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Type :thesis
Subject :RC Internal medicine
Main Author :Farah Kristiani
Title :Mathematical models based on difference and differential equations for dengue disease mapping in Bandung Indonesia
Place of Production :Tanjong Malim
Publisher :Fakulti Sains dan Matematik
Year of Publication :2019
Corporate Name :Universiti Pendidikan Sultan Idris
PDF Guest :Click to view PDF file

Abstract : Universiti Pendidikan Sultan Idris
This study aimed to introduce a new alternative mathematical model for the discrete space-time  compartment models. The study focuses on the development of three new models. The first model is a  stochastic model which considers the age-structure based on the difference equation, also known as  the ASDE model to estimate the relative risk of dengue disease transmission. This model takes into  account the spatial correlation in determining  the  newly  infective  number  of  dengue  cases   which  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 differential  equation.  Lastly,  the  third  model  is  the  WADE  model,  which  is  also  known  as  Wolbachia-Aedes mosquito differential equation. The basic reproduction numbers (R0) of  OBDE  and   WADE  models  as  the  threshold  of  dengue  disease  transmission  are determined, while the  stability of the models are analyzed. Results indicate that the ASDE  model  yielded  the  best   result  when  it  was  applied  to  the  juvenile  group. Meanwhile, OBDE model analysis shows that  the OBDE model was stable for free and endemic states. Additionally, this supports the fact that O  blood-type individuals have higher probability to be infected by dengue disease compared to the  non-O blood-type people. On the other hand, the analysis of WADE model shows that this model was  only stable in the free-state. Based on the form of basic reproduction number of WADE model, the  minimum number of Wolbachia-Aedes mosquitoes that must be released in a particular area to reach  the free-state condition can be determined. In conclusion, the ASDE  model  offers  better  results   in  estimating  the  relative  risks,  especially  for the juvenile  group.  In  addition,  the   other  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 to  be treated by the authorities with dengue vaccine  as  prevention  to  juveniles  as  recommended   by  ASDE  model  and  also  to  O blood-type people as suggested by OBDE model. Another treatment  is by releasing the Wolbachia-Aedes mosquitoes in a certain number as determined by WADE model.  

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