CP 15 ( Friday 26 , 15 : 20 – 16 : 50 ) Room B Mathematical Biology

s – Contributed Papers 91 CP 15 (Friday 26, 15:20 – 16:50) Room B Mathematical Biology 15:20-15:35 T. Adeniran, R.O Ayeni Dept. of Pure and Applied Math., Ladoke Akintola Univ. of Technology, Ogbomoso, Nigeria Title: The Effect of Immunisation Rate on a Mathematical Model of Yellow Fever Epidemic Abstract: We revisit the mathematical model of yellow fever which involves the interactions of two principal communities of hosts (humans) and vectors (aedes aegypti mosquitoes)[6]. We extend the model to a situation where immunisation is non – permanent. Using numerical technique, we evaluate S(t), R(t), I(t), N(t) and M(t) and show the immunisation and rate at which vaccine wanes have significant effects on the epidemic. 15:35–15:50 Asrul Sani, Dirk P. Kroese Mathematics Department, University of Queensland, Brisbane, Australia, 4072 Title: Stochastic Models For The Spread Of HIV In A Mobile Heterosexual Population Abstract: One of the most urgent world-wide public health problems is the AIDS (Acquired Immune Deficiency Syndrome) epidemic, caused by the Human Immunodeficiency Virus (HIV). The number of people infected with HIV/AIDS continues to rise at an alarming rate, especially in developing countries. The epidemic remains extremely dynamic, growing and changing character as the virus exploits new opportunities for transmission. An important factor in the dynamic transmission of HIV is the mobility of the population. In this paper we formulate various new stochastic models for the spread of HIV in a heterosexual mobile population, under the assumptions of constant and varying population sizes. We derive deterministic and diffusion analogues for these models, using a convenient rescaling technique, and analyze their stability conditions and equilibrium behavior. We illustrate the dynamic behavior of the models and their approximations via a range of numerical experiments. We show that the stochastic models are well approximated by their deterministic counterparts, and that around the endemic equilibrium the population process behaves like a multi-dimensional Ornstein-Uhlenbeck process. Keyword: HIV/AIDS, Stochastic Modelling, Markov process, Multiple Patch, Mobility, Density Dependence, Deterministic and Diffusion Approximation 15:50–16:05 Lusia Krismiyati Budiasih Departement of Mathematics, Institut Teknologi Bandung, Indonesia Title: Epidemiological Model for the Spread of Anti-Malarial Resistance and Its Economics Aspect Abstract: The spread of anti-malarial resistance is making malaria control increasingly difficult. Mathematical models for the transmission dynamics of resistant and sensitive strains of the parasite can be used as a tool to help to understand the factors that influence the spread of anti-malarial resistance, and they can help in thinking the strategic steps to control the spread of resistance. Now it can be found that malaria parasite resistant to chloroquine. With increasing the resistance, attention has begun to be pressed in treatment strategies by using some new drugs such as sulfadoxine-pyrimethamine (SP), and artemisinin-based combination treatments (ACT). Although there are strong theoretical arguments in favor of switching to ACT, the validity of these arguments in the economics aspects has not been previously analyzed. This paper presents an epidemiological framework to investigate the spread of antimalarial resistance. Several mathematical models, based on Macdonald-Ross model of malaria transmission, enable to examine the processes and parameters that influenced in the spread of resistance and also can be used to examine the optimal treatment strategies. In the simplest model, the resistance does not spread if the fraction of infected individuals treated is less than a threshold value. The threshold value is determined by the rates of infection and level of anti-malarial effectiveness. Using the developing of this model, it can be showed that in the appropriate level of treatment, the treatment strategy by using ACT early needs less cost than by SP in a few time and then replaced with ACT.