Optimal control of a two teams prey-predator interaction model

Aly, Shaban; Elettreby, M. F.

doi:10.18514/mmn.2015.1079

Cited by 4 publications

(2 citation statements)

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“…The interaction between human and animals or among animals themselves may results into disease transmission which destabilize the ecosystem. The studies of [3,6,9,17,26] employed modelling techniques to analyse ecological aspect of interacting species of various animals.…”

Section: Introductionmentioning

confidence: 99%

“…Vaccination provides a dormant pathogen in susceptible population which allows the vaccinated animal to produce strong antibodies against the weaker pathogen [3]. Currently, the phenomenon of prey predator ecosystem is well-studied with and without disease infection and these species in ecosystem do not exist alone [13] and the mechanisms of saving the population from extinction is biologically controlled in ecosystem [6]. The existence of ND in chickens is a big loss to human (farmers).…”

Section: Introductionmentioning

confidence: 99%

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Optimal control and cost effectiveness analysis for Newcastle disease eco-epidemiological model in Tanzania

Hugo

Makinde

Kumar

et al. 2016

Journal of Biological Dynamics

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In this paper, a deterministic compartmental eco-epidemiological model with optimal control of Newcastle disease (ND) in Tanzania is proposed and analysed. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin's maximum principle and the numerical values of model parameters were estimated using maximum likelihood estimator. Three control strategies were incorporated such as chicken vaccination (preventive), human education campaign and treatment of infected human (curative) and its' impact were graphically observed. The incremental cost effectiveness analysis technique used to determine the most cost effectiveness strategy and we observe that combination of chicken vaccination and human education campaign strategy is the best strategy to implement in limited resources. Therefore, ND can be controlled if the farmers will apply chicken vaccination properly and well in time. ARTICLE HISTORY

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control and cost effectiveness analysis for Newcastle disease eco-epidemiological model in Tanzania

Hugo

Makinde

Kumar

et al. 2016

Journal of Biological Dynamics

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Multi‐drug antimicrobial resistance model

Elettreby

Ahmed

2020

Math Methods in App Sciences

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In this paper, we give a simple mathematical model for a multi-drug antimicrobial resistance. The model describes the dynamics of the susceptible and three classes of infected populations. The first class of the infected society is sensitive to the first antimicrobial drug but resisted to the second drug. The other infected community responds to the second antimicrobial drug but resistant to the first drug, and the third class shows resistance to both of the two drugs. The stability conditions of the multi-drug antimicrobial resistance equilibrium states are derived. Also, we illustrated the analytical results by some numerical simulations. Finally, we used the multiobjective optimization approach to find the minimum doses of antimicrobial drugs.

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