Mathematical Modelling of Population Growth: The Case of Logistic and  Von Bertalanffy Models

Dawed, Mohammed Yiha; Koya, Purnachandra Rao; Goshu, Ayele Taye

doi:10.4236/ojmsi.2014.24013

Cited by 15 publications

(10 citation statements)

References 9 publications

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“…Moreover, for a particular value of birth parameter , the population sizes of both prey and predator converge to same asymptote. These findings are similar with those in [7] [8].…”

Section: Simulation Studysupporting

confidence: 83%

“…This result is different, for example, for the case of logistic prey model [7] for which the minimum point occurs at 0 min 1 1 log…”

Section: Case III ( )mentioning

confidence: 89%

“…The predator-prey problem has been interesting to many researchers [1]- [7]. Modelling population growth of interacting species involves differential equations [1] [2].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model

Goshu¹,

Koya²

2015

OJMSi

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The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey's grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor's series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.

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“…Moreover, for a particular value of birth parameter , the population sizes of both prey and predator converge to same asymptote. These findings are similar with those in [7] [8].…”

Section: Simulation Studysupporting

confidence: 83%

“…This result is different, for example, for the case of logistic prey model [7] for which the minimum point occurs at 0 min 1 1 log…”

Section: Case III ( )mentioning

confidence: 89%

See 1 more Smart Citation

Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model

Goshu¹,

Koya²

2015

OJMSi

Self Cite

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“…Wali et al (2012) also researched using logistic equation as a model for population growth in Uganda. Further work on population modeling is available (Dawed et al, 2014;Shepherd and Stojkov 2007, Law et al 2003, Wali et al, 2011 in Rwanda. Very little research has been done on the projection of population growth in Bangladesh.…”

Section: Introductionmentioning

confidence: 99%

Modeling on population growth and its adaptation: A comparative analysis between Bangladesh and India

Karim

Uddin

Rana

et al. 2020

JANS

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The biggest challenge in the world is population growth and determining how society and the state adapt to it as it directly affects the fundamental human rights such as food, clothing, housing, education, medical care, etc. The population estimates of any country play an important role in making the right decision about socio-economic and population development projects. Unpredictable population growth can be a curse. The purpose of this research article is to compare the accuracy process and proximity of three mathematical model such as Malthusian or exponential growth model, Logistic growth model and Least Square model to make predictions about the population growth of Bangladesh and India at the end of 21st century. Based on the results, it has been observed that the population is expected to be 429.32(in million) in Bangladesh and 3768.53 (in million) in India by exponential model, 211.70(in million) in Bangladesh and 1712.94(in million) in India by logistic model and 309.28 (in million) in Bangladesh and 2686.30 (in million) in India by least square method at the end of 2100. It was found that the projection data from 2000 to 2020 using the Logistic Growth Model was very close to the actual data. From that point of view, it can be predicted that the population will be 212 million in Bangladesh and 1713 million in India at the end of the 21st century. Although transgender people are recognized as the third sex but their accurate statistics data is not available. The work also provides a comparative scenario of how the state has adapted to the growing population in the past and how they will adapt in the future.

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“…The Lotka -Volterra predator-prey equations are first-order and nonlinear differential equations defined as [1,2,3,4,6,7,9].…”

Section: Lotka -Volterra Predator -Prey Modelsmentioning

confidence: 99%

Analysis of Prey – Predator System with Prey Population Experiencing Critical Depensation Growth Function

Dawed¹

2015

AJAM

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Abstract:In this paper we have presented a pair of coupled differential equations to represent a prey -predator system. It is assumed that the growth of the prey population follows critical depensation function and that of the predator population is negative in absence of the prey population. The critical depensation function is special since the growth rate is negative initially but positive later on. This function is stable both at the origin and at the carrying capacity while unstable at the critical mass quantity. The maximum and minimum rates of the critical depensation model are verified. It can be interpreted here that the prey represent fish and the predator represent a kind of birds that mostly feeding on fish to live. We showed the solution of the model is positive and bounded. The mathematical model of the system consisting of 7 parameters is constructed and shown that the non -dimensionalization decreases the number of model parameters to 4. The deterministic behavior of the model around feasible equilibrium points and criteria of the interior positive equilibrium points and their stability are explained. The trivial equilibrium point is always stable while the two axial equilibrium points and the lone interior equilibrium point are either stable or unstable depending on the conditions imposed on the parameters. The criterion for the existence of the limit cycle and the region of existence of interior equilibrium point are identified. Global stability of interior equilibrium points is also studied. For the interior equilibrium point of the model (i) the region of existence is identified (ii) Dulac's criteria is applied to find the limit cycle and (iii) Lyaponov function is used to analyze the global stability. Simulation study of the model is conducted in support of the analytical analysis. To solidify the analytical results numerical simulations are provided for hypothetical set of parametric values.

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Mathematical Modelling of Population Growth: The Case of Logistic and Von Bertalanffy Models

Cited by 15 publications

References 9 publications

Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model

Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model

Modeling on population growth and its adaptation: A comparative analysis between Bangladesh and India

Analysis of Prey – Predator System with Prey Population Experiencing Critical Depensation Growth Function

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