Global stability of general cholera models with nonlinear incidence and removal rates

Wang, Yi; Cao, Jinde

doi:10.1016/j.jfranklin.2015.03.030

Cited by 44 publications

(16 citation statements)

References 34 publications

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“…The epidemiological implication of this is that a waterborne disease can be eradicated from the entire community where individuals are exposed to multiple contaminated water sources irrespective of the initial sizes of the subpopulation provided

{scriptR}_{0} < 1

. This result is consistent with the global stability of the DFE result in Wang and Cao [].…”

Section: Model Analysissupporting

confidence: 85%

Stability Analysis and Optimal Vaccination of a Waterborne Disease Model With Multiple Water Sources

Collins

Govinder

2016

Natural Resource Modeling

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Abstract. Waterborne diseases are among the major health problems facing the world today. This is especially true in developing countries where there is limited access to clean water. In such settings, even when multiple water sources exist, they tend to be contaminated. In this paper, we formulate a waterborne disease model where individuals are exposed to multiple contaminated water sources. The fundamental mathematical features of the model such as the basic reproduction number R 0 and final epidemic size are obtained and analyzed accordingly. The global stability analysis of the disease-free equilibrium is performed. The model is later extended by considering vaccination as a possible control intervention strategy. An optimal control problem is constructed to investigate the existence of an optimal control function that reduces the spread of the disease with minimum cost. We support our analytical predictions by carrying out numerical simulations using published and estimated data from the recent cholera outbreak in Haiti.

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{scriptR}_{0} < 1

. This result is consistent with the global stability of the DFE result in Wang and Cao [].…”

Section: Model Analysissupporting

confidence: 85%

Stability Analysis and Optimal Vaccination of a Waterborne Disease Model With Multiple Water Sources

Collins

Govinder

2016

Natural Resource Modeling

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“…They used the optimal control theory via the Pontryagin's maximum principle and genetic algorithm based on the forward and backward difference approximation to minimize the infected populations and the costs. Other cholera models include but not limited to other works …”

Section: Introductionmentioning

confidence: 99%

“…Other cholera models include but not limited to other works. [35][36][37][38][39] In the present study, in order to understand the impact of media coverage on the spread and control of cholera, a mathematical model will be proposed to capture the dynamics of the effect of awareness programs. Moreover, one of our main aims is to explore the role of media coverage on the spread of cholera in the model.…”

Section: Introductionmentioning

confidence: 99%

Cholera model incorporating media coverage with multiple delays

Shu

Yang

2018

Math Methods in App Sciences

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In order to investigate the impact of awareness programs and time delays on the cholera outbreaks, we propose a cholera epidemic model, incorporating awareness programs by media as a separate class and two time‐delay factors. The bifurcation theory is applied to explore the variety of dynamics of this model for various combinations of the delays when R0>1. Moreover, we analyze the direction, stability, and period of the bifurcating periodic solutions arising through Hopf bifurcation by using the normal form concept and the center manifold theory. Finally, we present numerical simulations to verify the main theoretical results.

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“…They can minimize the risk if they become well-informed and aware about the prevalence. Other research articles are also studied to improve this modeling process [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study

Roy

Saha

2018

Adv Differ Equ

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In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of differential equations the model is analyzed qualitatively. The equilibrium points in the local and global stability proof are found to be stable under certain conditions. Further, we use Pontryagin's Minimum Principle in the time-dependent constant control case to derive necessary conditions for the optimal control of the disease. Sensitivity analysis is also performed to check the robustness of the model with respect to small changes in parametric values of the system. In order to predict the long term dynamics of the disease, projections are made. These studies reveal that HIV incidence could be substantially reduced by improving the test-and-treat strategy and implication of media awareness.

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Global stability of general cholera models with nonlinear incidence and removal rates

Cited by 44 publications

References 34 publications

Stability Analysis and Optimal Vaccination of a Waterborne Disease Model With Multiple Water Sources

Stability Analysis and Optimal Vaccination of a Waterborne Disease Model With Multiple Water Sources

Cholera model incorporating media coverage with multiple delays

Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study

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