UPSI Digital Repository (UDRep)
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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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