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.
