Mathematical Eco-Epidemiological Model on Prey-Predator System

Bezabih, Abayneh Fentie; Edessa, Geremew Kenassa; Koya, Purnachandra Rao

doi:10.11648/j.mma.20200503.17

Cited by 6 publications

(5 citation statements)

References 8 publications

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“…Basic Reproduction Number. For investing basic reproduction number R 0 , we will use next generation matrix method [23,24]. From our mathematical model, it is clear that the only relevant class of infected cells is tumor cells TðtÞ.…”

Section: Existence and Uniqueness Of The Solutionmentioning

confidence: 99%

Mathematical Modeling and Analysis on the Effects of Surgery and Chemotherapy on Lung Cancer

Ullah

Mallick

2023

Journal of Applied Mathematics

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Lung cancer is the biggest cause of cancer mortality worldwide and a major impediment to extending life expectancy. In comparison to other cancers, it has a relatively poor survival rate. In this paper, we have developed a mathematical model for lung cancer based on biological phenomena using nonlinear ordinary differential equations and analyzed it both analytically and numerically. According to the findings, CD8+ T cells and dendritic cells have a role in tumor cell variety. Surgery and chemotherapy have been used as treatment options, and we have observed that three doses of chemotherapy after surgery had the greatest results after examining several treatment options. During the treatment period, the cycle of each chemotherapy has been taken every 4 weeks, and the first dose has been taken after 28 days of surgery. Finally, we have evaluated the various starting dates for the best treatment choice and discovered that the patient who begins treatment sooner has a better probability of surviving.

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Section: Existence and Uniqueness Of The Solutionmentioning

confidence: 99%

Mathematical Modeling and Analysis on the Effects of Surgery and Chemotherapy on Lung Cancer

Ullah

Mallick

2023

Journal of Applied Mathematics

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“…Future Status of Expert Employees. Using the next generation matrix method [42], we will find the basic reproduction number R 0 . To examine the behaviour of dynamics of the expert's compartment, this class is considered for the discussion.…”

Section: Equilibrium Analysis By Solving the Following Equations Belo...mentioning

confidence: 99%

Mathematical Modeling for Optimal Management of Human Resources in Banking Sector of Bangladesh

Mallick,

Biswas

2023

Journal of Applied Mathematics

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A new mathematical model on human resources divided employees into two compartments, namely, fresher and expert employees, has been designed and analyzed. A system of ordinary nonlinear differential equations has three state variables including vacancies. This model describes the dynamics of the number of fresher employees and expert employees as well as vacancies and shows the impacts of training programs and benefits of provided facilities for employees. The equilibria of this proposed model are determined, and its stability at these points is checked. Moreover, characteristics of state variables with respect to parameters have been discussed. Using two optimal control variables, this study finds the maximum number of experts including the minimum cost of provided facilities as well as the training program based on Pontryagin’s maximum principle.

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“…Thus variables S t , I t , T t , and R t represent persons at different compartment which are positive quantities and will remain in ) * + for all time [9,10,13,16]. Theorem 2 [Boundedness] The positive solutions of mathematical models ( 1)-( 4) are bounded.…”

Section: Mathematical Analysis Of the Modelmentioning

confidence: 99%

“…Hence, feasible solution of the system of differential equations ( 1)-( 4) remains in the region Ωwhich is positively invariant set. Thus, the given mathematical model is meaningful and mathematically well posed in the domain of region Ω. hence, variables S t , I t , T t , &R t are bounded for all t [9,10,13,16].…”

Section: Mathematical Analysis Of the Modelmentioning

confidence: 99%

See 1 more Smart Citation

Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment

Bezabih¹,

Edessa²,

Koya³

2021

MMA

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In this paper, Mathematical Model of COVID-19 Pandemic is formulated and discussed. The positivity, boundedness, and existence of the solutions of the model equations are stated and proved. The Disease-free equilibrium point & endemic equilibrium points are identified. Stability Analysis of the model is done with the concept of Next generation matrix. we have investigated that Disease-free equilibrium point (DFEP) of the model is locally asymptotically stable if α≤β+δ+µ & unstable if α>β+δ+µ, The basic reproduction number (threshold value) R 0 is the largest eigen value in spectral radius matrix ρ. Thus, eigen values of spectral radius Matrix ρ are determined from the roots of characteristic polynomial equation, det[ρ-λI]=0, Hence, the basic reproduction number is R 0 =α / β. It is shown that if reproduction number is less than one, then COVID-19 cases will be reduced in the community. However, if reproduction number is greater than one, then covid-19 continue to persist in the Community. Lastly, numerical simulations are done with DEDiscover 2.6.4. Software. It is observed that with Constant treatment, increase or decrease contact rate among persons leads great variation on the basic reproduction number which is directly implies that infection rate plays a vital role on decline or persistence of COVID-19 pandemic.

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Mathematical Eco-Epidemiological Model on Prey-Predator System

Cited by 6 publications

References 8 publications

Mathematical Modeling and Analysis on the Effects of Surgery and Chemotherapy on Lung Cancer

Mathematical Modeling and Analysis on the Effects of Surgery and Chemotherapy on Lung Cancer

Mathematical Modeling for Optimal Management of Human Resources in Banking Sector of Bangladesh

Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment

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