Abstract: This paper studies the effect of time delay on stability
of mutualism population model with limited resources for both
species. First, the stability of the model without time delay is
analyzed. The model is then improved by considering a time delay in
the mechanism of the growth rate of the population. We analyze the
effect of time delay on the stability of the stable equilibrium point.
Result showed that the time delay can induce instability of the stable
equilibrium point, bifurcation and stability switches.
Abstract: Identifying parameters in an epidemic model is one
of the important aspect of modeling. In this paper, we suggest a
method to identify the transmission rate by using the multistage
Adomian decomposition method. As a case study, we use the data of
the reported dengue fever cases in the city of Shah Alam, Malaysia.
The result obtained fairly represents the actual situation. However, in
the SIR model, this method serves as an alternative in parameter
identification and enables us to make necessary analysis for a smaller
interval.
Abstract: A climate dependent model is proposed to simulate
the population of Aedes aegypti mosquito. In developing the model,
average temperature of Shah Alam, Malaysia was used to determine
the development rate of each stage of the life cycle of mosquito.
Rainfall dependent function was proposed to simulate the hatching
rate of the eggs under several assumptions. The proposed transition
matrix was obtained and used to simulate the population of eggs,
larvae, pupae and adults mosquito. It was found that the peak of
mosquito abundance comes during a relatively dry period following a
heavy rainfall. In addition, lag time between the peaks of mosquito
abundance and dengue fever cases in Shah Alam was estimated.