An eco-epidemiological mathematical model with treatment and disease infection in both prey and predator population

Hugo, Alfred

doi:10.5897/jene12.013

Cited by 6 publications

(9 citation statements)

References 16 publications

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“…Te local dynamics of all the critical points listed above are performed by substituting the values in the Jacobian matrix (7) and fnding the eigenvalues of the matrix.…”

Section: Local Stability Analysis Of the Critical Pointsmentioning

confidence: 99%

“…Proposition 8. Te model system (7) has an optimum control pair (u * 1 , u * 2 ) that minimizes the objective functional J(u 1 , u 2 ) over the domain Γ with a corresponding solution of (s * , I * , y * , z).…”

Section: Existence Of Optimal Controlsmentioning

confidence: 99%

“…Tese days, mathematical ecology and mathematical epidemiology are integrated applied mathematics subfelds that have combined to form a new feld of study known as mathematical ecoepidemiology [2,5,6]. In a given ecosystem, regular cycles of prey and predator populations fuctuate due to external factors like infectious diseases, secondary predation, or climate changes [7][8][9]. Interaction of prey-predator systems is a nonlinear and complex phenomenon; because of its complexity, a number of ecoepidemiological studies are conducted by including diferent assumptions in their interaction [2,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…In a given ecosystem, regular cycles of prey and predator populations fuctuate due to external factors like infectious diseases, secondary predation, or climate changes [7][8][9]. Interaction of prey-predator systems is a nonlinear and complex phenomenon; because of its complexity, a number of ecoepidemiological studies are conducted by including diferent assumptions in their interaction [2,7,8]. A variety of infectious diseases have plagued prey-predator populations.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

Mekonen,

Bezabih,

Rao

2024

International Journal of Mathematics and Mathematical Sciences

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In this paper, the impact of viral illnesses on the predator-prey relationship with an optimal control analysis is studied. An ecoepidemiological model of four compartments, namely, susceptible prey, susceptible predator, infected prey, and infected predator populations, in the interaction of the prey-predator system is formulated. The fundamental tenet of our ecoepidemiology model is that sick predators do not engage in predation. It is confirmed that the system’s solution exists, is positive, and is bounded. The system’s equilibrium points are determined and computed. Lyapunov functions and a linearizing form are used for local and global stability analysis, respectively. The next generation matrix approach is used to calculate the threshold value for diseased predators and prey at the disease-free equilibrium point. Optimal treatment options for vulnerable and infected populations are established by applying optimal control theory to the ecoepidemiology model of a prey-predator system. MATLAB software is utilized to obtain numerical simulations that validate the analytical outcomes. The optimal control problem simulations demonstrate that the number of infected populations in a given prey-predator system can be decreased by implementing control measures.

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“…Te local dynamics of all the critical points listed above are performed by substituting the values in the Jacobian matrix (7) and fnding the eigenvalues of the matrix.…”

Section: Local Stability Analysis Of the Critical Pointsmentioning

confidence: 99%

Section: Existence Of Optimal Controlsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

Mekonen,

Bezabih,

Rao

2024

International Journal of Mathematics and Mathematical Sciences

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show abstract

“…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%

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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Dynamical study on three-species population eco-epidemiological model with fractional order derivatives

et al. 2021

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An eco-epidemiological mathematical model with treatment and disease infection in both prey and predator population

Cited by 6 publications

References 16 publications

Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

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

Dynamical study on three-species population eco-epidemiological model with fractional order derivatives

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