A Fuzzy Logic Inference Model for the Evaluation of the Effect of Extrinsic Factors on the Transmission of Infectious Diseases
Abstract
:1. Introduction
- A fuzzy logic model that can estimate the transmission and death rates of COVID-19 based on five factors: temperature, population density, life expectancy, smoking index, and outsiders’ effect.
- A fuzzy inference system (FIS) that can apply the fuzzy logic model to any country or region, using data from 95 top-affected countries as a sample.
- An analysis of the significance and limitations of the fuzzy logic model and the FIS.
- Providing a flexible and intuitive way to model and analyse the factors of infectious disease transmission and to estimate the infection risk in different settings.
- Identifying the most influential factors and their interactions that affect the spread and severity of COVID-19.
- Suggesting effective prevention and control strategies based on the estimated transmission and death rates and the implications of the fuzzy logic model.
2. Data Collection, Processing, and Analysis
2.1. Data Collection
2.2. Data Processing and Analysis
2.2.1. Data Processing
2.2.2. Data Analysis
3. Creating Input Weights for Fuzzy Logic Based on Statistical Results and Fuzzy Inference System (FIS)
4. Fuzzy Inference System (FIS) to Find the Chance of Transmission of Some Infectious Agents in a Region/State
5. Results Analysis
6. Discussion
7. Conclusions
Future Work
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
M | Mean |
V | Variance |
O | Observation |
PV | Pooled Variance |
HMD | Hypothesised Mean Difference |
df | Degrees of Freedom |
tS | t Stat |
P1 | p(T ≤ t) one-tail |
tC1 | t Critical one-tail |
P2 | p(T ≤ t) two-tail |
tC2 | t Critical two-tail |
Appendix A
Sl. No. | Country | Affected Cases | Total Cases/1 M | Death | Density (per sqkm) | Life Expectancy | Temperature (°C) | Smoking | Global Export Sharing |
---|---|---|---|---|---|---|---|---|---|
1 | USA | 2,781,085 | 9545 | 130,813 | 35 | 79.11 | 27 | 0.137 | 8.6 |
2 | Brazil | 1,456,969 | 8073 | 60,813 | 25 | 76.57 | 24 | 0.153 | 1.9 |
12 | Russia | 661,165 | 4847 | 9683 | 9 | 72.99 | 22 | 0.409 | 2.3 |
8 | India | 606,907 | 559 | 17,860 | 420 | 70.42 | 39 | 0.1115 | 1.7 |
3 | UK | 313,483 | 4227 | 43,906 | 279 | 78.46 | 10 | 0.147 | 2.5 |
7 | Spain | 296,739 | 6408 | 28,363 | 92 | 83.99 | 32 | 0.292 | 1.7 |
10 | Peru | 288,477 | 9488 | 9860 | 26 | 77.44 | 16 | 0.054 | 0.2 |
16 | Chile | 282,043 | 15,852 | 5753 | 25 | 80.74 | 3 | 0.38 | 0.4 |
4 | Italy | 240,760 | 4005 | 34,788 | 201 | 84.01 | 33 | 0.24 | 2.8 |
9 | Iran | 232,863 | 2981 | 11,106 | 51 | 77.33 | 33 | 0.111 | 0.5 |
6 | Mexico | 231,770 | 2132 | 28,510 | 66 | 75.41 | 16 | 0.137 | 2.3 |
21 | Pakistan | 217,809 | 1090 | 4473 | 250 | 67.79 | 31 | 0.2245 | 0.1 |
18 | Turkey | 201,098 | 2477 | 5150 | 108 | 78.45 | 31 | 0.2595 | 0.9 |
29 | Saudi Arabia | 197,608 | 6322 | 1752 | 16 | 68.87 | 26 | 0.154 | 1.5 |
13 | Germany | 196,372 | 2373 | 9061 | 235 | 81.88 | 24 | 0.3035 | 8.1 |
5 | France | 165,719 | 2596 | 29,861 | 118 | 83.13 | 21 | 0.277 | 3 |
25 | South Africa | 159,333 | 3787 | 2749 | 49 | 83.5 | 21 | 0.1895 | 0.5 |
28 | Bangladesh | 153,277 | 1065 | 1926 | 1116 | 73.57 | 33 | 0.2025 | 0.2 |
14 | Canada | 104,271 | 2820 | 8615 | 4 | 82.96 | 26 | 0.1495 | 2.3 |
22 | Colombia | 102,009 | 2528 | 3470 | 45 | 77.87 | 14 | 0.111 | 0.2 |
73 | Qatar | 97,897 | 36,168 | 118 | 249 | 80.73 | 36 | 0.206 | 0.4 |
19 | China | 83,537 | 58 | 4634 | 148 | 77.47 | 27 | 0.247 | 12.9 |
23 | Egypt | 69,814 | 765 | 3034 | 102 | 72.54 | 36 | 0.251 | 0 |
17 | Sweden | 69,692 | 7312 | 5370 | 22 | 83.33 | 17 | 0.206 | 0.9 |
34 | Argentina | 67,197 | 1925 | 1351 | 16 | 77.17 | 8 | 0.2395 | 0.3 |
52 | Belarus | 62,698 | 6797 | 405 | 46 | 75.2 | 26 | 0.284 | 0.2 |
11 | Belgium | 61,598 | 5367 | 9761 | 380 | 82.17 | 20 | 0.2325 | 2.4 |
24 | Indonesia | 59,394 | 259 | 2987 | 144 | 72.32 | 27 | 0.399 | 0.9 |
20 | Ecuador | 58,257 | 3584 | 4576 | 64 | 77.71 | 9 | 0.0865 | 0.1 |
26 | Iraq | 51,524 | 1676 | 2050 | 92 | 71.08 | 44 | 0.31 | 0.5 |
15 | Netherlands | 50,335 | 2961 | 6113 | 409 | 82.78 | 19 | 0.2505 | 3 |
57 | UAE | 49,069 | 5416 | 316 | 118 | 72.5 | 28 | 0.24 | 1.6 |
53 | Kuwait | 47,859 | 12,370 | 359 | 240 | 75.85 | 43 | 0.225 | 0.4 |
37 | Ukraine | 45,887 | 1171 | 1185 | 72 | 81.77 | 31 | 0.317 | 0.2 |
92 | Singapore | 44,310 | 7763 | 26 | 8240 | 58.34 | 29 | 0.165 | 2.1 |
68 | Kazakhstan | 42,574 | 2823 | 188 | 7 | 73.9 | 21 | 0.266 | 0.3 |
69 | Oman | 42,555 | 10,126 | 188 | 16 | 78.58 | 33 | 0.11 | 0.2 |
32 | Portugal | 42,454 | 4400 | 1579 | 111 | 82.65 | 24 | 0.226 | 0.4 |
35 | Philippines | 38,805 | 472 | 1274 | 320 | 71.66 | 30 | 0.2575 | 0.3 |
33 | Poland | 35,146 | 976 | 1492 | 121 | 79.27 | 26 | 0.2805 | 1.4 |
44 | Panama | 34,463 | 9558 | 645 | 57 | 73.74 | 26 | 0.066 | 0 |
36 | Bolivia | 34,227 | 3681 | 1201 | 11 | 72.35 | 22 | 0.238 | 0 |
42 | Dominican Republic | 33,387 | 3649 | 754 | 223 | 74.65 | 26 | 0.141 | 0 |
41 | Afghanistan | 32,022 | 871 | 807 | 60 | 65.98 | 20 | 0.352 | 0 |
27 | Switzerland | 31,967 | 3765 | 1965 | 210 | 84.25 | 23 | 0.233 | 1.6 |
31 | Romania | 27,746 | 1601 | 1687 | 81 | 76.5 | 33 | 0.298 | 0.4 |
80 | Bahrain | 27,414 | 18,174 | 93 | 2224 | 77.73 | 36 | 0.282 | 0 |
51 | Armenia | 26,658 | 10,240 | 459 | 100 | 75.55 | 26 | 0.269 | 0 |
46 | Nigeria | 26,484 | 147 | 603 | 223 | 55.75 | 21 | 0.0925 | 0.3 |
56 | Israel | 26,452 | 3691 | 324 | 417 | 83.49 | 30 | 0.3025 | 0.3 |
30 | Ireland | 25,477 | 5172 | 1738 | 70 | 82.81 | 17 | 0.2215 | 0.9 |
50 | Honduras | 20,262 | 2622 | 542 | 88 | 75.87 | 24 | 0.177 | 0 |
40 | Guatemala | 19,011 | 1418 | 817 | 165 | 75.05 | 18 | 0.239 | 0 |
38 | Japan | 18,723 | 160 | 974 | 335 | 85.03 | 25 | 0.2215 | 3.8 |
74 | Ghana | 18,134 | 734 | 117 | 130 | 64.94 | 28 | 0.0675 | 0.1 |
64 | Azerbaijan | 18,112 | 2161 | 220 | 117 | 73.33 | 26 | 0.2345 | 0 |
43 | Austria | 17,941 | 2055 | 705 | 107 | 82.05 | 28 | 0.3515 | 0.9 |
49 | Moldova | 16,898 | 4579 | 549 | 119 | 72.3 | 33 | 0.2555 | 0 |
59 | Serbia | 15,195 | 1955 | 287 | 99 | 84.07 | 32 | 0.4165 | 0.1 |
90 | Nepal | 14,519 | 567 | 31 | 198 | 71.74 | 25 | 0.241 | 0 |
39 | Algeria | 14,272 | 396 | 920 | 18 | 77.5 | 28 | 0.156 | 0 |
60 | S. Korea | 12,904 | 259 | 282 | 512 | 75.69 | 12 | 0.45 | 3.1 |
63 | Morocco | 12,854 | 405 | 228 | 83 | 77.43 | 24 | 0.234 | 0.2 |
45 | Denmark | 12,815 | 2230 | 606 | 134 | 81.4 | 20 | 0.17 | 0.6 |
58 | Cameroon | 12,592 | 562 | 313 | 56 | 60.32 | 28 | 0.2235 | 0 |
54 | Czechia | 12,046 | 1197 | 349 | 136 | 79.85 | 21 | 0.383 | 0 |
82 | Ivory Coast | 9702 | 436 | 68 | 82 | 57.02 | 26 | 0.237 | 0.1 |
47 | Sudan | 9573 | 230 | 602 | 23 | 66.09 | 41 | 0.203 | 0 |
91 | Uzbekistan | 8996 | 336 | 27 | 75 | 72.04 | 30 | 0.131 | 0.1 |
61 | Norway | 8902 | 1651 | 251 | 17 | 82.94 | 13 | 0.2225 | 0.6 |
72 | Malaysia | 8643 | 268 | 121 | 98 | 76.65 | 30 | 0.222 | 1.3 |
78 | Australia | 8001 | 355 | 104 | 3 | 83.94 | 5 | 0.149 | 1.3 |
55 | Finland | 7241 | 1313 | 328 | 16 | 82.48 | 19 | 0.2085 | 0.4 |
71 | Senegal | 7054 | 465 | 121 | 85 | 76.47 | 29 | 0.1205 | 0 |
66 | El Salvador | 7000 | 1363 | 191 | 308 | 74.06 | 22 | 0.17 | 0 |
70 | Kenya | 6941 | 159 | 149 | 93 | 67.47 | 22 | 0.1335 | 0 |
83 | Kyrgyzstan | 6261 | 1356 | 66 | 33 | 71.95 | 28 | 0.27 | 0 |
86 | Venezuela | 6062 | 282 | 54 | 31 | 72.34 | 23 | 0.167 | 0.2 |
77 | Haiti | 6040 | 569 | 107 | 411 | 64.99 | 28 | 0.123 | 0 |
87 | Tajikistan | 6005 | 667 | 52 | 67 | 71.76 | 33 | 0.17 | 0 |
79 | Ethiopia | 5846 | 59 | 103 | 104 | 67.81 | 20 | 0.047 | 0 |
88 | Gabon | 5513 | 2637 | 42 | 8 | 67.03 | 28 | 0.147 | 0 |
89 | Guinea | 5404 | 434 | 33 | 53 | 62.64 | 26 | 0.069 | 0 |
62 | Bulgaria | 5154 | 913 | 232 | 63 | 75.49 | 31 | 0.353 | 0.2 |
67 | Bosnia and Herzegovina | 4788 | 1855 | 189 | 64 | 77.93 | 18 | 0.386 | 0 |
85 | Djibouti | 4704 | 4947 | 55 | 43 | 67.87 | 37 | 0.245 | 0 |
76 | Luxembourg | 4345 | 7426 | 110 | 242 | 82.79 | 20 | 0.236 | 0.1 |
94 | French Guiana | 4268 | 18,272 | 16 | 4 | 80.53 | 23 | 0.356 | 0 |
48 | Hungary | 4166 | 437 | 587 | 104 | 77.31 | 29 | 0.284 | 0.6 |
93 | Costa Rica | 3753 | 1145 | 17 | 100 | 80.94 | 25 | 0.134 | 0.1 |
65 | Greece | 3432 | 348 | 192 | 79 | 82.8 | 34 | 0.4265 | 0.2 |
84 | Thailand | 3179 | 46 | 58 | 136 | 77.74 | 28 | 0.2185 | 1.3 |
95 | Palestine | 2978 | 1023 | 8 | 820 | 79.1 | 20 | 0.22 | 0 |
81 | Somalia | 2924 | 190 | 90 | 25 | 64.88 | 29 | 0.24 | 0 |
75 | Croatia | 2912 | 832 | 110 | 73 | 79.02 | 29 | 0.3645 | 0.1 |
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Death Rate of Low Life Expectancy Countries | Death Rate of High Life Expectancy Countries | |
---|---|---|
Mean | 0.023584419 | 0.050352366 |
Variance | 0.000448951 | 0.001959616 |
Observations | 48 | 47 |
Pooled Variance | 0.001196161 | |
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | −3.771620183 | |
pt) one-tail | 0.000142487 | |
t Critical one-tail | 1.661403674 | |
p t) two-tail | 0.000284975 | |
t Critical two-tail | 1.985801814 |
Death Rates of Low-Smoking-Index Countries | Death Rate of High-Smoking-Index Countries | |
---|---|---|
Mean | 0.031749961 | 0.042013 |
Variance | 0.000926522 | 0.001787 |
Observations | 48 | 47 |
Pooled Variance | 0.001352228 | |
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | −1.360074066 | |
p(T ≤ t) one-tail | 0.088547179 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.177094358 | |
t Critical two-tail | 1.985801814 |
Affected Cases in Low Density | Affected Cases in High Density | |
---|---|---|
Mean | 157,615.1458 | 67,599.87234 |
Variance | 11,693,419,305 | |
Observations | 48 | 47 |
Pooled Variance | ||
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | 1.330035917 | |
p(T ≤ t) one-tail | 0.093379558 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.186759117 | |
t Critical two-tail | 1.985801814 |
Total Cases/1 M in Low Density | Total Cases/1 M in High Density | |
---|---|---|
Mean | 3595.5 | 3507.297872 |
Variance | 16,493,772.38 | 36,211,163.34 |
Observations | 48 | 47 |
Pooled Variance | 26,246,460.39 | |
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | 0.083897967 | |
p(T ≤ t) one-tail | 0.466658944 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.933317888 | |
t Critical two-tail | 1.985801814 |
Affected Cases in Low Outsiders’ Effect | Affected Cases in High Outsiders’ Effect | |
---|---|---|
Mean | 31,275.59 | 200,222.11 |
Variance | 2,965,654,152 | |
Observations | 49 | 46 |
Pooled Variance | ||
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | −2.557220227 | |
p(T ≤ t) one-tail | 0.006084732 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.012169463 | |
t Critical two-tail | 1.985801814 |
Total Cases/1 M for Low Indicators Value | Total Cases/1 M for High Indicators Value | |
---|---|---|
Mean | 2965.86 | 4176.09 |
Variance | 17,914,825.92 | 34,365,400.48 |
Observations | 49 | 46 |
Pooled Variance | 25,874,781.35 | |
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | −1.158896514 | |
p(T ≤ t) one-tail | 0.124732725 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.249465449 | |
t Critical two-tail | 1.985801814 |
Affected Cases of Low Life Expectancy | Affected Cases of High Life Expectancy | |
---|---|---|
Mean | 92,724.85 | 133,870.81 |
Variance | 57,743,028,575 | |
Observations | 48 | 47 |
Pooled Variance | ||
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | −0.603435983 | |
p(T ≤ t) one-tail | 0.273843824 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.547687647 | |
t Critical two-tail | 1.985801814 |
Effected Cases for Low Temperature | Effected Cases for High Temperature | |
---|---|---|
Mean | 103,716.69 | 122,645.11 |
Variance | 54,089,839,644 | |
Observations | 48 | 47 |
Pooled Variance | ||
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | −0.277171863 | |
p(T ≤ t) one-tail | 0.391131648 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.782263295 | |
t Critical two-tail | 1.985801814 |
Affected Cases in Low-Smoking Countries | Affected Cases in High-Smoking Countries | |
---|---|---|
Mean | 157,971.35 | 67,236.09 |
Variance | 13,200,648,298 | |
Observations | 48 | 47 |
Pooled Variance | ||
Hypothesised Mean Difference | 0 | |
Degrees of Freedom | 93 | |
t Stat | 1.340879173 | |
p(T ≤ t) one-tail | 0.091612808 | |
t Critical one-tail | 1.661403674 | |
p(T ≤ t) two-tail | 0.183225616 | |
t Critical two-tail | 1.985801814 |
Influencing Factors | 1 − p-Value | Weight Percentages |
---|---|---|
Outsiders’ effect | 0.987831 | 46 |
Life expectancy index | 0.452312 | 21 |
Temperature | 0.217737 | 10 |
Others | 0.5 | 23 |
Outsiders’ Index | Life Expectancy | Temperature | Others | Chances of Transmission | |
---|---|---|---|---|---|
low | 5 | 2 | 1 | 2 | [10,12.5] |
medium | 7.5 | 3 | 1.5 | 3 | (12.5, 16.5) |
high | 10 | 4 | 2 | 4 | [16.5,20] |
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Kalampakas, A.; Samanta, S.; Bera, J.; Das, K.C. A Fuzzy Logic Inference Model for the Evaluation of the Effect of Extrinsic Factors on the Transmission of Infectious Diseases. Mathematics 2024, 12, 648. https://doi.org/10.3390/math12050648
Kalampakas A, Samanta S, Bera J, Das KC. A Fuzzy Logic Inference Model for the Evaluation of the Effect of Extrinsic Factors on the Transmission of Infectious Diseases. Mathematics. 2024; 12(5):648. https://doi.org/10.3390/math12050648
Chicago/Turabian StyleKalampakas, Antonios, Sovan Samanta, Jayanta Bera, and Kinkar Chandra Das. 2024. "A Fuzzy Logic Inference Model for the Evaluation of the Effect of Extrinsic Factors on the Transmission of Infectious Diseases" Mathematics 12, no. 5: 648. https://doi.org/10.3390/math12050648
APA StyleKalampakas, A., Samanta, S., Bera, J., & Das, K. C. (2024). A Fuzzy Logic Inference Model for the Evaluation of the Effect of Extrinsic Factors on the Transmission of Infectious Diseases. Mathematics, 12(5), 648. https://doi.org/10.3390/math12050648