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In this research, a comprehensive stochastic model was developed to analyze the transmission dynamics of methicillin-resistant Staphylococcus aureus (MRSA) in both hospital-acquired and community-acquired contexts. The study explored the existence and uniqueness of solutions and established the presence of a global solution. The investigation focused on assessing the boundedness, extinction, and persistence of MRSA strains in terms of their means. The analysis of the model revealed a noteworthy phenomenon known as competitive exclusion, where the community-acquired MRSA strain gradually out-competes the hospital-acquired strain within hospital settings. In conclusion, effective interventions and preventive measures, such as improving hand hygiene compliance, implementing decolonization strategies, and enhancing disinfection rates, emerge as critical factors in controlling the transmission of these strains within hospital environments. [ABSTRACT FROM AUTHOR]

We proposed a deterministic compartmental model for the transmission dynamics of COVID-19 disease. We performed qualitative and quantitative analysis of the deterministic model concerning the local and global stability of the disease-free and endemic equilibrium points. We found that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity, while the endemic equilibrium point becomes locally asymptotically stable if the basic reproduction number is above unity. Furthermore, we derived the global stability of both the disease-free and endemic equilibriums of the system by constructing some Lyapunov functions. If R 0 ≤ 1 , it is found that the disease-free equilibrium is globally asymptotically stable, while the endemic equilibrium point is globally asymptotically stable when R 0 > 1. The numerical results of the general dynamics are in agreement with the theoretical solutions. We established the optimal control strategy by using Pontryagin's maximum principle. We performed numerical simulations of the optimal control system to investigate the impact of implementing different combinations of optimal controls in controlling and eradicating COVID-19 disease. From this, a significant difference in the number of cases with and without controls was observed. We observed that the implementation of the combination of the control treatment rate, u 2 , and the control treatment rate, u 3 , has shown effective and efficient results in eradicating COVID-19 disease in the community relative to the other strategies. [ABSTRACT FROM AUTHOR]

In this paper, the dysentery dynamics model with controls is theoretically investigated using the stability theory of differential equations. The system is considered as SIRSB deterministic compartmental model with treatment and sanitation. A threshold number R 0 is obtained such that R 0 ≤ 1 indicates the possibility of dysentery eradication in the community while R 0 > 1 represents uniform persistence of the disease. The Lyapunov–LaSalle method is used to prove the global stability of the disease-free equilibrium. Moreover, the geometric approach method is used to obtain the sufficient condition for the global stability of the unique endemic equilibrium for R 0 > 1. Numerical simulation is performed to justify the analytical results. Graphical results are presented and discussed quantitatively. It is found out that the aggravation of the disease can be decreased by using the constant controls treatment and sanitation. [ABSTRACT FROM AUTHOR]

Highlights • A new compartmental model for the co-dynamics of measles and dysentery diarrhea is proposed. • The system exhibits a backward bifurcation. • Optimal control and cost-effectiveness analysis are addressed. • Numerical simulations illustrate theoretical results and indicate suggestions for disease elimination. • The most cost-effective strategy for the control of the diseases is recommended. Abstract In this paper we propose a co-dynamics deterministic system for measles and dysentery diarrhea diseases in a single host population. Using center manifold theory, we show that the co-dynamics model may exhibit a backward bifurcation for some parameter values. Numerical simulations of the system show that the two diseases always coexist if R 0 > 1. The system is extended to include time-dependent control-variables: vaccination, treatment and sanitation of the environment, to minimize the number of infected humans and the cost of implementation of the controls. The Pontryagin Maximum Principle was employed to find the necessary conditions for the existence of the optimal controls. The numerical simulations show that the effective controls could reduce the diseases in the community. The incremental cost-effectiveness ratio was used to quantify the cost-effectiveness analysis. It is found that the control strategy which implements vaccination, treatment of dysentery diarrhea and sanitation of the environment is the most cost-effective. [ABSTRACT FROM AUTHOR]

In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease-free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for R0>1. The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is R0=1.1208. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (βh). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease. [ABSTRACT FROM AUTHOR]

Measles is an awfully contagious acute viral infection. It can be fatal, causing cough, red eyes, followed by a fever and skin rash with signs of respiratory infection. In this paper, we propose and analyze a model describing the transmission dynamics of a measles epidemic in the human population using the stability theory of differential equations. The model proposed undergoes a backward bifurcation for some parameter values. Sensitivity analysis is carried out on the model parameters in order to determine their impact on the disease dynamics. We extend the model to an optimal control problem by including time-dependent control variables: prevention, treatment of infected people and vaccination of the susceptible humans. In an attempt to minimize the infected people and the cost applied we design the cost functional. Next, we show that optimal control exists for the system, and the Pontryagin maximum principle is employed to characterize the continuous controls. Numerical simulation is performed to justify the analytical results and discussed quantitatively. [ABSTRACT FROM AUTHOR]