Computer Simulation And Modeling For Biological Problems :

Gamal Ahmed Mohamed Mosa

One of the most recent and interesting techniques is the Modelling and simulationof Human Biology. Iufoctious and cell diseases are very serious and areopen fields of study. Some of these dis,eases are never understood yet others needmore and more effort to be completely solved. Constructing mathematical andsimulation models for some of these diseases are the main object of this study. Understandingand possibly controlling and predicting the nature and dynamics ofthese diseases are the results of such research. The hepatitis C virus (HCV) andthe hepatitis B virus (HBV) are considered among the most dangerous infectiousdiseases in the world. Egypt has possibly the highest HCV and HBV prevalencein the world [28]. [8]. These two viruses are the common causes of cirrhosis andhepatocellular carcinoma (HCC). Hepatitis C virus infection is found in 0.5 % to8.0 % of blood donors worldwide. Because the infection is chronic in more than60 % of infected persons, the disease is an important public health and economicproblem [14]. On the other hand, the world health organization has estimated thataround 300 million persons worldwide suffer from chronic hepatitis D virus infection,25-30 % of whom eventually will die from chronic sequel [20]. Interest in (HSV)epidemiology has increased due to the [Hl’V} (AIDS) epidemic, as the transmissionrouts and cliuical features show many similarities for these two infections due to thefact that better understanding of (HBV) epidemiology could lead to new insightson the future development of the (HIV) epidemic [10]. Due to the importance ofiii•....__ . - _.- ----Ivthese two diseases, two mathematical models had been constructed to study theharmful behavior of these two diseases. The first is the deterministic model, whilethe second is the stochastic model. Moreover, a numerical simulation for these twomathematical models was also constructed. Due to the uncertainty concerning thedatabase of these diseases in Egypt, another Monte Carlo simnlation model hadbeen built and the results obtained from this model had been compared with theother results as obtained from the numerical simulation of the mathematical models.This thesis contains five chapters. Chapter one, is considered as a review of previouswork in the filed of human biology, where it introduces introduction to the mathematicalmodelling process and some simple examples of the filed of human biology,moreover, it produces a deterministic model of HBY as previous study. Finally,it produces a simple review of the Monte-Carlo simulation technique. In chaptertwo a stochastic model and Monte-Carlo simulation of the spread of HBV had beenformulated and discussed. The numerical simulation of the stochastic model provedthe threshold level below which the disease will die out, and above it, the diseasebecomes endemic. Moreover, The results obtained from Monte Carlo simulationmodel coulinned the other results as concluded from the other numerical simulationof the deterministic and stochastic mo?els. Chapter three, is a deterministic modeland its numerical simulation of the spread of HCY in Egypt. This public healthproblem had been studied both mathematically and by using computer simulationsfor the spread of HCY subtype (4a) and the relation between (HCY-subtype 4a) andother subtypes of HCY. The mutation factor (Jl) plays a key result for this study.We derived the values of reproduction numbers (ROI, Ro2) which defined as the expectednumber of secondary cases produced by a single infected individual enteringIl disease free population at equilibrium (11). The conditions on these numbers weredetermined for the disease to be endemic or die out. Intuitively the disease die out~_.- _._----vwhen both (~tl and (~2) are less than one in value otherwise the disease becomesendemic. The numerical simulation of deterministic model were used to predict thebehavior of the dynamics of the disease and to estimate the numbers of persons ineach stage. In chapter four a stochastic model and Monte-Carlo aimulation of thespread of (He V-subtype 4a) had been.formulated and discussed. The results obtainedfrom numerical simulation for stochastic model and Monte-Carlo simulationhad been compared with the other results as obtained from the numerical simulationof the deterministic model. Both types of results are found in good matching andfitting well to each other. Chapter five is the conclusions of this research. Software(Mathematica 5.0), has been used to enhance the numerical simulations forthe stochastic models. Furthermore, a program language (Visual-Basic under Excel)has been used to obtain the numerical simulation for the deterministic modeland Monte Carlo simulation model.