SEIR compartmental model with an exposed (latent) class

Integrates the deterministic SEIR system dS/dt = -beta S I / N, dE/dt = beta S I / N - sigma E, dI/dt = sigma E - gamma I, dR/dt = gamma I.

Usage

Seirep(S, E, I, R, beta, sigma, gamma, t_max = 160, dt = 0.1)

Arguments

S, E, I, R

Initial counts in the four compartments.

beta

Transmission rate.

sigma

Rate of progression from exposed to infectious.

gamma

Recovery rate.

t_max

Integration horizon. Default 160.

dt

Runge-Kutta step. Default 0.1.

Value

List with estimate (final size), S, E, I, R, N, R0, latent_period, infectious_period, peak_I, peak_time, final_size, conservation_error, beta, sigma, gamma, t_max, dt, method.

Details

The exposed class E holds individuals who are infected but not yet infectious; they progress at rate sigma, so the mean latent period is 1 / sigma. The basic reproduction number is \(R0 = beta / gamma\): the latent stage delays but does not alter the number of secondary cases, because every exposed individual eventually becomes infectious. Population N = S + E + I + R is conserved.

Integrated with classical fourth-order Runge-Kutta at a fixed step, so the result is deterministic and identical in every language arm.

References

Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review 42(4), 599-653. doi:10.1137/S0036144500371907

Examples

Seirep(S = 990, E = 10, I = 0, R = 0, beta = 0.3, sigma = 0.2, gamma = 0.1)
#> $estimate
#> [1] 940.735
#> 
#> $S
#> [1] 58.87991
#> 
#> $E
#> [1] 0.04684648
#> 
#> $I
#> [1] 0.3382567
#> 
#> $R
#> [1] 940.735
#> 
#> $N
#> [1] 1000
#> 
#> $R0
#> [1] 3
#> 
#> $latent_period
#> [1] 5
#> 
#> $infectious_period
#> [1] 10
#> 
#> $peak_I
#> [1] 198.6041
#> 
#> $peak_time
#> [1] 55.1
#> 
#> $final_size
#> [1] 940.735
#> 
#> $conservation_error
#> [1] 1.477929e-12
#> 
#> $beta
#> [1] 0.3
#> 
#> $sigma
#> [1] 0.2
#> 
#> $gamma
#> [1] 0.1
#> 
#> $t_max
#> [1] 160
#> 
#> $dt
#> [1] 0.1
#> 
#> $method
#> [1] "SEIR compartmental model (Hethcote 2000)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"