School of Mathematical Sciences

This paper estimates the time-varying world integration of the Malaysian stock market and examines if the paths of the time-varying integration match the economic events of the country. We employed weekly time series data for the period between February 1988 and September 2009 to coincide with the liberalisation of the Malaysian market since the late 1980s. To capture the time-varying degree of market integration, we employed the Kalman Filter technique, which produces time-varying coefficients in estimating International Capital Asset Pricing Model (ICAPM). The changes in the level of market integration coincide with the economic events that took place in the country and provide some evidence to the practical application and suitability of the Kalman Filter technique in studying stock market integration.

The debate on determining the degree of integration of stock markets with world stock market has increased markedly in the past decade due to its crucial impact on the economy of a country. This paper examines the dynamics of stock market integration of Malaysia stock market with the world market. A conditional international capital asset pricing model (ICAPM) has been used in this study. The degree of stock market integration is time-varying, according to the Kalman filter approach. The results show that the 97/98 Asian financial crisis and the current global crisis have different impact on the integration level. In particular, Malaysia stock market was obviously segmented from the world market during the 97/98 Asian financial crisis but this phenomenon is totally different with the current global crisis, where Malaysia is integrated to the world.

The paper observed the impact of the profit rate and failure rate to the profit of Musharakah Mutanaqisah Homeownership Partnership (MMP) that exercise in local Islamic Bank in Malaysia while the probability of the housing
project’s failure is considered into this facility. The retrospective method is a retrospective method of calculating the outstanding balance in actuarial mathematics. Moreover, this study derived a probability of abandoned housing project
equations implementing from the actuarial mathematics. The failure rate is assumed to be exponentially distributed. The profit
will varies due to the changes of variables like profit rate, failure rate and tenure. This study also presented the intention of IB in bearing the losses of MMP when abandoned housing project occurred.

This study discusses the Stability of equilibrium states of a model in an attempt to suggest control of and Eradication strategies for malaria in a community. The model exhibits two equilibria namely; the trivial equilibrium state and diseases free equilibrium state. The Model analysis shows that combination of both treatment and preventive method can eradicate malaria cases.[Abdullahi Mohammed Baba: A Mathematical Model for Assessing the Control of and Eradication strategies for Malaria in a Community. [ABDULLAHI MOHAMMED BABA. A Mathematical Model for Assessing the Control of and Eradication strategies for Malaria in a Community. Report and Opinion 2012;4(2):7-12]. (ISSN: 1553-9873). http://www.sciencepub.net/report. 2

We propose a new deterministic model for the dynamics of malaria and the effectiveness of drugs and the positivity of the model investigated. The human population was portioned into three distinct compartments of susceptible, infected and the recovered, while the mosquito population was portioned into two distinct Compartments of susceptible and the infected, giving rise to a set of five ordinary differential equations. A parameter ( A ) is introduced to measure the effectiveness of anti malarial drugs in the infected compartment. The dynamics of the model was obtained. It was observed that both the disease free equilibrium states will be stable if ( ) A > 60% and if the mosquitoes population is reduced the human population will also be stable. Numerical simulations were presented to show some results

To investigate the optimal control strategy for Plasmodium knowlesi malaria in humans and macaques. Methodology: A Plasmodium knowlesi malaria model was developed using a deterministic system of differential equation and extended to include an optimal control of the disease. The optimal control model was analysis dynamically and numerically. Results: if the cost of biological control against the mosquito Larvae, the forest dwelling mosquitoes and chemical control against the adult mosquitoes is more than cost of treatment of the infected human, we observed that the control strategy yields increase in susceptible humans, decrease in the infected humans, infected macaques and mosquito population. This is one of the best strategies but treatment is very important for total elimination of Plasmodium knowlesi malaria in a community. Conclusion: Numerical simulations of the problem, suggest that applying the three control measure can effectively reduce if not eliminate the spread of Plasmodium knowlesi malaria in a community.

Malaria as among vector-borne diseases is reemerging in areas where control efforts were once effective and emerging in areas though free of the disease as a consequence of human migration and rapid growth of international traffic from malaria prevalent areas of the world to malaria free zone. In this paper we develop a mathematical model for the spread of Plasmodium knowlesi malaria from infected humans to mosquitoes. The stability 4483 analysis of the model is investigated rigorously. The model is extended to assess the impact of time dependent preventive (biological and chemical control) against the mosquitoes and treatment for infected humans. The existence of optimal control is established analytically by the use of optimal control theory. Numerical simulations of the problem, suggest that applying the three control measure can effectively reduce if not eliminate the spread of Plasmodium knowlesi malaria in a community.

Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.

Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.

This paper considers a mathematical model for the spread of Plasmodium knowlesi malaria. The model incorporates recruitment of human, mosquito and macaque populations through a constant immigration, with a fraction of infective immigrants. The basic properties of model and equilibriums for the models are analyzed rigorously. The sensitivity analysis of the model is carried out to recognize the most sensitive parameters for the disease transmission. Thus, control strategy is presented and studied. Optimal control theory is applied to investigate optimal strategies for controlling the spread of the malaria using quarantine, insecticide spray and culling as the control variables. The results obtained from numerical simulation of the model show possible significant reduction of the disease spread using the combine control strategies.

A mathematical model for the transmission dynamics of Knowlesi malaria is developed. The model, which consists of 8 ordinary differential equations, is analyzed rigorously. The Knowlesi malaria model was extended to incorporate the effect of seasonality in the transmission rates of knowlesi malaria; the seasonal forcing basic reproduction number is investigated analytically. The sensitivity analysis of the basic reproduction number of the sensuality is investigated. Numerical analysis is carried out considering different strength of seasonality to determine the effect of seasonal biting rates on the susceptible humans, mosquitoes and macaques.

Model to forecast malaria outbreaks Phys. Today Abstract. The most significant and efficient measures against Plasmodium knowlesi outbreaks are efficient anti malaria drug, biological control in form of predatory mosquitoes and culling control strategies. In this paper optimal control theory is applied to a system of ordinary differential equation. It describes the disease transmission and Pontryagin's Maximum Principle is applied for analysis of the control. To this end, three control strategies representing biological control, culling and treatment were incorporated into the disease transmission model. The simulation results show that the implementation of the combination strategy during the epidemic is the most cost-effective strategy for disease transmission.

Rapid transmission of the novel coronavirus and its resulting condition has caught most countries of the world off-guard. This work develops a fractional order model with seven compartments to describe the transmission and effects of control strategies of coronavirus. The Caputo fractional derivative operator of order (0,1) is applied to obtain the scheme of fractional differential equations (FDEs) of the model. The stability analysis is carried out and non-negative unique solution within the domain is verified. Laplace-Adomian Decomposition Method is applied to work out an approximate solution of the FDEs. The solution of the FDEs in the form of infinite series is obtained. The obtained results are compared with the differential transform method case, which converges rapidly to its exact value. Numerical simulations are presented to show the reliability and simplicity of the method.