{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T05:03:59Z","timestamp":1764047039377,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,5]],"date-time":"2022-01-05T00:00:00Z","timestamp":1641340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>We analyze the empirical series of malaria incidence, using the concepts of autocorrelation, Hurst exponent and Shannon entropy with the aim of uncovering hidden variables in those series. From the simulations of an agent model for malaria spreading, we first derive models of the malaria incidence, the Hurst exponent and the entropy as functions of gametocytemia, measuring the infectious power of a mosquito to a human host. Second, upon estimating the values of three observables\u2014incidence, Hurst exponent and entropy\u2014from the data set of different malaria empirical series we predict a value of the gametocytemia for each observable. Finally, we show that the independent predictions show considerable consistency with only a few exceptions which are discussed in further detail.<\/jats:p>","DOI":"10.3390\/app12010496","type":"journal-article","created":{"date-parts":[[2022,1,5]],"date-time":"2022-01-05T20:42:16Z","timestamp":1641415336000},"page":"496","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1665-1858","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Sequeira","sequence":"first","affiliation":[{"name":"ISTAR-IUL, Instituto Universit\u00e1rio de Lisboa (ISCTE-IUL), Av. das For\u00e7as Armadas, 1649-026 Lisboa, Portugal"},{"name":"Hospital Santa Cruz, Av. Prof. Dr. Reinaldo dos Santos, 2790-134 Carnaxide, Portugal"}]},{"given":"Jorge","family":"Lou\u00e7\u00e3","sequence":"additional","affiliation":[{"name":"ISTAR-IUL, Instituto Universit\u00e1rio de Lisboa (ISCTE-IUL), Av. das For\u00e7as Armadas, 1649-026 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6562-5325","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Mendes","sequence":"additional","affiliation":[{"name":"Instituto de Medicina Molecular Jo\u00e3o Lobo Antunes, Faculdade de Medicina, Universidade de Lisboa, Av. Prof. Egas Moniz, 1649-028 Lisboa, Portugal"}]},{"given":"Pedro G.","family":"Lind","sequence":"additional","affiliation":[{"name":"Department of Computer Science, OsloMet\u2013Oslo Metropolitan University, N-0130 Oslo, Norway"},{"name":"Artificial Intelligence Lab, Oslo Metropolitan University, N-0166 Oslo, Norway"},{"name":"NordSTAR\u2014Nordic Center for Sustainable and Trustworthy AI Research, Pilestredet 52, N-0166 Oslo, Norway"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,5]]},"reference":[{"key":"ref_1","first-page":"14","article-title":"The death of Alexander the Great","volume":"7","author":"Retief","year":"2005","journal-title":"Acta Theol. Suppl."},{"key":"ref_2","unstructured":"World Health Organization (2020). World Malaria Report, World Health Organization. Available online: https:\/\/www.who.int."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"110030","DOI":"10.1016\/j.jtbi.2019.110030","article-title":"Transition from endemic behavior to eradication of malaria due to combined drug therapies: An agent-model approach","volume":"484","author":"Sequeira","year":"2020","journal-title":"J. Theor. Biol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sequeira, J., Lou\u00e7\u00e3, J., Mendes, A.M., and Lind, P.G. (2020). A Model for Assessing the Quantitative Effects of Heterogeneous Affinity in Malaria Transmission along with Ivermectin Mass Administration. Appl. Sci., 10.","DOI":"10.3390\/app10238696"},{"key":"ref_5","unstructured":"Box, G.E.P., and Jenkins, G.M. (1970). Time Series Analysis: Forecasting and Control, Holden Day."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1061\/TACEAT.0006518","article-title":"The Long-Term Storage Capacity of Reservoir","volume":"116","author":"Hurst","year":"1951","journal-title":"Trans. Am. Soc. Civ. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.physa.2004.06.130","article-title":"Time-dependent Hurst exponent in financial time series","volume":"344","author":"Carbone","year":"2004","journal-title":"Physica A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/1010093","article-title":"Fractional Brownian motions, fractional noises and applications","volume":"10","author":"Mandelbrot","year":"1968","journal-title":"SIAM Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1029\/WR004i005p00909","article-title":"Noah, Joseph and operational hydrology","volume":"4","author":"Mandelbrot","year":"1968","journal-title":"Water Resour. Res."},{"key":"ref_10","unstructured":"Mandelbrot, B.B. (1982). The Fractal Geometry of Nature, W.H. Freeman Editors."},{"key":"ref_11","first-page":"327","article-title":"Use of time-series analysis in infectious disease surveillance","volume":"76","author":"Allard","year":"1998","journal-title":"Bull. World Health Organ."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Permanasari, A.E., Hidayah, I., and Bustoni, I.A. (2013, January 7\u20138). SARIMA (Seasonal ARIMA) implementation on time series to forecast the number of Malaria incidence. Proceedings of the International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia.","DOI":"10.1109\/ICITEED.2013.6676239"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6834","DOI":"10.1038\/srep06834","article-title":"Can we predict the unpredictable?","volume":"4","author":"Golestani","year":"2014","journal-title":"Sci. Rep."},{"key":"ref_14","first-page":"482851","article-title":"Forecasting malaria cases using climatic factors in delhi, India: A time series analysis","volume":"2014","author":"Kumar","year":"2014","journal-title":"Malar. Res. Treat."},{"key":"ref_15","first-page":"7","article-title":"Malaria Disease Distribution in Sudan Using Time Series ARIMA Model","volume":"4","author":"Musa","year":"2015","journal-title":"Int. J. Public Health Sci."},{"key":"ref_16","first-page":"220","article-title":"Times Series Analysis Of Malaria Cases In Ejisu- Juaben Municipality","volume":"4","author":"Appiah","year":"2015","journal-title":"Int. J. Sci. Technol. Res."},{"key":"ref_17","first-page":"1022","article-title":"Application of Different Time Series Models on Epidemiological Data\u2014Comparison and Predictions for Malaria Prevalence","volume":"2","author":"Sarkar","year":"2017","journal-title":"SM J. Biom. Biostat."},{"key":"ref_18","first-page":"1","article-title":"Modelling the influence of climate on malaria occurrence in Chimoio Municipality, Mozambique","volume":"10","author":"Mendes","year":"2017","journal-title":"Parasites Vectors"},{"key":"ref_19","unstructured":"Chatfield, C. (2006). The Analysis of Time Series, Chapman & Hall\/CRC."},{"key":"ref_20","unstructured":"Shumway, R.H., and Stoffer, D.S. (2006). Time Series Analysis and Its Applications, Springer."},{"key":"ref_21","first-page":"43","article-title":"Time Series Analysis of Malaria Cases in Kasena Nankana Municipality","volume":"7","author":"Alhassan","year":"2017","journal-title":"Int. J. Stat. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Aregawi, M., Lynch, M., Bekele, W., Kebede, H., Jima, D., Taffese, H.S., Yenehun, M.A., Lilay, A., Williams, R., and Thomson, M. (2014). Time series analysis of trends in malaria cases and deaths at hospitals and the effect of antimalarial interventions, 2001\u20132011, Ethiopia. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0106359"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"70","DOI":"10.11648\/j.ajtas.20160502.15","article-title":"Malaria Distribution in Kucha District of Gamo Gofa Zone, Ethiopia: A Time Series Approach","volume":"5","author":"Bedane","year":"2016","journal-title":"Am. J. Theor. Appl. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1186\/1475-2875-6-129","article-title":"Forecasting malaria incidence based on monthly case reports and environmental factors in Karuzi, Burundi, 1997\u20132003","volume":"6","author":"Otero","year":"2007","journal-title":"Malar. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1186\/1475-2875-11-389","article-title":"Morbidity and mortality due to malaria in Est Mono district, Togo, from 2005 to 2010: A times series analysis","volume":"11","author":"Landoh","year":"2012","journal-title":"Malar. J."},{"key":"ref_26","first-page":"2","article-title":"Prediction of Monthly Malaria Incidence in Uganda and its Implications for Preventive Interventions","volume":"6","author":"Muwanika","year":"2017","journal-title":"J. Med. Diagn. Meth."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Okech, B.A., Mwobobia, I.K., Kamau, A., Muiruri, S., Mutiso, N., Nyambura, J., Mwatele, C., Amano, T., and Mwandawiro, C.S. (2008). Use of integrated malaria management reduces malaria in Kenya. PLoS ONE, 3.","DOI":"10.1371\/journal.pone.0004050"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1186\/s12936-017-1866-0","article-title":"Malaria mortality characterization and the relationship between malaria mortality and climate in Chimoio, Mozambique","volume":"16","author":"Mendes","year":"2017","journal-title":"Malar. J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_30","first-page":"1","article-title":"A Package for Measuring emergence, Self-organization, and Complexity Based on Shannon entropy","volume":"4","author":"Gershenson","year":"2017","journal-title":"Front. Robot. AI"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"283","DOI":"10.2307\/2335090","article-title":"The expected value of the adjusted rescaled Hurst range of independent normal summands","volume":"63","author":"Anis","year":"1976","journal-title":"Biometrica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5543","DOI":"10.1016\/j.physa.2008.05.053","article-title":"Some comments on Hurst exponent and the long memory processes on capital markets","volume":"387","year":"2008","journal-title":"Physica A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3844","DOI":"10.1016\/j.physa.2010.05.025","article-title":"On Hurst exponent estimation under heavy tailed distributions","volume":"389","author":"Barunik","year":"2010","journal-title":"Physica A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"9068","DOI":"10.1038\/srep09068","article-title":"A Dynamical Systems Explanation of the Hurst Effect and Atmospheric Low-Frequency Variability","volume":"5","author":"Franzke","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1046\/j.1365-3156.2002.00924.x","article-title":"Forecasting malaria incidence from historical morbidity patterns in epidemic-prone areas of Ethiopia: A simple seasonal adjustment method performs best","volume":"7","author":"Abeku","year":"2002","journal-title":"Trop. Med. Int. Health"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"e2020080","DOI":"10.1590\/s1679-49742021000100007","article-title":"Evaluation of prediction models for the occurrence of malaria in the state of Amap\u00e1, Brazil, 1997\u20132016: An ecological study","volume":"30","author":"Lima","year":"2021","journal-title":"Epidemiol. Serv. Sa\u00fade Bras\u00edlia"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Graves, T., Gramacy, R., Watkins, N., and Franzke, C. (2017). A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA, 1951\u20131980. Entropy, 19.","DOI":"10.3390\/e19090437"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Gao, J.B., Hu, J., and Tung, W.W. (2011). Tung, Facilitating joint chaos and fractal analysis of biosignals through nonlinear adaptive filtering. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0024331"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1098\/rsif.2011.0846","article-title":"Culturomics meets random fractal theory: Insights into long-range correlations of social and natural phenomena over the past two centuries","volume":"9","author":"Gao","year":"2012","journal-title":"J. R. Soc. Interface"},{"key":"ref_40","first-page":"1","article-title":"Ecological diagnosis from biotic data by Hurst exponent and the R\/S analysis adaptation to short time series","volume":"23","author":"Flynn","year":"2013","journal-title":"Biomatem\u00e1tica"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"461","DOI":"10.5028\/jatm.v9i4.683","article-title":"The Long-Range Memory and the Fractal Dimension: A Case Study for Alc\u00e2ntara","volume":"9","author":"Schuch","year":"2017","journal-title":"J. Aerosp. Technol. Manag."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"96","DOI":"10.25115\/eea.v37i2.2603","article-title":"Different methodologies and uses of the Hurst exponent in econophysics","volume":"37","author":"Garcia","year":"2019","journal-title":"Estud. Econ. Appl."},{"key":"ref_43","first-page":"28","article-title":"Generalized approach to Hurst exponent estimating by time series","volume":"8","author":"Kirichenko","year":"2018","journal-title":"Inf. Control Meas. Econ. Environ. Prot."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5019","DOI":"10.1016\/j.physa.2013.06.041","article-title":"Generalized Hurst exponent approach to efficiency in MENA markets","volume":"392","author":"Sensoy","year":"2013","journal-title":"Physica A"},{"key":"ref_45","first-page":"1199","article-title":"Generalized Hurst Exponents as a Tool to Estimate Atrial Fibrillation Organization from the Surface ECG","volume":"40","author":"Alcaraz","year":"2013","journal-title":"Comput. Cardiol."},{"key":"ref_46","first-page":"22","article-title":"Forecasting Based On a SARIMA Model of Urban Malaria for Kolkata","volume":"4","author":"Ganguly","year":"2016","journal-title":"Am. J. Epidemiol. Infect. Dis."},{"key":"ref_47","first-page":"222","article-title":"Time series analysis of meteorological factors influencing Malaria in south eastern Iran","volume":"10","author":"Ostovar","year":"2016","journal-title":"J. Arthropod. Borne Dis."},{"key":"ref_48","first-page":"64","article-title":"Developing Stochastic Model For Forecasting Malaria Cases In Addis Zemen, South Gondar, Ethiopia: A Time Series Analysis","volume":"15","author":"Getnet","year":"2017","journal-title":"Nat. Sci."},{"key":"ref_49","first-page":"1","article-title":"Time series analysis of malaria in kumasi: Using arima models to forecast Time series analysis of malaria in kumasi: Using arima models to forecast","volume":"3","author":"Anokye","year":"2018","journal-title":"Cogent Soc. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1093\/ije\/20.3.808","article-title":"The use of transfer function models, intervention analysis and related time series methods in epidemiology","volume":"20","author":"Helfenstein","year":"1991","journal-title":"Int. J. Epidemiol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1186\/1475-2875-7-76","article-title":"Models for short term malaria prediction in Sri Lanka","volume":"7","author":"Vounatsou","year":"2008","journal-title":"Malar. J."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1186\/1475-2875-9-251","article-title":"Development of temporal modelling for forecasting and prediction of malaria infections using time-series and ARIMAX analyses: A case study in endemic districts of Bhutan","volume":"9","author":"Wangdi","year":"2010","journal-title":"Malar. J."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/S1471-4922(00)01763-3","article-title":"Malaria early warning in Kenya Simon","volume":"17","author":"Hay","year":"2001","journal-title":"Trends Parasitol."}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/12\/1\/496\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:12:47Z","timestamp":1760364767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/12\/1\/496"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,5]]},"references-count":53,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["app12010496"],"URL":"https:\/\/doi.org\/10.3390\/app12010496","relation":{},"ISSN":["2076-3417"],"issn-type":[{"type":"electronic","value":"2076-3417"}],"subject":[],"published":{"date-parts":[[2022,1,5]]}}}