Fractional Stochastic Differential Equation Approach for Spreading of Diseases
The nonlinear fractional stochastic differential equation approach with Hurst parameter <i>H</i> within interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/5/719 |
| _version_ | 1797499999777456128 |
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| author | Leonardo dos Santos Lima |
| author_facet | Leonardo dos Santos Lima |
| author_sort | Leonardo dos Santos Lima |
| collection | DOAJ |
| description | The nonlinear fractional stochastic differential equation approach with Hurst parameter <i>H</i> within interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> to study the time evolution of the number of those infected by the coronavirus in countries where the number of cases is large as Brazil is studied. The rises and falls of novel cases daily or the fluctuations in the official data are treated as a random term in the stochastic differential equation for the fractional Brownian motion. The projection of novel cases in the future is treated as quadratic mean deviation in the official data of novel cases daily since the beginning of the pandemic up to the present. Moreover, the rescaled range analysis (RS) is employed to determine the Hurst index for the time series of novel cases and some statistical tests are performed with the aim to determine the shape of the probability density of novel cases in the future. |
| first_indexed | 2024-03-10T03:55:32Z |
| format | Article |
| id | doaj.art-d558b84a8a0c489296e703d772aceb88 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T03:55:32Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d558b84a8a0c489296e703d772aceb882023-11-23T10:56:10ZengMDPI AGEntropy1099-43002022-05-0124571910.3390/e24050719Fractional Stochastic Differential Equation Approach for Spreading of DiseasesLeonardo dos Santos Lima0Federal Center for Technological Education of Minas Gerais, Belo Horizonte 30510-000, MG, BrazilThe nonlinear fractional stochastic differential equation approach with Hurst parameter <i>H</i> within interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> to study the time evolution of the number of those infected by the coronavirus in countries where the number of cases is large as Brazil is studied. The rises and falls of novel cases daily or the fluctuations in the official data are treated as a random term in the stochastic differential equation for the fractional Brownian motion. The projection of novel cases in the future is treated as quadratic mean deviation in the official data of novel cases daily since the beginning of the pandemic up to the present. Moreover, the rescaled range analysis (RS) is employed to determine the Hurst index for the time series of novel cases and some statistical tests are performed with the aim to determine the shape of the probability density of novel cases in the future.https://www.mdpi.com/1099-4300/24/5/719fractional Brownian motionspreading |
| spellingShingle | Leonardo dos Santos Lima Fractional Stochastic Differential Equation Approach for Spreading of Diseases Entropy fractional Brownian motion spreading |
| title | Fractional Stochastic Differential Equation Approach for Spreading of Diseases |
| title_full | Fractional Stochastic Differential Equation Approach for Spreading of Diseases |
| title_fullStr | Fractional Stochastic Differential Equation Approach for Spreading of Diseases |
| title_full_unstemmed | Fractional Stochastic Differential Equation Approach for Spreading of Diseases |
| title_short | Fractional Stochastic Differential Equation Approach for Spreading of Diseases |
| title_sort | fractional stochastic differential equation approach for spreading of diseases |
| topic | fractional Brownian motion spreading |
| url | https://www.mdpi.com/1099-4300/24/5/719 |
| work_keys_str_mv | AT leonardodossantoslima fractionalstochasticdifferentialequationapproachforspreadingofdiseases |