Fuzzy Parameter Based Mathematical Model on Forest Biomass

2018 ◽  
Vol 13 (04) ◽  
pp. 179-193 ◽  
Author(s):  
Prabir Panja
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Time Delay ◽  
Human Population ◽  
Equilibrium Points ◽  
Forest Biomass ◽  
Simulation Results ◽  
The Stability ◽  
Fuzzy Parameter

In this paper, a fuzzy mathematical model has been developed by considering forest biomass, human population and technological effort for the conservation of forest biomass as separate compartments. We have assumed that the forest biomass and human population grows logistically. We have considered that forest biomass decreases due to industrialization, food, shelter, etc., for humans. For the conservation of forest biomass, some modern technological efforts have been used in this model. Also, time delay of use of modern technological effort for the conservation of forest biomass has been considered on forest biomass. According to the assumptions, a fuzzy mathematical model on forest biomass is formulated. Next we have determined different possible equilibrium points. Also, the stability of our proposed system around these equilibrium points has been discussed. Finally, some numerical simulation results have been presented for better understanding of our proposed mathematical model.

scholarly journals The Analysis of SEIRS-SEI Epidemic Models on Malaria with Regard to Human Recovery Rate

2017 ◽  
Vol 6 (3) ◽  
pp. 132-140
Author(s):  
Resmawan Resmawan ◽  
Paian Sianturi ◽  
Endar Hasafah Nugrahani
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Recovery Rate ◽  
Human Population ◽  
Equilibrium Points ◽  
Epidemic Models ◽  
Existence And Stability ◽  
Simulation Results ◽  
Model Formation ◽  
The Given

This article discusses SEIRS-SEI epidemic models on malaria with regard to human recovery rate. SEIRS-SEI in this model is an abbreviation of the population class used in the model, ie Susceptible, Exposed, Infected, and Recovered populations in humans and Susceptible, Exposed, and Infected populations in mosquito. These epidemic models belong to mathematical models which clarify a phenomenon of epidemic transmission of malaria by observing the human recovery rate after being infected and susceptible. Human population falls into four classes, namely susceptible humans, exposed humans, infected humans, and recovered humans. Meanwhile, mosquito population serving as vectors of the disease is divided into three classes, including susceptible mosquitoes, exposed mosquitoes, and infected mosquitoes. Such models are termed SEIRS-SEI epidemic models. Analytical discussion covers model formation, existence and stability of equilibrium points, as well as numerical simulation to find out the influence of human recovery rate on population dynamics of both species. The results show that the fixed point without disease ( ) is stable in condition  and unstable in condition . The simulation results show that the given treatment has an influence on the dynamics of the human population and mosquitoes. If the human recovery rate from the infected state becomes susceptible to increased, then the number of infected populations of both species will decrease. As a result, the disease will not spread and within a certain time will disappear from the population.

scholarly journals ANALISIS DINAMIK MODEL PENDANGKALAN DANAU LIMBOTO DENGAN PEMBERSIHAN ECENG GONDOK DAN PENGERUKAN ENDAPAN

2020 ◽  
Vol 14 (4) ◽  
pp. 597-608
Author(s):  
Sri Lestari Mahmud ◽  
Novianita Achmad
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Stability Condition ◽  
Water Hyacinth ◽  
First Order ◽  
Lake Volume ◽  
Cleaning Solution ◽  
Simulation Results ◽  
The Stability ◽  
First Order Differential Equations

This article discusses about mathematical model of Limboto lake silting with water hyacinth cleaning solution. Modelling begins with constructing a model based on the factors that affect silting which is then formed into a system of first order differential equations. Furthermore, the model is analyzed by looking for equilibrium and stability. To see the condition of lake silting based on the stability condition, a numerical simulation was performed. The simulation results show that with water hyacinth cleaning, the lake will maintain its existence, which is indicated by an increase the Limboto lake volume, although there is still a decrease in volume due to the presence of sediment and nutrients from the river.

scholarly journals An Application of a Delay CSOH Model on the Coconut Farm

2019 ◽  
Vol 8 (6S3) ◽  
pp. 174-187
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Time Delay ◽  
Equilibrium Points ◽  
Critical Value ◽  
Interior Equilibrium ◽  
Fundamental Properties ◽  
Barn Owls ◽  
The Stability ◽  
The Mathematical Model

In this paper, we introduce the mathematical model that represents the quantity and population dynamics on the coconut farm. The model encompasses the number of coconuts and population of squirrels, barn owls, and squirrel hunters. We study the fundamental properties of the model that include positivity, boundedness, and equilibrium points. We also investigate the effect of the time delay on the stability of the equilibrium points. The results of the analysis show that when the time delay reaches its critical value, the interior equilibrium point lost its stability, and there occurs the Hopf bifurcation.

scholarly journals PEMODELAN MATEMATIKA TERHADAP PENYEBARAN VIRUS KOMPUTER DENGAN PROBABILITAS KEKEBALAN

2021 ◽  
Vol 3 (2) ◽  
pp. 122-132
Author(s):  
Neni Nur Laili Ersela Zain ◽  
Pardomuan Robinson Sihombing
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Local Stability ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Minimum Size ◽  
Computer Viruses ◽  
Simulation Results ◽  
The Basic Reproduction Number

The increase in the number of computer viruses can be modeled with a mathematical model of the spread of SEIR type of diseases with immunity probability. This study aims to model the pattern of the spread of computer viruses. The method used in this research is the analytical method with the probability of mathematical immunity. Based on the analysis of the model, two equilibrium points free from disease E1 and endemic equilibrium points E2 were obtained. The existence and local stability of the equilibrium point depends on the basic reproduction number R0. Equilibrium points E1 and E2 tend to be locally stable because R0<1 which means there is no spread of disease. While the numerical simulation results shown that the size of the probability of immunity will affect compartment R and the minimum size of a new computer and the spread of computer viruses will affect compartments S and E on the graph of the simulation results. The conclusion obtained by the immune model SEIR successfully shows that increasing the probability of immunity significantly affects the increase in the number of computer hygiene after being exposed to a virus.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

scholarly journals Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chunru Li ◽  
Zujun Ma
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Media Coverage ◽  
New Product ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Significant Difference ◽  
Form Theory ◽  
The Difference ◽  
The Stability

In this paper, a mathematical model with time-delay-related parameters and media coverage to describe the diffusion process of new products is proposed, in which the time-delay-related parameters denote the stage in which potential customers decide whether to adopt a new product. Then, the stability and the Hopf bifurcation of the proposed model are analyzed in detail. The center manifold theorem and the normal form theory are used to investigate the stability of the bifurcating periodic solution. Moreover, a numerical simulation is conducted to investigate the difference between the model with delay-dependent parameters and that with delay-independent parameters. The results show that there is significant difference between the two models.

scholarly journals Experimental and Mathematical Model for the Antimalarial Activity of Methanolic Root Extract of Azadirachta indica (Dongoyaro) in Mice Infected with Plasmodium berghei NK65

2020 ◽  
pp. 68-82
Author(s):  
Adeniyi Michael Olaniyi ◽  
Momoh Johnson Oshiobugie ◽  
Aderele Oluwaseun Raphael
Keyword(s):  
Mathematical Model ◽  
Azadirachta Indica ◽  
Plasmodium Berghei ◽  
Antimalarial Activity ◽  
Equilibrium Points ◽  
Standard Procedure ◽  
Root Extract ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Group B

The study determines the experimental and mathematical model for the anti-plasmodial activity of methanolic root extract of Azadirachta indica in Swiss mice infected with Plasmodium berghei NK65. Phytochemical analyses, antimalarial activity of the methanolic root extract of A. indica was determined in mice infected with Plasmodium berghei NK65 using standard procedure. Liver biomarker enzymes were also determined. The model P. berghei induced free and P. berghei infected equilibrium were determined. The stability of the model equilibrium points was rigorously analyzed. The phytochemicals present in the extract include: alkaloid, flavonoid, saponin and phenolic compounds etc. The experimental study consists of five groups of five mice each per group. Group A, B, C, D and E were healthy, infected without treatment, infected mice treated with fansidar (10 mg/kg), chloroquine (10 mg/kg) and 250 mg/kg body weight of A. indica methanolic root extract respectively. The extract showed anti-plasmodial activity of 73.96%. The result was significant when compared with group B mice, though it was lower than that exhibited by fansidar (88.91%) and chloroquine (92.18%) for suppressive test. There were significant decrease (P<0.05) in plasma AST and ALT levels in the treated infected mice compared to the infected untreated mice. The results of the model showed that the P.berghei induced free equilibrium is locally and globally asymptotically stable at threshold parameter,  less than unity and unstable when  is greater than unity. Numerical simulations were carried out to validate the analytic results which are in agreement with the experimental analysis of this work.

scholarly journals Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kaushik Dehingia ◽  
Hemanta Kumar Sarmah ◽  
Yamen Alharbi ◽  
Kamyar Hosseini
Keyword(s):  
Time Delay ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Cancer Model ◽  
Delay Effect ◽  
Discrete Time Delay ◽  
The Stability ◽  
Vital Parameters

AbstractIn this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system’s parameters. Some numerical simulations are presented to verify the obtained mathematical results.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals “Stability Analysis of Three Species Ammensalism Model with Time Delay”

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3664-3670
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Global Stability ◽  
Analytical Study ◽  
Present Model ◽  
Ecological Model ◽  
Equilibrium Points

The present model is devoted to an analytical study of a three species syn-ecological model which the 1 st species ( ) N1 ammensal on the 2 nd species ( ) N2 and 2 nd species ( ) N2 ammensal on the 3 rd species ( ) N3 . Here 1 st species and 2 nd species are neutral to each other. A time delay is established between 1 st species and 2 nd species and 2 nd species and 3rd species. All attainable equilibrium points of the model are known and native stability for each case is mentioned and also the global stability of co-existing state is discussed by constructing appropriate Lyapunov operate. Further, precise solutions of perturbed equations are derived. The steadiness analysis is supported by numerical simulation victimization MatLab.

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