The application of fuzzy theory is vital in all scientific disciplines.The construction of mathematical models with fuzziness is little studied in the literature.With this in mind and for a better understanding of the...The application of fuzzy theory is vital in all scientific disciplines.The construction of mathematical models with fuzziness is little studied in the literature.With this in mind and for a better understanding of the disease,an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classicalmodel ofmalaria transmission.The parametersβandδ,being function of the malaria virus load,are considered fuzzy numbers.Three steady states and the reproduction number of the model are analyzed in fuzzy senses.A numerical technique is developed in a fuzzy environment to solve the studied model,which retains essential properties such as positivity and dynamic consistency.Moreover,numerical simulations are carried out to illustrate the analytical results of the developed technique.Unlike most of the classical methods in the literature,the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.展开更多
We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartmen...We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.展开更多
文摘The application of fuzzy theory is vital in all scientific disciplines.The construction of mathematical models with fuzziness is little studied in the literature.With this in mind and for a better understanding of the disease,an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classicalmodel ofmalaria transmission.The parametersβandδ,being function of the malaria virus load,are considered fuzzy numbers.Three steady states and the reproduction number of the model are analyzed in fuzzy senses.A numerical technique is developed in a fuzzy environment to solve the studied model,which retains essential properties such as positivity and dynamic consistency.Moreover,numerical simulations are carried out to illustrate the analytical results of the developed technique.Unlike most of the classical methods in the literature,the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.
基金The work has been supported by a grant received from the Ministry of Education,Government of India under the Scheme for the Promotion of Academic and Research Collaboration(SPARC)(ID:SPARC/2019/1396).
文摘We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.
