Optimal Control Analysis of a Mathematical Model for Breast Cancer

Oke, Segun Isaac; Matadi, Maba Boniface; Xulu, S. S.

doi:10.3390/mca23020021

Cited by 32 publications

(13 citation statements)

References 41 publications

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“…The objective functional (15) includes the cost control function for personal protection 1 2 B 1 u 2 1 (t), the cost control function for application of prophylaxis (liver-stage therapy) 1 2 B 2 u 2 2 (t), cost of treating infectious humans 1 2 B 3 u 2 3 (t) and 1 2 B 4 u 2 4 (t), which represents the cost control function associated with spraying of insecticides. In this work, as in other studies [14,17,22,25], the cost control functions take a quadratic form.…”

Section: Analysis Of the Optimal Control Modelmentioning

confidence: 99%

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Olaniyi

Okosun

Adesanya

et al. 2020

Journal of Biological Dynamics

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A mathematical model of malaria dynamics with naturally acquired transient immunity in the presence of protected travellers is presented. The qualitative analysis carried out on the autonomous model reveals the existence of backward bifurcation, where the locally asymptotically stable malaria-free and malaria-present equilibria coexist as the basic reproduction number crosses unity. The increased fraction of protected travellers is shown to reduce the basic reproduction number significantly. Particularly, optimal control theory is used to analyse the non-autonomous model, which incorporates four control variables. The existence result for the optimal control quadruple, which minimizes malaria infection and costs of implementation, is explicitly proved. Effects of combining at least any three of the control variables on the malaria dynamics are illustrated. Furthermore, the cost-effectiveness analysis is carried out to reveal the most cost-effective strategy that could be implemented to prevent and control the spread of malaria with limited resources.

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Section: Analysis Of the Optimal Control Modelmentioning

confidence: 99%

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Olaniyi

Okosun

Adesanya

et al. 2020

Journal of Biological Dynamics

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“…is the probability that a human will survive the exposed state, to become infectious, while 1 (µ h +τ h +δ h ) is the average duration of the infectious period of a human. In Equation (14),…”

Section: Stability Of the Disease-free Equilibrium (Dfe)mentioning

confidence: 99%

Qualitative Analysis of a Dengue Fever Model

Gbadamosi

Ojo

Oke

et al. 2018

MCA

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In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh-Hurwitz criterion, along with Descartes' rule of signs change, established the local asymptotically stability of the model whenever R 0 < 1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model.

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“…The authors in [7] examined the significance of short-term human travellers on transmission dynamics of Malaria. The chance of an individual developing breast cancer depends on the level of the immune system, the efficacy of the anti-cancer drug and the rate at which the ketogenic diet is taken [8,9]. [10] in 2015 used an SIR epidemic model to model the 2014 Ebola outbreak in West Africa and introduced vaccination to the susceptible as part of the control system.…”

Section: Introductionmentioning

confidence: 99%

On the reproduction number and the optimal control of infectious diseases in a heterogenous population

et al. 2020

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The effect of infectious diseases cannot be overemphasised. The continuing surfacing of the infectious diseases gives the stakeholders a great concern. In this paper, the nature of the spread of Ebola virus outbreak in West Africa in 2014 is studied. We develop a model that analyses the spread of infectious diseases, and the reproduction number is determined by using the next generation matrix method. Finally, the effects of treatment of the infected individuals and vaccination of the susceptible population as the control strategies are looked into. The optimal control system showed that the combination of the two strategies proved more effective.

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Optimal Control Analysis of a Mathematical Model for Breast Cancer

Cited by 32 publications

References 41 publications

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Qualitative Analysis of a Dengue Fever Model

On the reproduction number and the optimal control of infectious diseases in a heterogenous population

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