Optimizing Contact Network Topological Parameters of Urban Populations Using the Genetic Algorithm
<p>Cumulative evolution of COVID-19 cases over 35 days in selected cities during GA training. Actual data are depicted in red, and simulation results are shown in blue, with each simulation identified by the network model used and the city’s population. (<b>a</b>) BA, Águas de Santa Bárbara (5931); (<b>b</b>) BA, Bernardino de Campos (10,787); (<b>c</b>) BA, Pirajú (28,574); (<b>d</b>) SW, Santa Cruz do Rio Pardo (46,110); (<b>e</b>) SW, Avaré (87,538); (<b>f</b>) BA, Ourinhos (110,489); (<b>g</b>) SW, Itapetininga (160,150); (<b>h</b>) BA, Presidente Prudente (221,073); (<b>i</b>) BA, Jundiaí (407,016).</p> "> Figure 2
<p>Accumulated COVID-19 case trends over 10 days following the training period in selected cities. Simulations, labeled according to the network model and city population, are compared against actual data: real cases are shown in red and simulated results are shown in blue. (<b>a</b>) BA, Águas de Santa Bárbara (5931); (<b>b</b>) BA, Pirajú (28,574); (<b>c</b>) BA, Bauru (364,225); (<b>d</b>) SW, Boituva (57,292); (<b>e</b>) SW, Bragança Paulista (163,980); (<b>f</b>) BA, Cerqueira César (19,213); (<b>g</b>) SW, Itapetininga (160,150); (<b>h</b>) BA, Jundiaí (407,016); (<b>i</b>) BA, Presidente Prudente (221,073).</p> "> Figure 3
<p>Comparison between clustering coefficient, entropy, and the mean number of edges per node divided by the size of the networks for the data results of both network models considered here.</p> ">
Abstract
:1. Introduction
Variables/Parameters | Papers |
---|---|
Disease rates (contact, recovery, transmission, mortality rates) | [56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] |
Other rates related to the disease transition states (cure, death, phases of a same state) | [56,57,59,60,61,62,64,65,66,67,71] |
Rates related to disease control (vaccination, quarantine, protection, treatment rates, therapies settings) | [56,57,61,62,63,66,72,73] |
Period parameters (latency, infectiousness) | [57,59,62,64,65,66] |
Parameters of statistical models | [69] |
Number of cases, deaths, recovered patients, and susceptible individuals | [64,72,74,75,76] |
Population structure, movement, migration | [62,64,65] |
Initial conditions for simulations | [57,64,65,67] |
2. Methodology
2.1. The Epidemiological Model
2.2. The GA Model
3. Results
Model | Parameter | Description | Value | Reference |
---|---|---|---|---|
SIR | N | Population size | City population | [86] |
, , , | Parameters for creating the individual networks | Optimized from GA | - | |
C | Interaction parameter | Optimized from GA | - | |
Probability of infection | Calculated for each individual per time step | - | ||
Probability of cure | 1/21 | [3,84,85] | ||
Probability of death due to disease | 0.01 | [3,84,85] | ||
Probability of a recovered individual becoming susceptible | 0.00837 | [3,84,85,87] | ||
GA | Size of GA population | 50 | Experimental | |
Gene swap probability in crossover process | 0.3 | Experimental | ||
Elitism | 1 | Experimental | ||
Standard deviation for Gaussian random numbers generation | 0.1 | Experimental | ||
Number of generations | 50 | Experimental |
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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City | Population | Network | C | |||
---|---|---|---|---|---|---|
Águas de Santa Bárbara | 5931 | SW | 11.22 | 0.28 | 112 | 0.358 |
Águas de Santa Bárbara | 5931 | BA | 10.06 | 1.25 | 109 | 0.291 |
Bernardino de Campos | 10,787 | SW | 56.35 | 0.74 | 98 | 0.098 |
Bernardino de Campos | 10,787 | BA | 11.36 | 16.80 | 51 | 0.106 |
Cerqueira César | 19,213 | SW | 127.12 | 0.55 | 139 | 0.088 |
Cerqueira César | 19,213 | BA | 10.01 | 9.11 | 63 | 0.071 |
Piraju | 28,574 | SW | 25.48 | 0.63 | 96 | 0.074 |
Piraju | 28,574 | BA | 17.14 | 1.42 | 134 | 0.130 |
Santa Cruz do Rio Pardo | 46,110 | SW | 28.66 | 0.42 | 172 | 0.080 |
Santa Cruz do Rio Pardo | 46,110 | BA | 19.36 | 5.36 | 70 | 0.155 |
Boituva | 57,292 | SW | 59.70 | 0.80 | 161 | 0.077 |
Boituva | 57,292 | BA | 19.46 | 2.30 | 95 | 0.089 |
Embu-Guaçu | 68,053 | SW | 43.05 | 0.67 | 144 | 0.062 |
Embu-Guaçu | 68,053 | BA | 20.01 | 4.66 | 59 | 0.068 |
Avaré | 87,538 | SW | 12.39 | 0.21 | 98 | 0.052 |
Avaré | 87,538 | BA | 34.35 | 1.93 | 91 | 0.138 |
Assis | 101,381 | SW | 19.78 | 0.28 | 158 | 0.063 |
Assis | 101,381 | BA | 12.13 | 7.09 | 63 | 0.055 |
Ourinhos | 110,489 | SW | 30.54 | 0.44 | 135 | 0.056 |
Ourinhos | 110,489 | BA | 40.83 | 7.76 | 52 | 0.068 |
Atibaia | 139,606 | SW | 69.46 | 0.72 | 164 | 0.049 |
Atibaia | 139,606 | BA | 49.78 | 11.94 | 62 | 0.054 |
Itapetininga | 160,150 | SW | 21.50 | 0.01 | 114 | 0.067 |
Itapetininga | 160,150 | BA | 109.12 | 10.22 | 52 | 0.052 |
Bragança Paulista | 163,980 | SW | 52.44 | 0.79 | 136 | 0.054 |
Bragança Paulista | 163,980 | BA | 10.21 | 7.90 | 56 | 0.065 |
Presidente Prudente | 221,073 | SW | 23.46 | 0.33 | 180 | 0.047 |
Presidente Prudente | 221,073 | BA | 25.94 | 6.15 | 62 | 0.078 |
Embu das Artes | 270,790 | SW | 107.48 | 0.46 | 117 | 0.048 |
Embu das Artes | 270,790 | BA | 141.91 | 1.36 | 128 | 0.055 |
Bauru | 364,225 | SW | 69.39 | 0.02 | 184 | 0.055 |
Bauru | 364,225 | BA | 13.72 | 9.91 | 70 | 0.050 |
Jundiaí | 407,016 | SW | 33.36 | 0.48 | 199 | 0.038 |
Jundiaí | 407,016 | BA | 46.42 | 1.38 | 148 | 0.102 |
Mogi das Cruzes | 432,905 | SW | 44.84 | 0.49 | 106 | 0.049 |
Mogi das Cruzes | 432,905 | BA | 11.56 | 12.37 | 38 | 0.059 |
City | Population | Network | / | / | C | |
---|---|---|---|---|---|---|
Águas de Santa Bárbara | 5931 | SW | 11.22 | 0.28 | 112 | 0.254 |
Águas de Santa Bárbara | 5931 | BA | 10.06 | 1.25 | 109 | 0.394 |
Bernardino de Campos | 10,787 | SW | 56.35 | 0.74 | 98 | 0.290 |
Bernardino de Campos | 10,787 | BA | 11.36 | 16.80 | 51 | 0.374 |
Cerqueira César | 19,213 | SW | 127.12 | 0.55 | 139 | 0.090 |
Cerqueira César | 19,213 | BA | 10.01 | 9.11 | 63 | 0.156 |
Piraju | 28,574 | SW | 25.48 | 0.63 | 96 | 0.075 |
Piraju | 28,574 | BA | 17.14 | 1.42 | 134 | 0.876 |
Santa Cruz do Rio Pardo | 46,110 | SW | 28.66 | 0.42 | 172 | 0.173 |
Santa Cruz do Rio Pardo | 46,110 | BA | 19.36 | 5.36 | 70 | 0.172 |
Boituva | 57,292 | SW | 59.70 | 0.80 | 161 | 0.069 |
Boituva | 57,292 | BA | 19.46 | 2.30 | 95 | 0.295 |
Embu-Guaçu | 68,053 | SW | 43.05 | 0.67 | 144 | 0.113 |
Embu-Guaçu | 68,053 | BA | 20.01 | 4.66 | 59 | 0.153 |
Avaré | 87,538 | SW | 12.39 | 0.21 | 98 | 0.129 |
Avaré | 87,538 | BA | 34.35 | 1.93 | 91 | 0.377 |
Assis | 101,381 | SW | 19.78 | 0.28 | 158 | 0.077 |
Assis | 101,381 | BA | 12.13 | 7.09 | 63 | 0.103 |
Ourinhos | 110,489 | SW | 30.54 | 0.44 | 135 | 0.146 |
Ourinhos | 110,489 | BA | 40.83 | 7.76 | 52 | 0.238 |
Atibaia | 139,606 | SW | 69.46 | 0.72 | 164 | 0.017 |
Atibaia | 139,606 | BA | 49.78 | 11.94 | 62 | 0.077 |
Itapetininga | 160,150 | SW | 21.50 | 0.01 | 114 | 0.123 |
Itapetininga | 160,150 | BA | 109.12 | 10.22 | 52 | 0.098 |
Bragança Paulista | 163,980 | SW | 52.44 | 0.79 | 136 | 0.118 |
Bragança Paulista | 163,980 | BA | 10.21 | 7.90 | 56 | 0.084 |
Presidente Prudente | 221,073 | SW | 23.46 | 0.33 | 180 | 0.039 |
Presidente Prudente | 221,073 | BA | 25.94 | 6.15 | 62 | 0.167 |
Embu das Artes | 270,790 | SW | 107.48 | 0.46 | 117 | 0.125 |
Embu das Artes | 270,790 | BA | 141.91 | 1.36 | 128 | 0.213 |
Bauru | 364,225 | SW | 69.39 | 0.02 | 184 | 0.112 |
Bauru | 364,225 | BA | 13.72 | 9.91 | 70 | 0.109 |
Jundiaí | 407,016 | SW | 33.36 | 0.48 | 199 | 0.025 |
Jundiaí | 407,016 | BA | 46.42 | 1.38 | 148 | 0.461 |
Mogi das Cruzes | 432,905 | SW | 44.84 | 0.49 | 106 | 0.157 |
Mogi das Cruzes | 432,905 | BA | 11.56 | 12.37 | 38 | 0.227 |
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Sergio, A.R.; Schimit, P.H.T. Optimizing Contact Network Topological Parameters of Urban Populations Using the Genetic Algorithm. Entropy 2024, 26, 661. https://doi.org/10.3390/e26080661
Sergio AR, Schimit PHT. Optimizing Contact Network Topological Parameters of Urban Populations Using the Genetic Algorithm. Entropy. 2024; 26(8):661. https://doi.org/10.3390/e26080661
Chicago/Turabian StyleSergio, Abimael R., and Pedro H. T. Schimit. 2024. "Optimizing Contact Network Topological Parameters of Urban Populations Using the Genetic Algorithm" Entropy 26, no. 8: 661. https://doi.org/10.3390/e26080661