Abstract
The study will investigate the Bifurcation analysis of a mathematical model for malaria transmission under treatment and control. The following objectives will guide the study: Carry out a detailed research on malaria transmission, Study the metamorphosis of plasmodium parasite, Construct a mathematical model for the transmission of malaria under treatment and control, Provide useful and analytical contributions that will help in exterminating malaria in our society and Pave way for further studies into the transmission dynamics of malaria. The study will use experimental design for the analysis which the method of data collection will be statistical inference, making decisions about the parameters of a population, based on random sampling
Introduction
Mathematical models are representations of physical phenomena and concepts using mathematical language. The system been modeled will now be represented in a mathematical equation which provides detailed description of the system’s operational method(s).
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family such as the integral curves of a family of vector fields, and the solutions of a family of ordinary differential equation. Bifurcation is most commonly applied in the study of dynamical systems. A bifurcation occurs when a small change in the parameter values of a system causes a sudden qualitative or topological change in the system. It occurs in both continuous systems ( ODEs, DDEs, PDEs) and discrete systems ( described by maps).
Malaria is an infectious disease caused by a parasite that live part of its life in humans and part in mosquito. It is responsible for the death of many people worldwide especially in Africa and children are the greatest victim. The greatest havoc caused by malaria worldwide was during the World War II when it was responsible for more deaths than the deaths by gun.
Malaria is primarily caused by parasite of genus plasmodium.
Plasmodium is a single-celled parasite and there are about hundred species of plasmodium. However, plasmodium causing malaria in humans earlier on was believed to be four viz plasmodium falciparum, plasmodium vivax, plasmodium malariae and plasmodium ovale. The recent work of an Indian Doctor, Dr. Knowlesi has disproved this as he discovered another plasmodium parasite that causes malaria in human beings, it goes by the name plasmodium knowlesi.
Malaria is caused when an infected anopheles mosquito bites a human being, the plasmodium parasite in form of sporozite is injected into the human system via saliva from the mosquito. The developmental process of the sporozite through schizont, to merozoite is what causes malaria in humans.
Initially the treatment of malaria was not known owing to the fact that the actual cause of it was unknown. Historically, malaria was thought of as being the result of inhaling bad air. Malaria has its origin from Italy “Mal aria” or bad air. A French scientist, Alphonse Laveran, discovered that the real cause of malaria is the singled-celled plasmodium parasite and years later, scientist discovered that anopheles mosquitoes are the vectors responsible for transmitting malaria.
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A PROPOSAL ON BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL FOR MALARIA TRANSMISSION UNDER TREATMENT AND CONTROL
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