Optimal Control Problem for Cholera Disease and Cost-Effectiveness Analysis

Cholera is a disease that continues to be a threat to public health globally and is an indicator of inequity and lack of social development in countries. For this reason, strategies for its control need to be investigated. In this work, an optimal control problem related to cholera disease was formulated by introducing personal protection, drug treatment and water sanitation as control strategies. First, the existence and characterization of controls to minimize the performance index or cost function was proved by using classic control theory. Then, the theoretical results were validated with numerical experiments by using data reported in the literature. Finally, the effectiveness and efficiency of the proposed controls were determined through a cost-effectiveness analysis. The results showed that the use of the three controls simultaneously is the cheapest and most effective strategy to control the disease

Mathematical Modelling of Transmission Dynamics of Anthrax in Human and Animal Population.

Anthrax is an infectious disease that can be categorised under zoonotic diseases. It is caused by the bacteria known as Bacillus anthraces. Anthrax is one of the most leading causes of deaths in domestic and wild animals. In this paper, we develop and investigated a mathematical model for the transmission dynamics of the disease. Ordinary differential equations were formulated from the mathematical model. We performed the quantitative and qualitative analysis of the model to explain the transmission dynamics of the anthrax disease. We analysed and determined the model’s steady states solutions. The disease-free equilibrium of the anthrax model is analysed for locally asymptotic stability and the associated epidemic basic reproduction number. The model’s disease free equilibrium has shown to be locally asymptotically stable when the basic reproductive number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Sensitivity analysis was performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the diseases. Keywords: Anthrax model, Basic reproductive number, Asymptotic stability, Endemic equilibrium, Sensitivity analysis

Mathematical assessment of the role of environmental factors on the dynamical transmission of cholera

In this paper, we investigate the impact of environmental factors on the dynamical transmission of cholera within a human community. We propose a mathematical model for the dynamical transmission of cholera that incorporates the virulence of bacteria and the commensalism relationship between bacteria and the aquatic reservoirs on the persistence of the disease. We provide a theoretical study of the model. We derive the basic reproduction number R 0 which determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever R 0 ≤1 , while when R 0 > 1 , the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is locally asymptotically stable on a positively invariant region of the positive orthant. The sensitivity analysis of the model has been performed in order to determine the impact of related parameters on outbreak severity. Theoretical results are supported by numerical simulations, which further suggest the necessity to implement sanitation campaigns of aquatic environments by using suitable products against the bacteria during the periods of growth of aquatic reservoirs