Analysis of a waterborne disease model with socioeconomic classes

Collins, Obiora Cornelius; Robertson, Suzanne L.; Govinder, K. S.

doi:10.1016/j.mbs.2015.08.016

Cited by 12 publications

(13 citation statements)

References 23 publications

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“…On the other hand, the spread of virus/worm in computer networks have been modeled with DEs and optimal attack strategies have been decided [7] and the result can be useful to set network security protocols up. Another model including the influence of socioeconomic classes is constructed for multi patches [8]. As a different way to model waterborne diseases, networks are incorporated to express both indirect environmentto-human and direct human-to-human transmission routes [9].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Problem of a Non-integer Order Waterborne Pathogen Model in Case of Environmental Stressors

Yıldız

2019

Front. Phys.

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In this work, we extend a mathematical model, which has been proposed for susceptible and infected compartments together with pathogen population, by including recovered subgroup. It is known that environmental pollution, such as contaminated drinking water and lack of an ordinary toilet, affects individuals and such negative impacts can be defined as "stressors." In order to include the influence of such stressors, susceptible subpopulation has been divided into two groups as the one affected by stress or not. Thus, spread of the disease is expressed in terms of a five-dimensional system. Moreover, we extend this model with the use of a time fractional derivative due to non-local effects of water pollution and we prove that the solution is non-negative and bounded from above. Then, we perform stability analysis for the disease-free equilibrium point. Afterward, the next step is to apply optimal control theory to optimize the decay rate of pathogens and the stress related parameters so that the number of infected individuals and the pathogen population can be minimized. Finally, we present some numerical results to find out the most appropriate control policy and the effect of the fractional order.

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Section: Introductionmentioning

confidence: 99%

Optimal Control Problem of a Non-integer Order Waterborne Pathogen Model in Case of Environmental Stressors

Yıldız

2019

Front. Phys.

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“…Even with the availability of control measures, affordability is often the greatest obstacle for many communities where diseases are endemic. The spread of waterborne diseases are often associated with poverty, limited resources, and low socioeconomic status [2,7]. Optimal control theory can point to efficient approaches to reduce the spread of a disease with minimum costs [4,8].…”

Section: Introductionmentioning

confidence: 99%

“…Understanding how these factors interact to influence the dynamics of waterborne diseases are challenging, making the dynamics of waterborne diseases complex. Several theoretical studies have taken some of these factors into account to improve the understanding of waterborne disease dynamics and subsequently investigate the possible means of reducing the diseases [7,11,19,[21][22][23][24][25][26]. Even though these studies have contributed immensely in improving the understanding of waterborne disease dynamics, theoretical studies for waterborne disease dynamics and control are not complete.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Study

Collins

Duffy

2018

Journal of Applied Mathematics

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A mathematical model is formulated that captures the essential dynamics of waterborne disease transmission under the assumption of a homogeneously mixed population. The important mathematical features of the model are determined and analysed. The model is extended by introducing control intervention strategies such as vaccination, treatment, and water purification. Mathematical analyses of the control model are used to determine the possible benefits of these control intervention strategies. Optimal control theory is utilized to determine how to reduce the spread of a disease with minimum cost. The model is validated using a cholera outbreak in Haiti.

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“…[], Collins and Govinder [], Collins et al. []). Models such as these can assist understanding and the development of effective strategies (Capasso and Paveri‐Fontana [], Codeco [], Hartley et al.…”

Section: Introductionmentioning

confidence: 99%

“…[], Collins and Govinder [], Collins et al. []). So, to devise better intervention measures to reduce the spread of waterborne diseases, we consider the transmission dynamics using an n‐patch model.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Intervention Strategies Using an N‐patch Waterborne Disease Model

Collins

Duffy

2016

Natural Resource Modeling

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Waterborne diseases are an important concern in public health, especially in communities with limited access to clean water. Different community subpopulations can require different copping strategies for the same diseases. Modeling is one method to assist understanding and the development of effective strategies. To this end, we investigated the use of meta-population models with three types of control interventions: vaccination, treatment, and water purification. Important mathematical features of the model are determined and examined. Optimal control, applied to the model, is also formulated to determine the effective strategies to reduce the spread of the disease. For example, using optimal control, a four-fold reduction in infected individuals is possible. The value of such an improvement to the communities involved would be significant.

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Analysis of a waterborne disease model with socioeconomic classes

Cited by 12 publications

References 23 publications

Optimal Control Problem of a Non-integer Order Waterborne Pathogen Model in Case of Environmental Stressors

Optimal Control Problem of a Non-integer Order Waterborne Pathogen Model in Case of Environmental Stressors

Analysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Study

Optimal Control Intervention Strategies Using an N‐patch Waterborne Disease Model

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