Modeling the Combined Effect of Hepatitis B Infection and Heavy Alcohol Consumption on the Progression Dynamics of Liver Cirrhosis

Dano, Lemesa Bedjisa; Koya, Purnachandra Rao; Keno, Temesgen Duressa

doi:10.1155/2022/6936396

Cited by 10 publications

(8 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Defnition 1. Te normalized forward sensitivity index of R 0 that can be diferentiable with respect to a particular parameter M is defned as [31,32]…”

Section: Sensitivity Analysismentioning

confidence: 99%

Optimal Control Strategies of COVID-19 Dynamics Model

Keno

Etana

2023

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper, we proposed the optimal control for the dynamics of COVID-19 with cost effectiveness strategies. First, we showed that model solution is positive, and bounded in a fixed domain. Besides, we used next-generation matrix to compute the basic reproduction number. If the basic reproduction number is less than one, then the disease-free equilibrium point is both locally and globally stable, respectively, via the help of Jacobian matrix and Lyapunov function, otherwise the endemic equilibrium occurs. The sensitivity analysis was determined with regard to all basic parameters. Then the model is fitted with COVID-19 infected cases reported from October 1, 2022 to October 30, 2022 in Ethiopia. The values of model parameters are then estimated from the data reported using the least-square method. Furthermore, using Pontryagin maximum principle, the model is extended to optimal control incorporating three control namely: personal protective, vaccination, and treatment of infected humans. Finally, based upon the numerical simulation of optimal controls and cost effectiveness analysis, the most optimal and less costly strategy to minimize the disease is combination of vaccination and treatment of infected.

show abstract

“…Defnition 1. Te normalized forward sensitivity index of R 0 that can be diferentiable with respect to a particular parameter M is defned as [31,32]…”

Section: Sensitivity Analysismentioning

confidence: 99%

Optimal Control Strategies of COVID-19 Dynamics Model

Keno

Etana

2023

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section, we carried out a sensitivity analysis of the parameters in the basic reproduction number to identify their impact on the transition dynamics of the COVID-19 pandemic. To go through this section, we used the normalized sensitivity index definition as stated in [30]. The Normalized forward sensitivity index of a variable, R c , that…”

Section: Sensitivity Analysismentioning

confidence: 99%

Modeling and Optimal Control Analysis Applied to Real Cases of COVID-19 Pandemic with Double Dose Vaccination in Ethiopia

Legesse,

Rao,

Keno

2023

Journal of Applied Mathematics

Self Cite

View full text Add to dashboard Cite

The novel coronavirus is a recently discovered member of one of the largest families of viruses with symptoms ranging from a simple cold to excruciating respiratory agony. In the present paper, a deterministic mathematical model is formulated to estimate the transmission dynamics of COVID-19 with the inclusion of control strategies like (i) double-dose vaccination, (ii) prevention, and (iii) treatment. In addition, instead of considering all infectious humans as one unit, we separate them into symptomatic and asymptomatic groups, and the impact is analyzed. This separation is meaningful because various reports indicate that the asymptomatic cases will spread the disease more than the symptomatic cases. The model is proved to be mathematically well-posed and biologically meaningful by showing positivity and boundedness of the solution using the appropriate initial conditions. For the reproduction number, a parametric formula is constructed, and also the associated numerical value is calculated from the reported real data in Ethiopia. Moreover, disease-free and endemic equilibria are determined, and their local and global stabilities are discussed using the Lyapunov function technique. These equilibria are found to be locally asymptotically stable if R 0 < 1 and R 0 > 1 , respectively. Following the model fitting and estimation of the parameter values, sensitivity analysis was performed in order to analyze the impact of each parameter on transmission dynamics. In other words, this study can be used to evaluate how major model parameters affect transmission dynamics and control. Utilizing Pontryagin’s maximal principle, the best control measures are implemented with the aim of lowering the burdens associated with infection, prevention, and treatment. To comprehend and visualize the impact of control techniques on the development of the disease and to illustrate the analytical findings generated in this study, numerical simulation studies are conducted. Finally, the output of the study illustrates that adhering to all the control strategies has a big impact on minimizing the transmission of the disease in society. Which means that if the control strategies are well managed by the concerned body, then the burden of the disease is reduced quickly in the Ethiopian population.

show abstract

“…The sensitivity analysis is used to identify the parameters that have a large influence on the basic reproduction number ðR 0 Þ. To perform the sensitivity analysis, the method described in [23][24][25] is used. Definition 4 (see [23,24]).…”

Section: Model Parameter Sensitivity Analysismentioning

confidence: 99%

Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

Keno

Dano

Makinde

2022

Computational and Mathematical Methods

Self Cite

View full text Add to dashboard Cite

In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.

show abstract

Modeling the Combined Effect of Hepatitis B Infection and Heavy Alcohol Consumption on the Progression Dynamics of Liver Cirrhosis

Cited by 10 publications

References 27 publications

Optimal Control Strategies of COVID-19 Dynamics Model

Optimal Control Strategies of COVID-19 Dynamics Model

Modeling and Optimal Control Analysis Applied to Real Cases of COVID-19 Pandemic with Double Dose Vaccination in Ethiopia

Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

Contact Info

Product

Resources

About