Simulate a Renewal Epidemic Model
simulate_renewal_epidemic.RdThis function simulates an epidemic using a renewal model based on the specified time-varying reproduction number (Rt), the serial interval distribution characterized by a gamma distribution, and an initial number of cases.
Arguments
- Rt_fun
A function that takes a vector of time points and returns a vector of reproduction numbers (Rt) corresponding to those time points.
- nt
An integer specifying the number of time points (duration of the epidemic simulation).
- mean_si
A numeric value representing the mean of the serial interval distribution.
- sd_si
A numeric value representing the standard deviation of the serial interval distribution.
- i_0
An integer specifying the initial number of cases at time point 1.
- X
An optional matrix of covariates with
ntrows.
Value
A list containing the following components:
- i_t
A numeric vector of the incidence of new cases at each time point.
- lambda_t
A numeric vector of the total infectiousness at each time point.
- w_dist
A numeric vector of the discretized serial interval distribution.
- r_t
A numeric vector of the reproduction number (Rt) at each time point.
- t
A numeric vector of the time points from 1 to nt.
Details
The renewal model is a common approach for simulating the spread of infectious diseases. The total infectiousness at each time point is computed as the convolution of past incidence with the serial interval distribution. The incidence at each time point is then simulated as a Poisson random variable with a mean equal to the product of the total infectiousness and the time-varying reproduction number.
Examples
rt_fun <- function(t) {
1.5 * exp(-0.05 * t)
}
simulate_renewal_epidemic(rt_fun, 100, 5, 2, 10)
#> t i_t R_t lambda_t w_dist
#> 1 1 10 1.42684414 1.000000e+01 1.202812e-03
#> 2 2 0 1.35725613 1.202812e-02 3.121540e-02
#> 3 3 1 1.29106196 3.121540e-01 1.171737e-01
#> 4 4 2 1.22809613 1.172940e+00 1.943497e-01
#> 5 5 1 1.16820117 1.977118e+00 2.092807e-01
#> 6 6 0 1.11122733 2.273615e+00 1.731352e-01
#> 7 7 2 1.05703213 2.191264e+00 1.200194e-01
#> 8 8 2 1.00548007 1.917754e+00 7.330704e-02
#> 9 9 1 0.95644223 1.583953e+00 4.071768e-02
#> 10 10 2 0.90979599 1.380728e+00 2.100546e-02
#> 11 11 2 0.86542472 1.353204e+00 1.021454e-02
#> 12 12 2 0.82321745 1.398768e+00 4.732806e-03
#> 13 13 0 0.78306867 1.481441e+00 2.106387e-03
#> 14 14 0 0.74487796 1.595075e+00 9.060961e-04
#> 15 15 1 0.70854983 1.656625e+00 3.785690e-04
#> 16 16 1 0.67399345 1.528375e+00 1.542214e-04
#> 17 17 0 0.64112240 1.245436e+00 6.145378e-05
#> 18 18 0 0.60985449 9.893817e-01 2.401538e-05
#> 19 19 0 0.58011154 8.325695e-01 9.223817e-06
#> 20 20 0 0.55181916 6.984244e-01 3.488238e-06
#> 21 21 2 0.52490662 5.373851e-01 1.300919e-06
#> 22 22 0 0.49930663 3.722733e-01 4.790949e-07
#> 23 23 0 0.47495515 2.918871e-01 1.744290e-07
#> 24 24 0 0.45179132 3.646919e-01 6.284573e-08
#> 25 25 0 0.42975720 4.575370e-01 2.242704e-08
#> 26 26 1 0.40879769 4.527898e-01 7.933068e-09
#> 27 27 0 0.38886039 3.636594e-01 2.783419e-09
#> 28 28 0 0.36989545 2.785920e-01 9.692738e-10
#> 29 29 0 0.35185543 2.669968e-01 3.351808e-10
#> 30 30 0 0.33469524 2.771459e-01 1.151559e-10
#> 31 31 0 0.31837196 2.518534e-01 3.932399e-11
#> 32 32 0 0.30284478 1.937908e-01 1.335243e-11
#> 33 33 0 0.28807486 1.295745e-01 4.509726e-12
#> 34 34 0 0.27402529 7.755453e-02 1.515565e-12
#> 35 35 0 0.26066092 4.254312e-02 5.069278e-13
#> 36 36 0 0.24794833 2.176758e-02 1.688649e-13
#> 37 37 0 0.23585575 1.052483e-02 5.595524e-14
#> 38 38 0 0.22435293 4.856392e-03 1.854072e-14
#> 39 39 0 0.21341111 2.154664e-03 5.995204e-15
#> 40 40 0 0.20300292 9.246319e-04 1.998401e-15
#> 41 41 0 0.19310236 3.855768e-04 6.661338e-16
#> 42 42 0 0.18368464 1.568343e-04 2.220446e-16
#> 43 43 0 0.17472624 6.241584e-05 1.110223e-16
#> 44 44 0 0.16620474 2.436559e-05 0.000000e+00
#> 45 45 0 0.15809884 9.349972e-06 0.000000e+00
#> 46 46 0 0.15038827 3.533251e-06 0.000000e+00
#> 47 47 0 0.14305374 1.316840e-06 0.000000e+00
#> 48 48 0 0.13607693 4.846801e-07 0.000000e+00
#> 49 49 0 0.12944038 1.763738e-07 0.000000e+00
#> 50 50 0 0.12312750 6.351817e-08 0.000000e+00
#> 51 51 0 0.11712250 2.265805e-08 0.000000e+00
#> 52 52 0 0.11141037 8.011946e-09 0.000000e+00
#> 53 53 0 0.10597682 2.810200e-09 0.000000e+00
#> 54 54 0 0.10080827 9.783184e-10 0.000000e+00
#> 55 55 0 0.09589179 3.382201e-10 0.000000e+00
#> 56 56 0 0.09121509 1.161724e-10 0.000000e+00
#> 57 57 0 0.08676648 3.966261e-11 0.000000e+00
#> 58 58 0 0.08253483 1.346467e-11 0.000000e+00
#> 59 59 0 0.07850956 4.546918e-12 0.000000e+00
#> 60 60 0 0.07468060 1.527556e-12 0.000000e+00
#> 61 61 0 0.07103839 5.109246e-13 0.000000e+00
#> 62 62 0 0.06757380 1.701972e-13 0.000000e+00
#> 63 63 0 0.06427819 5.639933e-14 0.000000e+00
#> 64 64 0 0.06114331 1.876277e-14 0.000000e+00
#> 65 65 0 0.05816131 5.995204e-15 0.000000e+00
#> 66 66 0 0.05532475 1.998401e-15 0.000000e+00
#> 67 67 0 0.05262653 6.661338e-16 0.000000e+00
#> 68 68 0 0.05005990 2.220446e-16 0.000000e+00
#> 69 69 0 0.04761845 1.110223e-16 0.000000e+00
#> 70 70 0 0.04529608 0.000000e+00 0.000000e+00
#> 71 71 0 0.04308696 0.000000e+00 0.000000e+00
#> 72 72 0 0.04098558 0.000000e+00 0.000000e+00
#> 73 73 0 0.03898669 0.000000e+00 0.000000e+00
#> 74 74 0 0.03708529 0.000000e+00 0.000000e+00
#> 75 75 0 0.03527662 0.000000e+00 0.000000e+00
#> 76 76 0 0.03355616 0.000000e+00 0.000000e+00
#> 77 77 0 0.03191960 0.000000e+00 0.000000e+00
#> 78 78 0 0.03036287 0.000000e+00 0.000000e+00
#> 79 79 0 0.02888205 0.000000e+00 0.000000e+00
#> 80 80 0 0.02747346 0.000000e+00 0.000000e+00
#> 81 81 0 0.02613356 0.000000e+00 0.000000e+00
#> 82 82 0 0.02485901 0.000000e+00 0.000000e+00
#> 83 83 0 0.02364662 0.000000e+00 0.000000e+00
#> 84 84 0 0.02249337 0.000000e+00 0.000000e+00
#> 85 85 0 0.02139635 0.000000e+00 0.000000e+00
#> 86 86 0 0.02035284 0.000000e+00 0.000000e+00
#> 87 87 0 0.01936022 0.000000e+00 0.000000e+00
#> 88 88 0 0.01841601 0.000000e+00 0.000000e+00
#> 89 89 0 0.01751785 0.000000e+00 0.000000e+00
#> 90 90 0 0.01666349 0.000000e+00 0.000000e+00
#> 91 91 0 0.01585081 0.000000e+00 0.000000e+00
#> 92 92 0 0.01507775 0.000000e+00 0.000000e+00
#> 93 93 0 0.01434240 0.000000e+00 0.000000e+00
#> 94 94 0 0.01364292 0.000000e+00 0.000000e+00
#> 95 95 0 0.01297754 0.000000e+00 0.000000e+00
#> 96 96 0 0.01234462 0.000000e+00 0.000000e+00
#> 97 97 0 0.01174257 0.000000e+00 0.000000e+00
#> 98 98 0 0.01116987 0.000000e+00 0.000000e+00
#> 99 99 0 0.01062511 0.000000e+00 0.000000e+00
#> 100 100 0 0.01010692 0.000000e+00 0.000000e+00