(8.23-4) #infection period, rate of progression from E to I is 8.23 − 4

beta <- R0 * sigma

print(beta)

#Define the Parameter

par <- c(

beta <-0.9172577, #Human to human infection rate

gamma <- 1/21, #Rate of progression from I to R

sigma <- 1/(8.23 – 4) #infection period

)

#Assuming the initial Condition

SEIR.init <- c(

S <- 100, #Number of High risk susceptible class of human population

E <- 10, #Number of Exposed class

I <- 1, #Number of Infected human

R <- 0 #Number of Recovered class of human population

)

#Time Points

times <- seq(0, 60, by = 1) # Time span for simulation (days)

# SEIR Model function

SEIR.dyn <- function(t, var, par) {

S <- var[1]

E <- var[2]

I <- var[3]

R <- var[4]

N = S+E+I+R

beta <- par[1]

gamma <- par[2]

sigma <- par[3]

# Derivatives

dS <- -beta * S * I / N

dE <- beta *S*I/N – sigma*E

dI <- sigma * E – gamma *I

dR <- gamma * I

return(list(c(dS, dE, dI, dR)))

}

# Solve the SIR model using differential equations

SEIR.sol <- lsoda(y = SEIR.init,

times = times,

func = SEIR.dyn,

parms = par)

#Extract the results

SEIR.t<-SEIR.sol[,1] # Time

SEIR.S<-SEIR.sol[,2] # Susceptible population over time

SEIR.E<-SEIR.sol[,3] # Exposed population over time

SEIR.I<-SEIR.sol[,4] # Infected population over time

SEIR.R<-SEIR.sol[,5] #Recovery population over time

#Plot the Model

plot(0, 0, type=’n’, xlim=c(0,60),ylim=c(0,120), xlab=’time’, ylab=’population’,

main = “Epidemic Curve Model of Monkeypox Disease in High-risk Group”)

points(SEIR.t,SEIR.S,type=’l’,col=’blue’,lwd=3)

points(SEIR.t,SEIR.E,type=’l’,col=’gold’,lwd=3)

points(SEIR.t,SEIR.I,type=’l’,col=’red’,lwd=3)

points(SEIR.t,SEIR.R,type=’l’,col=’green’,lwd=3)

legend(“top”, legend=c(“Susceptible”, “Exposed”, “Infected”, “Recoverd”),

col=c(‘blue’,’gold’, ‘red’,’green’), lty=rep(1, 3))

Key characteristics of the mpox disease:

Transmission

– Description: mpox virus is mainly transmitted to humans from wild animals such as non-primate humans and rodents. However, transmission in Indonesia is known to be humans to humans, linked to contact with bodily fluids, a skin lesion on an infected individual, and respiratory droplets.

– Value or range: By the end of 2023, the total confirmed cases had reached 72 cases distributed throughout the 6 provinces where 98.6% cases were concentrated in Java, the most populous island.

– Source of information/data: Technical report of the mpox in Indonesia by Indonesia Ministry of Health, Peter et al (2022)

Pathogenicity

– Description: Each case can have >1 coinfection and comorbidities, such as HIV, STIs (Syphilis, HSV), active TB, diabetes and hypertension. Confirmed cases can be asymptomatic, cases with mild conditions, and cases with severe conditions. Although mpox is considered a mild, it is a self-limiting disease.

– Value or range: The incubation period ranges from 1-21 days with an average incubation period of around 7 days. In mpox cases, the incubation period is calculated from the date of exposure until the onset of symptoms. In Indonesia, of the 69 symptomatic cases, only 28 cases had data on exposure to symptom onset.

– Source of information/data: Technical report of the mpox in Indonesia by Ministry of Health

Symptoms

– Description: The most frequently reported symptom is a lesion, which grows into several stages, namely vesicles, macules, papules and crusts. Lesions can grow on the face, feet, soles, genital area, mouth, entire body, chest, hands/palms, perianus and others (anus, head, neck, thighs, back, elbows and/or buttocks).

– Value or range: Of the 69 confirmed cases with symptoms (symptomatic) in Indonesia, the most frequently reported symptoms included lesions 100% (69 cases), followed by fever 86.9% (60 cases), rash 68.1% (47 cases), and lymphadenopathy 57.9% (40 cases).

– Source of information/data: Technical report of the mpox in Indonesia by Ministry of Health

Control measures

– Description: Communication, Information and Education are the main primary prevention measures carried out. Next, the mpox vaccination is given twice with a minimum span of 4 weeks from the first vaccine. In Indonesia, priority for the mpox vaccine is given to homosexual individuals who have had risky sexual relations in the last 2 weeks and to laboratory personnel who examine mpox samples.

– Value or range: Mpox vaccination is targeted at four administrative areas in DKI Jakarta, namely in Central Jakarta as many as 140 individuals, West Jakarta as many as 142 individuals, South Jakarta as many as 120 individuals and East Jakarta as many as 93 individuals with a total vaccination target of 495 individuals.

– Source of information/data: Technical report of the mpox in Indonesia by Ministry of Health

The code and SEIR curve model will be provided below