Week | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Cases | 4 | 1 | 0 | 1 | 2 | 5 | 12 | 17 | 22 | 16 | 15 | 53 | 55 | 45 |
Week | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 |
Cases | 84 | 102 | 127 | 261 | 210 | 155 | 109 | 116 | 125 | 76 | 52 | 19 | 15 | 1 |
Compartment models with classical derivatives have diverse applications and attracted a lot of interest among scientists. To model the dynamical behavior of the particles that existed in the system for a long period of time with little chance to be removed, a power-law waiting time technique was introduced in the most recent work of Angstmann et al. [
Citation: |
Table 1. Data provided by the Secretaria be Salud Distrital de Bogotá D.C. First row corresponds to the week number of year 2009. Second row presents the number of infectious individuals by AH1N1/09 detected in each week
Week | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Cases | 4 | 1 | 0 | 1 | 2 | 5 | 12 | 17 | 22 | 16 | 15 | 53 | 55 | 45 |
Week | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 |
Cases | 84 | 102 | 127 | 261 | 210 | 155 | 109 | 116 | 125 | 76 | 52 | 19 | 15 | 1 |
Table 2. Values of various parameters and initial conditions
Model | $ \mu $ | $ \mu_1 $ | $ \beta $ | $ \Omega_2 $ | $ \Omega_3 $ | $ \alpha_2 $ | $ \alpha_3 $ |
cSEIR | 5.038e+01 | 1.0e-08 | 2.89e-03 | 2.25e-01 | 1.373e+00 | 1 | 1 |
frSEIR | 5.038e+01 | 1.0e-08 | 2.89e-03 | 2.25e-01 | 1.373e+00 | 0.6 | 0.88 |
tfrSEIR | 5.038e+01 | 1.0e-08 | 2.89e-03 | 2.25e-01 | 1.373e+00 | 0.6 | 0.88 |
Model | $ \lambda_2 $ | $ \lambda_3 $ | $ S_0 $ | $ E_0 $ | $ I_0 $ | $ R_0 $ | |
cSEIR | 0 | 0 | 100 | 0 | 1 | 0 | |
frSEIR | 0 | 0 | 100 | 0 | 1 | 0 | |
tfrSEIR | 0.015 | 0.09 | 100 | 0 | 1 | 0 |
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Flux flow of tempered fractional SEIR model
The endemic steady state plotted as the functions of
The endemic steady state plotted as the functions of
Plots of Infected
Plots of Infected
The variation of Infected
The variation of Infected
The variation of Infected
Comparing with the real data of confirmed cases of pandemic AH1N1/09 influenza from Bogotá D.C.
Numerical solution of the tfrSEIR model adjusted to real data of people infected with influenza AH1N1/09 in Bogotá D.C.