Optimal control of malaria transmission dynamics combining some usual strategies and an imperfect vaccine

2020 ◽  
Vol 40 (1) ◽  
pp. 33
Author(s):  
Ousmane Koutou ◽  
Boureima Sangaré ◽  
Bakary Traoré
Keyword(s):  
Optimal Control ◽  
Malaria Transmission ◽  
Transmission Dynamics

scholarly journals Parameter-dependent transmission dynamics and optimal control of foot and mouth disease in a contaminated environment

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Francis Mugabi ◽  
Joseph Mugisha ◽  
Betty Nannyonga ◽  
Henry Kasumba ◽  
Margaret Tusiime
Keyword(s):  
Optimal Control ◽  
Deterministic Model ◽  
Foot And Mouth Disease ◽  
Decay Rates ◽  
Mouth Disease ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Optimality System ◽  
Foot And Mouth ◽  
Environmental Decontamination

AbstractThe problem of foot and mouth disease (FMD) is of serious concern to the livestock sector in most nations, especially in developing countries. This paper presents the formulation and analysis of a deterministic model for the transmission dynamics of FMD through a contaminated environment. It is shown that the key parameters that drive the transmission of FMD in a contaminated environment are the shedding, transmission, and decay rates of the virus. Using numerical results, it is depicted that the host-to-host route is more severe than the environmental-to-host route. The model is then transformed into an optimal control problem. Using the Pontryagin’s Maximum Principle, the optimality system is determined. Utilizing a gradient type algorithm with projection, the optimality system is solved for three control strategies: optimal use of vaccination, environmental decontamination, and a combination of vaccination and environmental decontamination. Results show that a combination of vaccination and environmental decontamination is the most optimal strategy. These results indicate that if vaccination and environmental decontamination are used optimally during an outbreak, then FMD transmission can be controlled. Future studies focusing on the control measures for the transmission of FMD in a contaminated environment should aim at reducing the transmission and the shedding rates, while increasing the decay rate.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

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