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Lipid Concentration Effect on Blood Flow Through an Inclined Arterial Channel with Magnetic Field
Kubugha Wilcox Bunonyo,
Emeka Amos
Issue:
Volume 5, Issue 3, September 2020
Pages:
129-137
Received:
8 May 2020
Accepted:
22 May 2020
Published:
4 June 2020
Abstract: The purpose of this research is to formulate mathematical models to investigate lipid concentration effect on blood flow though an inclined arterial channel with magnetic field. The formulated coupled partial differential equations were made dimensionless and reduced to ordinary differential equation using a perturbation technique, the nonlinear ordinary differential equations were solved analytically for the blood velocity and lipid concentration profiles respectively with some resultant pertinent parameters. Numerical simulations were carried out using Mathematica codes developed by the authors for the flow profiles by carefully varying the pertinent parameters to study the effect of each of the parameters on velocity and concentration profiles respectively. It is notice that the solutal Grashoff number, Darcy number, angle of inclination, time and the treatment parameters respectively causes the velocity profiles to increase, while the parameters such as the onset, length of stenosis, Schmidt number, magnetic field intensity, and pulse rate respectively decelerate the velocity profile. Secondly, the parameters such as length of stenosis, the pulse rate, Schmidt number and the treatment parameters decelerate the concentration profile while the onset parameter increases the concentration profile and the results were presented graphically. We can conclude that lipid concentration and some of the resulted pertinent parameters either increases or decreases the flow profiles and of great importance in studying blood velocity in arterial channel.
Abstract: The purpose of this research is to formulate mathematical models to investigate lipid concentration effect on blood flow though an inclined arterial channel with magnetic field. The formulated coupled partial differential equations were made dimensionless and reduced to ordinary differential equation using a perturbation technique, the nonlinear or...
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Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria
Anthony Anya Okeke,
Ahmed Dauda Abubakar,
Jerimiah Jerry Gambo,
Phidelia Ramatu Waziri-Ugwu
Issue:
Volume 5, Issue 3, September 2020
Pages:
138-145
Received:
4 May 2020
Accepted:
25 May 2020
Published:
16 June 2020
Abstract: In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming. The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the population from extinction. The data for this work are obtained from fish owners of selected pond in Bade (Gashua). Although, fish farming has been commercialized in Bade but there is little or no literature available in studying fish harvesting strategies. The Logistic model is appropriate for population growth of fishes when overcrowding and competition for the resource are taken into consideration. The objectives of the study where to estimate the highest continuing yield from fish harvesting strategies implemented. We compare the results obtained between the three strategies and observed the best harvesting strategy for the selected fish farm is periodic (seasonal) harvesting. The periodic harvesting strategy optimizes the harvest while maintaining stable the population of fish if the harvesting is lower or equal with the bifurcation point. Our findings can assist fish farmers in Bade, Yobe State, North East Nigeria, to increase fish supply to meet its demand and positively affect the economic growth of the area.
Abstract: In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming. The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the populatio...
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Modelling the Dynamics of COVID-19 Disease with Contact Tracing and Isolation in Ghana
Eric Neebo Wiah,
Ernest Danso-Addo,
Daniel Ekow Bentil
Issue:
Volume 5, Issue 3, September 2020
Pages:
146-155
Received:
9 June 2020
Accepted:
23 June 2020
Published:
6 July 2020
Abstract: We have formulated a mathematical model to investigate the transmission dynamics of the current novel COVID-19 disease outbreak in Ghana. The coronavirus originated from Wuhan,, China. Majority of people who contact the disease experience mild to moderate respiratory illness and recover. The elderly and people with underlying health issues experience severe complications. A plethora of measures have been taken by the government of Ghana to curtail the disease. The model considers, among other things, quarantining and testing of immigrants, contact tracing and isolation in the form of quarantining or hospitalization, as control measures in mitigating the spread of the pandemic. Our model considers the following classes: susceptible, exposed, infectious, quarantine, treatment and recovery class. The steady-state solution was calculated and the basic reproduction number for this model calculated and used as a threshold to determine the asymptotic behaviour of the model. Our analytical and numerical results show a close dependence of the basic reproductive number on epidemic parameters. The aim of this paper was to incorporate the various intervention strategies into the model and ascertain their impact on COVID-19. Some of the methods employed in the analysis include the Next Generation Matrix and the Jacobian Matrix. Our simulations results correlate well with data and indicate that early quarantine and a high quarantine rate are crucial to the control of COVID-19. Thus, current preventative measures, such as isolation, contact tracing and treatment are, indeed, critical components in the control of COVID-19 until appropriate cure or vaccine is found.
Abstract: We have formulated a mathematical model to investigate the transmission dynamics of the current novel COVID-19 disease outbreak in Ghana. The coronavirus originated from Wuhan,, China. Majority of people who contact the disease experience mild to moderate respiratory illness and recover. The elderly and people with underlying health issues experien...
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Modeling and Stability Analysis of a Three Species Ecosystem with the Third Species Response to the First Species in Sigmoid Functional Response Form
Geremew Kenassa Edessa,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 3, September 2020
Pages:
156-166
Received:
1 May 2020
Accepted:
18 June 2020
Published:
4 August 2020
Abstract: In this paper, a three species eco system, involving three pairs is considered modeled to examine the stability. Among the three species, one plays dual roles which are a host and an enemy with Monod response. In the first place model assumptions and formulation was carried out for investigations. The biological feasibility of the system is checked. That is positivity and boundedness of the model is verified. It is shown that biologically valid. The dynamical behavior of the proposed model system was analyzed qualitatively. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. All the equilibrium states are identified and the local asymptotic stability of some of the equilibrium states is examined by considering the set criteria. It is observed that among the states, the state in which the Prey and its Host species are exist is stable and the state where the Predator/Ammensal species is washed out is asymptotically stable. The global stability of the co-existence of the species was investigated by constructing a suitable Lyapunov function. To support our analytical studies, some numerical simulations was performed susing some mathematical software and the results were forwarded in the last section.
Abstract: In this paper, a three species eco system, involving three pairs is considered modeled to examine the stability. Among the three species, one plays dual roles which are a host and an enemy with Monod response. In the first place model assumptions and formulation was carried out for investigations. The biological feasibility of the system is checked...
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Modelling of Malaria Transmission Using Delay Differential Equation
Kipkirui Mibei,
Kirui Wesley,
Adicka Daniel
Issue:
Volume 5, Issue 3, September 2020
Pages:
167-175
Received:
10 May 2020
Accepted:
14 July 2020
Published:
4 August 2020
Abstract: Malaria is one of the major causes of deaths and ill health in endemic regions of sub-Saharan Africa and beyond despite efforts made to prevent and control its spread. Epidemiological models on how malaria is spread have made a substantial contribution on the understanding of disease changing aspects. Previous researchers have used Susceptible –Exposed-Infectious-Recovered (SEIR) model to explain how malaria is spread using ordinary differential equations. In this paper we develop mathematical SEIR model to define the dynamics of the spread of malaria using Delay differential equations with four control measures such as long lasting treated insecticides bed nets, intermittent preventive treatment of malaria in pregnant women (IPTP), intermittent preventive treatment of malaria in infancy (IPTI) and indoor residual spraying. The model is analyzed and reproduction number derived using next generation matrix method and its stability is checked by Jacobean matrix. Positivity of solutions and boundedness of the model is proved. We show that the disease free equilibrium is locally asymptotically stable if R0<1 (R0 – reproduction number) and is unstable if R0>1. Numerical simulation shows that, with proper treatment and control measures put in place the disease is controlled.
Abstract: Malaria is one of the major causes of deaths and ill health in endemic regions of sub-Saharan Africa and beyond despite efforts made to prevent and control its spread. Epidemiological models on how malaria is spread have made a substantial contribution on the understanding of disease changing aspects. Previous researchers have used Susceptible –Exp...
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Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies
Rotich Kiplimo Titus,
Lagat Robert Cheruiyot,
Choge Paul Kipkurgat
Issue:
Volume 5, Issue 3, September 2020
Pages:
176-182
Received:
17 July 2020
Accepted:
29 July 2020
Published:
10 August 2020
Abstract: Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunity or death. This implies that, mathematical model will place individuals into four compartments, that is, Susceptible (S), Exposed (E), Infective (I) and Recovered (R), representing a SEIR model. Due to its fast fatal capacity, changes in population due to births do not affect the disease dynamics, but for the purpose of monitoring deaths, a compartment for deaths (D) is incorporated. The analysis of intervention strategies necessitates modification of SEIR model to include Quarantine (Q), Isolation (I), and Homebased care (H) compartments. In this paper, Public health Education Campaign, Quarantine and testing, Isolation, Treatment, use of facemask and Social distance intervention strategies were analyzed. Numerical results indicated that the most responsive mitigation strategy is use of quality facemask and observance of social distance. At 90% adherence to this plan reduces the force of infection from β=0.0197 to β=0.0033. This will consequently reduce the basic reproductive ratio from R0=14.0362 to R0=2.3388, which prevents 99.37% of population from contracting the disease. However, it is shown that a combination of other intervention strategies have synergetic effect of bringing down reproductive ratio to less than one. Sensitivity analysis indicated that isolation and treatment of infected individuals in government facilities is the most effective method with elasticity of v=-6.4, but due to financial implications, the alternative homebased care need to be fortified. This means, for Covid-19 pandemic to die off, we require early identification of infected individuals through mass testing and immediate isolation. In order to optimize financial constraints associated with isolation, currently at α=11%, the threshold efficacy of other intervention strategies should be enhanced to; public health campaign є > 50%, complacency ξ < 30%, facemask quality c > 89%, social distance r > 2m, and mass testing τ > 0.27. With these interventions, it is estimated that the reproductive ratio, reduces to less than one after 225 days from the first occurrence of Covid-19, and the epidemic will then begin to decline gradually to insignificant levels.
Abstract: Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunit...
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Mathematical Eco-Epidemiological Model on Prey-Predator System
Abayneh Fentie Bezabih,
Geremew Kenassa Edessa,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 3, September 2020
Pages:
183-190
Received:
2 June 2020
Accepted:
23 June 2020
Published:
20 August 2020
Abstract: This paper presents infectious disease in prey-predator system. In the present work, a three Compartment mathematical eco-epidemiology model consisting of susceptible prey- infected prey and predator are formulated and analyzed. The positivity, boundedness, and existence of the solution of the model are proved. Equilibrium points of the models are identified. Local stability analysis of Trivial, Axial, Predator-free, and Disease-free Equilibrium points are done with the concept of Jacobian matrix and Routh Hourwith Criterion. Global Stability analysis of endemic equilibrium point of the model has been proved by defining appropriate Liapunove function. The basic reproduction number in this eco-epidemiological model obtained to be Ro=[β (μ3)2] ⁄ [qp2 (qp1Λ - μ1μ3)]. If the basic reproduction number Ro > 1, then the disease is endemic and will persist in the prey species. If the basic reproduction number Ro=1, then the disease is stable, and if basic reproduction number Ro < 1, then the disease is dies out from the prey species. Lastly, Numerical simulations are presented with the help of DEDiscover software to clarify analytical results.
Abstract: This paper presents infectious disease in prey-predator system. In the present work, a three Compartment mathematical eco-epidemiology model consisting of susceptible prey- infected prey and predator are formulated and analyzed. The positivity, boundedness, and existence of the solution of the model are proved. Equilibrium points of the models are ...
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Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures
Demsis Dejene,
Tesfaye Worku,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 3, September 2020
Pages:
191-201
Received:
8 June 2020
Accepted:
28 June 2020
Published:
16 September 2020
Abstract: In this paper, a deterministic five compartmental mathematical model is developed and conducted simulations to study the dynamics of COVID-19 with the inclusion of self-protection and isolation as control measures. The model is shown mathematically and biologically valid by verifying that the solutions are both positive and bounded. Using next generation matrix method, the reproduction number is formulated. The disease free equilibrium point is found and shown that it is conditionally locally and globally asymptotically stable. Further, following Lyapunov function method Endemic equilibrium point is found and shown that it is conditionally globally asymptotically stable. Numerical simulation study is conducted by assigning reasonable values to the parameters. It is concluded that the spread of the disease can be brought under control if the control measures like Self-protection including social distancing and Isolation are implemented affectively. The results and the discussion are presented in the body of the paper lucidly.
Abstract: In this paper, a deterministic five compartmental mathematical model is developed and conducted simulations to study the dynamics of COVID-19 with the inclusion of self-protection and isolation as control measures. The model is shown mathematically and biologically valid by verifying that the solutions are both positive and bounded. Using next gene...
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