In Week 1, I stated that I’m interested in Hepatitis Model, so to answer the first question

What model structure would the disease you are interested be and please start adjusting the R code to that structure.

I first started looking at the literatures,

I found for Hepatitis SEIR model is used before. My reasoning can be found here. SEIR model simulation for Hepatitis Hepatitis C Virus Dynamic Transmission Models

The SEIR model is considered to be an appropriate transmission dynamic model for a pathogen with a period of latency between time of infection and time that an infectious individual becomes infectious to others (according to Infectious Disease Epidemiology (Oxford Specialist Handbooks).

So, if I were to develop a model for Hepatitis, I would use SEIR model. After that I will update the R code.

beta: For hepatitis, the transmission rate is estimated to be between 0.5 and 2.0 1/person-time.
gamma: The recovery rate is estimated to be between 1/200 and 1/100 days.
delta: The rate of progression is estimated to be between 1/100 and 1/50 days.
I also increase SIR curves for time 0 to 1000 days

Full R Code:
library(deSolve)
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]
delta <- par[3]
dS <- -beta * S * I / N
dE <- beta * S * I / N – gamma * E
dI <- gamma * E – delta * I
dR <- delta * I
list(c(dS, dE, dI, dR))
}
beta <- 2
gamma <- 1 / 200
delta <- 1 / 100
SEIR.par <- c(beta, gamma, delta)
SEIR.init <- c(99, 1, 0, 0)
SEIR.t <- seq(0, 1000, by = 0.1)
SEIR.sol <- lsoda(SEIR.init, SEIR.t, SEIR.dyn, SEIR.par)
TIME <- SEIR.sol[, 1]
S <- SEIR.sol[, 2]
E <- SEIR.sol[, 3]
I <- SEIR.sol[, 4]
R <- SEIR.sol[, 5]
N <- S + E + I + R
plot(TIME, S, type = ‘l’, col = ‘blue’, main = ‘Hepatitis SEIR model’, xlab = ‘t’, ylab = ‘Number of individuals’)
lines(TIME, E, type = ‘l’, col = ‘red’)
lines(TIME, I, type = ‘l’, col = ‘green’)
lines(TIME, R, type = ‘l’, col = ‘purple’)
legend(‘topleft’, c(‘Susceptible’, ‘Exposed’, ‘Infected’, ‘Recovered’), col = c(‘blue’, ‘red’, ‘green’, ‘purple’), lty = 1)

Please state the key characteristics of the disease you are focusing on e.g. transmission, pathogenicity, symptoms, control measures etc.

Transmission: Hepatitis is a blood-borne virus that can be transmitted through contact with infected blood or body fluids, such as semen, vaginal fluids, and saliva.

Pathogenicity: Hepatitis can cause acute or chronic infection. Acute hepatitis is a short-term infection that usually clears up on its own.Chronic hepatitis on the other hand can last for many years and can lead to serious liver damage, such as cirrhosis and liver cancer.

Symptoms: The symptoms of hepatitis can vary from person to person. Some people may not have any symptoms at all, while others may experience symptoms such as fatigue, fever, loss of appetite, nausea, vomiting, abdominal pain, dark urine, and jaundice (yellowing of the skin and eyes).

Control measures: There are a number of control measures that can be used to prevent the spread of hepatitis

1) Safe sex practices: Using condoms during sex can help to prevent the transmission of hepatitis through semen and vaginal fluids.

2) Needle safety: Needles and other sharp objects should be disposed of safely to prevent the transmission of hepatitis through blood.

3) Universal precautions: Healthcare workers should use universal precautions to prevent the transmission of blood-borne pathogens.

And again,
beta: For hepatitis, the transmission rate is estimated to be between 0.5 and 2.0 1/person-time.
gamma: The recovery rate is estimated to be between 1/200 and 1/100 days.
delta: The rate of progression is estimated to be between 1/100 and 1/50 days.

Dear Arjan,

Thank you for your insightful comment. Here are my initial thoughts.

Whether to include multiple stages of infection: The model is being used to simulate the long-term dynamics of HCV transmission and the impact of different interventions, then it may be necessary to include multiple stages of infection, such as acute infection, chronic infection, and liver disease.

Varying the beta: The beta parameter represents the transmission rate of HCV. It is important to consider how beta may vary in different populations and settings. For example, beta may be higher in populations where there is a high prevalence of HCV and where there is high-risk behavior, such as sharing needles. It may also be higher in healthcare settings where there is a risk of accidental exposure to HCV-infected blood.

Modeling the impact of control measures: There are a number of different control measures that can be used to reduce the transmission of HCV, such as needle-sharing prevention programs, harm reduction programs, and treatment as prevention. The impact of these control measures can be modeled by multiplying the beta parameter by a reduction factor. This reduction factor would depend on the coverage and efficacy of the control measure.

Please let me know your thoughts.

What model structure would the disease you are interested in, and please start adjusting the R code to that structure.

The SEIR (Susceptible Exposed Infectious Recovered/Removed) model is widely used in model studies on hepatitis and is effective in evaluating the transmissibility of HCV, predicting future morbidity, and evaluating the effectiveness of prevention and treatment.

SEIR Model structure:
Susceptible (S): Individuals at risk of acquiring hepatitis C.
Exposed (E): Individuals exposed to the virus but not yet infectious.
Acute Infectious (I1): Individuals with active acute hepatitis C infection.
Chronic Infectious (I2): Individuals with chronic hepatitis C infection.
Recovered (R): Individuals who have cleared the infection naturally or through treatment.

Parameters (with suggested values from the literature):
β (beta): the transmission rate/coefficient.
σ (sigma): the rate at which exposed individuals become infectious
γ (gamma): the rate at which infectious individuals recover
ρ (delta): Disease-induced mortality rate
μ (mu): the Natural mortality rate

N is the total system population.
𝑁(𝑡) = 𝑆(𝑡) + 𝐸(𝑡) + 𝐼(𝑡) + 𝑅(𝑡)

############################ R Code ############################
# Load deSolve library
library(deSolve)

params <- c(
  beta = 0.21, # Transmission rate 
  sigma = 0.1, # Rate of progression from exposed to infectious
  gamma = 0.064, # Recovery rate
  delta = 0.006, # Disease-induced mortality rate
  mu = 0.064 # Natural mortality rate 
)

initial <- c(
  S = 0.9,
  E = 0.01,
  I = 0.01,
  R = 0.0
)
times <- seq(0, 1000, by = 0.1)  # Time span for simulation (years)
# SEIR Model function
seir_func <- function(time, var, par) {
  with(as.list(c(var, par)), {
    dS <- -beta * S * I
    dE <- beta * S * I - sigma * E
    dI <- sigma * E - (gamma + delta) * I
    dR <- gamma * I - mu * R
    return(list(c(dS, dE, dI, dR)))
  })
}
result <- lsoda(initial, times, seir_func, params)

TIME <- result[,1]
S <- result[,2]
E <- result[,3]
I <- result[,4]
R <- result[,5]
N <- S + E + I + R

plot(0, 0, type='n', xlim=c(0,200),ylim=c(0,1) , xlab = "Time (years)", ylab = "Population", main = "Hepatitis C Model")
points(TIME,S,type='l',col='blue',lwd=3)
points(TIME,E,type='l',col='red',lwd=3)
points(TIME,I,type='l',col='orange',lwd=3)
points(TIME,R,type='l',col='green',lwd=3)
# Add a legend
legend("topright", legend = c("Susceptible", "Exposed", "Infectious", "Recovered"), col=c('blue','red','orange','green'),lty=rep(1,4))

######################### End of R Code #########################

Please state the key characteristics of the disease you are focusing on e.g. transmission, pathogenicity, symptoms, control measures, etc. You can write it as text or start using the parameter table in the template provided. Anything you want to let me know about the disease you are going to work on would be useful.

1- Transmission:
– Description: Hepatitis C in Egypt is primarily transmitted through medical procedures using improperly sterilized equipment, such as syringes and needles. Intravenous drug use, transfusions, and sexual transmission.
– Approximate Value: The transmission rate varies, but past unsafe medical practices significantly contributed to high prevalence.
– Source of Information: Research studies, including the WHO and Egyptian Ministry of Health.

2. Pathogenicity:
– Description: Chronic HCV infection can lead to liver fibrosis, cirrhosis, and hepatocellular carcinoma (HCC). Egypt has a high prevalence of genotype 4, which is associated with a higher risk of liver disease progression.
– Approximate Value: HCV-related liver disease is a leading cause of morbidity and mortality in Egypt.
– Source of Information: Scientific studies, healthcare reports, and publications from Egyptian health authorities.

3. Symptoms of HCV:
– Description: Hepatitis C is often asymptomatic in its early stages. Symptoms may include fatigue, jaundice, abdominal pain, and complications like ascites.
– Approximate Value: Many HCV-infected individuals in Egypt are asymptomatic, making early detection and screening important.
– Source of Information: Clinical studies, healthcare data, and reports from Egyptian healthcare providers.

4. Preventive Measures:
– Description: Prevention efforts in Egypt include safe injection practices, improved healthcare infection control, harm reduction programs, and public health campaigns promoting awareness and testing.
-Value: These measures have contributed to reducing new infections and improving care.
– Source of Information: Reports and initiatives by the Egyptian Ministry of Health and international health organizations.

5. Treatment Cure Rates:
– Description: Egypt has implemented widespread access to direct-acting antiviral (DAA) treatments, resulting in high cure rates for chronic HCV infection.
-Value: Cure rates with DAAs often exceed 95%.
– Source of Information: Clinical trials, healthcare data, and WHO reports on HCV treatment in Egypt.

6. Genotype Distribution:
– Description: Genotype 4 is the most prevalent in Egypt, accounting for a significant portion of HCV cases.
-Value: Genotype 4 is highly prevalent, with some regional variations.
– Source of Information: Genotype prevalence studies and genetic analyses in Egypt.

7. Impact on Public Health:
– Description: Hepatitis C has been a major public health concern in Egypt, leading to extensive efforts to control the epidemic.
-Value: The disease has posed significant challenges, but recent interventions have improved outcomes.
– Source of Information: Public health reports, research studies, and WHO assessments of the HCV situation in Egypt.

*What model structure would the disease you are interested be and please start adjusting the R code to that structure.

My interested disease discussed in the previous session was Dengue Fever. The model structure that I would like to develop for my topic is SEIR (Susceptible-Exposure-Infected-Recovered). I would like to use this model to describe the transmission prediction of Dengue in Thailand.

The reason to use the SEIR model is because the virus included incubation or latency period which occur just before infection. In the case of Dengue, the exposure time is approximately 8-9 days before manifestation of the disease once It is transmitted by an infected mosquito. Therefore, take the exposured population into account reflects the realistic disease dynamic and enhances the model’s ability to predict the transmission of dengue used for work towards in reducing the burden of this mosquito-borne disease in the future.

*R Code:

# Define the SEIR dynamics 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]

dS <- -(beta * S * I) / N
dE <- (beta * S * I) / N – sigma * E
dI <- sigma * E – gamma * I
dR <- gamma * I

# Return the rates of change as a list
return(list(c(dS,dE, dI, dR)))
}
install.packages(“deSolve”)
library(deSolve)

# Define initial conditions, time points, and parameters
R0<-3.42 # Basic Reproduction Number (Liu et al., 2020)
gamma <- 1/7 # Infectious period of 7 days, infectious period (7days)= 1/gamma (CDC:
https://www.cdc.gov/dengue/training/cme/ccm/page47478.html)
beta <- R0*gamma # 3.42/7
sigma <- 1/7 # incubation period of dengue 5-7 days
SEIR.par <- c(beta,sigma,gamma)
SEIR.init <- c(5000,1000,50,50) # Assume total population of 5000,Exposed 1000, Infected 50, recovery 50)
SEIR.t <- seq(0,365,by=1) # 0-365 days,increase every 1 day

SEIR.sol <- lsoda(SEIR.init, SEIR.t, SEIR.dyn, SEIR.par) # Solve the SIR model using lsoda

TIME <- SEIR.sol[,1]
S <- SEIR.sol[,2]
E <- SEIR.sol[,3]
I <- SEIR.sol[,4]
R <- SEIR.sol[,5]
N <- S + E + I + R

# Plot the results
plot(TIME, S, type = “l”, col = “blue”, lwd = 2, ylim = c(0, 5000), xlab = “Time”, ylab = “Population”, main = “SEIR model for Degnue “)
lines(TIME, E, type = “l”, col = “yellow”, lwd = 2)
lines(TIME, I, type = “l”, col = “red”, lwd = 2)
lines(TIME, R, type = “l”, col = “green”, lwd = 2)
legend(“right”, legend = c(“Susceptible”, “Exposure”, “Infected”, “Recovered”), col = c(“blue”,”yellow”, “red”, “green”), lty = 1, cex = 0.8)

# I am not able to upload the Plot picture ka Ajarn, I will submit by email na ka.

• Incubation period refers to the time between exposure to a pathogen and the onset of symptoms of the disease it causes. The incubation period of the dengue virus is 3–14 days, with an average of 4–7 days.
Source: https://www.ecdc.europa.eu/en/dengue-fever/facts
• Viremic period is known as the “period of infectivity”. In sick persons, viremia typically coincides with the presence of fever. Both symptomatic and asymptomatic persons are viremic and can transmit DENV to mosquitoes that bite them during this approximately 7-day period.
Source:https://www.cdc.gov/dengue/training/cme/ccm/page45915.html#:~:text=Intrinsic%20Incubation%20Period%20(3%2D14,the%20human%20can%20become%20ill.

*Reference:
Liu, Y., Lillepold, K., Semenza, J. C., Tozan, Y., Quam, M. B. M., & Rocklov, J. (2020, Mar). Reviewing estimates of the basic reproduction number for dengue, Zika and chikungunya across global climate zones. Environ Res, 182, 109114. https://doi.org/10.1016/j.envres.2020.109114

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

Farkhan SEIR Model (I’m just helping to make sure it is display correctly in the WordPress.)