Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model

Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as " R 0 ", to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana-Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.

Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class

In this paper, a nonlinear fractional-order chikungunya disease model that incorporates asymptomatic infectious individuals is proposed and analyzed. The main interest of this work is to investigate the role of memory effects on the dynamics of chikungunya. Qualitative analysis of the model's equilibria showed that there exists a threshold quantity which governs persistence and extinction of the disease. Model parameters were estimated based on the 2015 weekly reported cases in Colombia. The Adams-Bashforth-Moulton method was used to numerically solve the proposed model. We investigated the role of asymptomatic infectious patients on short- and long-term dynamics of the diseases. We also determined threshold levels for the efficacy of preventative strategies that results in effective management of the disease. We believe that our model can provide invaluable insights for public health authorities to predict the effect of chikungunya transmission and analyze its underlying factors and to guide new control efforts.

MODELING OPTIMAL CONTROL OF AFRICAN TRYPANOSOMIASIS DISEASE WITH COST-EFFECTIVE STRATEGIES

An optimal control model of African trypanosomiasis to minimize the cost of implementing control efforts and the number of infected humans, cattle, and tsetse-fly populations in their respective communities was formulated. Time-dependent controls such as public health education, human and cattle treatments, and tsetse-fly trapping were considered. Using Pontryagin’s maximum principle, the necessary conditions and the existence of an optimal control solution of an optimal control problem were analyzed. Using forward and backward in time fourth-order Runge–Kutta scheme, numerical simulations of the optimal control problem were performed. The results showed that the strategy involving public health education, treatment of humans, cattle treatment, and trapping of tsetse-flies was the most effective in reducing the number of infected individuals in their respective populations. Furthermore, the incremental cost-effectiveness analysis was performed, which showed that the tsetse-fly trapping was the most cost-effective strategy to implement in source limited settings.