A Novel Study on Mathematical Models of Plasmodium Life Cycle in Human Hepatocyte and Mosquito Midgut

Abstract

In historical annals, potentially lethal human infectious disease newline Malaria occupies a mark-able position. Most of the infectious diseases newlineare transmitted by mosquitoes. One of the ancient diseases affecting human newlineis malaria, which is caused by Plasmodium parasites. In nineteenth century, newlineFrench Scientist Charles L.A. Larven demonstrated that malaria was caused newlineby Protozoan Parasite. Carrying out the research under the guidance of Sir newlinePatrick Manson, Sir Ronald Ross identified the life cycle of malaria parasites newlineknown as Plasmodium Life Cycle. His invention of the transmission of newlinemalaria by the mosquitoes later provided the method of control leading to newlinethe prevention of the disease. newlineA mosquito borne disease, malaria, is caused by Plasmodium newlineparasites by the transmission of Anopheles mosquitoes. There are many newlinecontrol strategies handled against mosquito to establish a healthy society. newlineMathematical models developed by the researcher to analyze the control newlinemechanism are described in the present work. newlineThe thesis consists of 9 chapters. newlineChapter 1 is the introductory one. In this chapter, the origin of the newlinethesis is briefly described. The motivation for the thesis is presented, the newlinescope has been explained and the preliminary definitions are furnished with newlinea brief summary.v newlineChapter 2 is devoted to survey of literature. Here earlier research newlineworks done by various researchers on Plasmodium Life Cycle are briefly newlinesketched. It also includes the fundamental survey necessary for the analysis newlineof the mathematical model of Plasmodium Life Cycle. newlineChapter 3 contributes, a mathematical model for the Plasmodium newlineLife Cycle in hepatocyte. The aim of this work is to examine the conditions newlinefor the attainment of stability of Plasmodium Life Cycle model. The newlinesystem of Plasmodium Life Cycle in random noise has been investigated. newlineThe research work presented here seeks to offer a new mechanism in this newlinehitherto unexplored area. The conditions for the existence of the equilibrium newlinepoint of the system has been derived. Global stability properties for the newlinemodel are investigated by constructing Lyapunov function. By employing newlinethe perturbation in the Plasmodium Life Cycle system, the robustest is newlineretained for deterministic model. The analysis leads to the equilibrium newlineof the stochastic perturbation wherein the total number of plasmodium newlineparasites remains stationary. By considering stochastic differential equation newlineand Ito process, it is shown that the zero solution of the stochastic system newlineis asymptotically mean square stable with the construction of Lyapunov newlinefunction. Theoretical results are numerically supported and the diagrams newlineare presented to illustrate the results.vi newlineA Plasmodium Life Cycle mathematical model is developed with newlinethe introduction of varying population at each stage and also random noise newlineof Plasmodium Life Cycle model has been investigated in chapter 4. The newlineexistence of interior equilibrium point of the system is discussed. With newlinebonding condition, the global stability properties are investigated for the newlinemodel. The perturbation has been allowed and thereby concluded that the newlinedeterministic model is observed to be robust. The conditions for the total newlinenumber of plasmodium parasites to remain stable are framed out. Theoretical newlineresults are numerically upheld and the necessary diagrams were delineated. newlineThe Chapter 5 describes the control procedure by backstepping newlineto break-up the life cycle states of plasmodium parasite. According to newlinereduce the energy rate of reproduction among plasmodium parasite, the newlineLyapunov function is framed. The Pseudo controls are introduced so as newlineto achieve global stability for Plasmodium Life Cycle and the illustrations newlinewas presented. newlineIn Chapter 6, a mathematical model of the Plasmodium Life newlineCycle in mosquito midgut is constructed. The complexity and stability newlineof Plasmodium Life Cycle model in mosquito midgut are examined. newlineThe conditions for the existence of equilibrium point of the system are newlinepresented. Global stability conditions of the model have been investigated newlineby considering the conditions around the interior equilibrium point.vii newlineHypothetical outcomes are numerically upheld and with the aid of pictorial newlinenotation were delineated. newlineIn Chapter 7, dissipation and boundedness properties are described newlinewith respect to the states of the Plasmodium Life Cycle. newlineChapter 8 is the study about abrupt changes in the dynamical newlinesystem, its exponential power and control technique has been examined, also newlinethe existence of bifurcation has been investigated and pictorial representation newlinewere produced. newlineIn Chapter 9, the conclusion of the thesis is provided. newlineThe numerical simulation illustrate the hypothetical outcomes for newlinethe Plasmodium Life Cycle model