SEIRA: SEIR with a parallel asymptomatic infectious compartment

The latent class splits into two infectious streams, symptomatic and asymptomatic: dS/dt = -S (beta I + kappa beta A) / N, dE/dt = S (beta I + kappa beta A) / N - sigma E, dI/dt = p sigma E - gamma I, dA/dt = (1 - p) sigma E - gamma_a A, dR/dt = gamma I + gamma_a A.

Usage

Seiarp(S, E, I, A, R, params, t_max = 160, dt = 0.1)

Arguments

S, E, I, A, R: Initial counts in the five compartments.
params: Six rates in this order: beta, sigma, gamma, p, kappa, gamma_a.
t_max: Integration horizon. Default 160.
dt: Runge-Kutta step. Default 0.1.

Value

List with estimate (final size), S, E, I, A, R, N, R0, R0_symptomatic, R0_asymptomatic, asymptomatic_fraction, peak_I, peak_time, final_size, conservation_error, the six rates, t_max, dt, method.

Details

A fraction p of those leaving the latent class become symptomatic and a fraction 1 - p asymptomatic; asymptomatic carriers transmit at a relative infectiousness kappa and clear at their own rate gamma_a. Because the two infectious streams are in parallel, Anderson & May's average over the infectious classes gives R0 = beta (p / gamma + kappa (1 - p) / gamma_a), the sum over routes of (transmission rate) x (probability of entering the route) x (mean time spent in it). Setting p = 1 collapses the A compartment and recovers the SEIR value R0 = beta / gamma.

References

Anderson, R. M. & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press. ISBN 0-19-854040-X.

Examples

Seiarp(S = 990, E = 10, I = 0, A = 0, R = 0,
       params = c(0.3, 0.2, 0.1, 0.05, 0.1, 0.5))
#> $estimate
#> [1] 12.57325
#> 
#> $S
#> [1] 987.4267
#> 
#> $E
#> [1] 1.397653e-05
#> 
#> $I
#> [1] 5.331888e-06
#> 
#> $A
#> [1] 6.230547e-06
#> 
#> $R
#> [1] 12.57325
#> 
#> $N
#> [1] 1000
#> 
#> $R0
#> [1] 0.207
#> 
#> $R0_symptomatic
#> [1] 0.15
#> 
#> $R0_asymptomatic
#> [1] 0.057
#> 
#> $asymptomatic_fraction
#> [1] 0.95
#> 
#> $peak_I
#> [1] 0.2632282
#> 
#> $peak_time
#> [1] 7.6
#> 
#> $final_size
#> [1] 12.57325
#> 
#> $conservation_error
#> [1] 1.023182e-12
#> 
#> $beta
#> [1] 0.3
#> 
#> $sigma
#> [1] 0.2
#> 
#> $gamma
#> [1] 0.1
#> 
#> $p
#> [1] 0.05
#> 
#> $kappa
#> [1] 0.1
#> 
#> $gamma_a
#> [1] 0.5
#> 
#> $t_max
#> [1] 160
#> 
#> $dt
#> [1] 0.1
#> 
#> $method
#> [1] "SEIRA with asymptomatic compartment (Anderson & May 1991)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"