Analysis of a model of gambiense sleeping sickness in humans and cattle

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.

Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo

This paper deals with modeling and simulation of the novel coronavirus in which the infectious individuals are divided into three subgroups representing three forms of infection. The rigorous analysis of the mathematical model is provided. We provide also a rigorous derivation of the basic reproduction numberR 0 . ForR 0 < 1 , we prove that the Disease Free Equilibium (DFE) is Globally Asymptotically Stable (GAS), thus COVID-19 extincts; whereas forR 0 > 1 , we found the co-existing phenomena under some assumptions and parametric values. Elasticity indices forR 0 with respect to different parameters are calculated with baseline parameter values estimated. We also prove that a transcritical bifurcation occurs atR 0 = 1 . Taking into account the control strategies like screening, treatment and isolation (social distancing measures), we present the optimal control problem of minimizing the cost due to the application of these measures. By reducing the values of some parameters, such as death rates (representing a management effort for all categories of people) and recovered rates (representing the action of reduction in transmission, improved screening, treatment for individuals diagnosed positive to COVID-19 and the implementation of barrier measures limiting contamination for undiagnosed individuals), it appears that after 140 - 170 days, the peak of the pandemic is reached and shows that by continuing with this strategy, COVID-19 could be eliminated in the population.

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

In this paper, a mathematical model for the transmission dynamics of Trypanosoma brucei rhodesiense that incorporates three species—namely, human, animal and vector—is formulated and analyzed. Two controls representing awareness campaigns and insecticide use are investigated in order to minimize the number of infected hosts in the population and the cost of implementation. Qualitative analysis of the model showed that it exhibited backward bifurcation generated by awareness campaigns. From the optimal control analysis we observed that optimal awareness and insecticide use could lead to effective control of the disease even when they were implemented at low intensities. In addition, it was noted that insecticide control had a greater impact on minimizing the spread of the disease compared to awareness campaigns.