Theoretical advancement in dengue transmission model in Malaysia using fractional order differential equations
This thesis aims to deploy and develop fractional-order differential equations that possess hereditary properties in modelling the dengue transmission dynamics. Dengue models are generally of integer-order derivative systems, that cannot fully explain the behaviour of dengue transmission, which i...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/91953/1/FS%202020%2025%20-%20IR.pdf |
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| Summary: | This thesis aims to deploy and develop fractional-order differential equations that
possess hereditary properties in modelling the dengue transmission dynamics.
Dengue models are generally of integer-order derivative systems, that cannot fully
explain the behaviour of dengue transmission, which involves memory effect. In
this study, three different deterministic fractional-order models are constructed, including
the basic framework model, temperature-driven model, and dengue control
model, using Caputo’s derivative definition. The susceptible-infected-recovered
(SIR) model is considered in the formulation. The significant differences between
the integer-order model and the fractional-order model, and the relation of the order
of the derivative with the dynamical behaviour of the dengue epidemic are addressed.
Furthermore, this thesis discusses the effect of the temperature in the dengue
transmission, and the efficacy of current dengue control measures, particularly in
Malaysia. The theoretical analysis of the existence and stability of the equilibrium
point is presented in detail. Additionally, sensitivity analysis is performed to assess
the importance of model parameters in disease transmission and disease prevalence.
The recorded dengue cases in Malaysia are used in numerical simulations. Numerical
results reveal that the convergence rate of fractional-order models is more gradual
compared to the integer-order model. A lower value of the order corresponds to a
slower decaying time and reduction in the size of epidemics. The temperature-driven
models show that the fractional-order model is more stable since there is no oscillatory
behaviour observed in the solutions, unlike in the integer-order model. These
models also predict that dengue can be persisted even in the non-optimal temperature
condition. The dengue control model shows that vector control tools are the
most efficient way to combat the spread of dengue viruses, and the combination of
them with individual protection makes it more effective. In fact, with the massive application of individual protection only, the number of cases can be reduced. Conversely,
mechanical control alone cannot suppress the excessive number of cases in
the population, although it can significantly reduce the number of Aedes mosquitoes.
Overall, these findings have significant implications in understanding the transmission
dynamics of dengue, and the proposed fractional-order models are found to be
a great alternative in describing the real epidemic of dengue transmission. |
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