Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia

This study aimed to introduce a new alternative mathematical model for the discrete space-timecompartment models. The study focuses on the development of three new models. The first model is astochastic model which considers the age-structure based on the difference equation, also known asthe ASDE m...

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Main Author:	Farah Kristiani
Format:	thesis
Language:	eng
Published:	2019
Subjects:	RC Internal medicine
Online Access:	https://ir.upsi.edu.my/detailsg.php?det=5446
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topic	RC Internal medicine
spellingShingle	RC Internal medicine Farah Kristiani Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia
description	This study aimed to introduce a new alternative mathematical model for the discrete space-timecompartment models. The study focuses on the development of three new models. The first model is astochastic model which considers the age-structure based on the difference equation, also known asthe ASDE model to estimate the relative risk of dengue disease transmission. This model takes intoaccount the spatial correlation in determining the newly infective number of dengue caseswhich can be applied to juveniles and adults by using different birth and death probabilities.The second model is the OBDE model which is based on the development of O blood-type differentialequation. Lastly, the third model is the WADE model, which is also known asWolbachia-Aedes mosquito differential equation. The basic reproduction numbers (R0) of OBDE andWADE models as the threshold of dengue disease transmission are determined, while thestability of the models are analyzed. Results indicate that the ASDE model yielded the bestresult when it was applied to the juvenile group. Meanwhile, OBDE model analysis shows thatthe OBDE model was stable for free and endemic states. Additionally, this supports the fact that Oblood-type individuals have higher probability to be infected by dengue disease compared to thenon-O blood-type people. On the other hand, the analysis of WADE model shows that this model wasonly stable in the free-state. Based on the form of basic reproduction number of WADE model, theminimum number of Wolbachia-Aedes mosquitoes that must be released in a particular area to reachthe free-state condition can be determined. In conclusion, the ASDE model offers better resultsin estimating the relative risks, especially for the juvenile group. In addition, theother two models with the space-time variables are applied to support the real condition.The implication of the study reveals that the ASDE model can determine the risk areas that need tobe treated by the authorities with dengue vaccine as prevention to juveniles as recommendedby ASDE model and also to O blood-type people as suggested by OBDE model. Another treatmentis by releasing the Wolbachia-Aedes mosquitoes in a certain number as determined by WADE model.
format	thesis
qualification_name
qualification_level	Doctorate
author	Farah Kristiani
author_facet	Farah Kristiani
author_sort	Farah Kristiani
title	Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia
title_short	Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia
title_full	Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia
title_fullStr	Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia
title_full_unstemmed	Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia
title_sort	mathematical models based on difference and differential equations for dengue disease mapping in bandung indonesia
granting_institution	Universiti Pendidikan Sultan Idris
granting_department	Fakulti Sains dan Matematik
publishDate	2019
url	https://ir.upsi.edu.my/detailsg.php?det=5446
_version_	1747833196645449728
spelling	oai:ir.upsi.edu.my:54462020-12-21 Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia 2019 Farah Kristiani RC Internal medicine This study aimed to introduce a new alternative mathematical model for the discrete space-timecompartment models. The study focuses on the development of three new models. The first model is astochastic model which considers the age-structure based on the difference equation, also known asthe ASDE model to estimate the relative risk of dengue disease transmission. This model takes intoaccount the spatial correlation in determining the newly infective number of dengue caseswhich can be applied to juveniles and adults by using different birth and death probabilities.The second model is the OBDE model which is based on the development of O blood-type differentialequation. Lastly, the third model is the WADE model, which is also known asWolbachia-Aedes mosquito differential equation. The basic reproduction numbers (R0) of OBDE andWADE models as the threshold of dengue disease transmission are determined, while thestability of the models are analyzed. Results indicate that the ASDE model yielded the bestresult when it was applied to the juvenile group. Meanwhile, OBDE model analysis shows thatthe OBDE model was stable for free and endemic states. Additionally, this supports the fact that Oblood-type individuals have higher probability to be infected by dengue disease compared to thenon-O blood-type people. On the other hand, the analysis of WADE model shows that this model wasonly stable in the free-state. Based on the form of basic reproduction number of WADE model, theminimum number of Wolbachia-Aedes mosquitoes that must be released in a particular area to reachthe free-state condition can be determined. In conclusion, the ASDE model offers better resultsin estimating the relative risks, especially for the juvenile group. In addition, theother two models with the space-time variables are applied to support the real condition.The implication of the study reveals that the ASDE model can determine the risk areas that need tobe treated by the authorities with dengue vaccine as prevention to juveniles as recommendedby ASDE model and also to O blood-type people as suggested by OBDE model. Another treatmentis by releasing the Wolbachia-Aedes mosquitoes in a certain number as determined by WADE model. 2019 thesis https://ir.upsi.edu.my/detailsg.php?det=5446 https://ir.upsi.edu.my/detailsg.php?det=5446 text eng closedAccess Doctoral Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik Addawe, J. & Lope, J. (2012). Analysis of Age-structured Malaria Transmission Model.Philippine Science Letters, 5(2), 169-186.Afizah, N. & Lee, HL. (2013). Wolbachia-based strategy for dengue control the way forward. DengueBulletin, 37, 107 - 115.Alexander, M. & Moghadas, S. (2005). 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