Bifurcation Analysis of Toxoplasmosis Epidemic Control on Increased Controlled Rate of Suppressing the Rate of Infected Births

Abstract

The toxoplasmosis epidemic is an infectious disease caused by the parasitic Toxoplasma Gondii. This disease attacks the human immune system and other organs in the body, resulting in damage to tissues. The spread of the disease is carried out in various ways, one of them is eating foods that are less hygienic or not cooked properly, resulting in parasites remain active. Provision of controlled therapy is one solution in controlling the epidemic against suppression of the birth rate infected with toxoplasmosis. This study discusses the bifurcation analysis of a mathematical model for controlling the toxoplasmosis epidemic. Bifurcation analysis is carried out on the controlled rate and rate of birth control of toxoplasmosis. From the mathematical model of controlling the toxoplasmosis epidemic, stability and existence analysis are performed at each equilibrium point. Next, a function of two independent parameters is constructed which influences the spread of the disease, namely the controlled rate and the rate of infected births. Then, a bifurcation analysis of each region is obtained from each function of the two free parameters. From the bifurcation analysis, three regional conditions were obtained which showed the dynamics of the toxoplasmosis epidemic of two independent parameters with each interpretation of the bifurcation region.