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Communication in Biomathematical Sciences
Published by Indonesian Biomathematical Society
ISSN : -     EISSN : 25492896     DOI : 10.5614/cbms
Core Subject : Social,
Social Sciences
Full research articles in the area of Applications of Mathematics in biological processes and phenomena
Arjuna Subject : Matematika - Matematika Terapan
Articles 6 Documents
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Search results for , issue "Vol. 2 No. 2 (2019)" : 6 Documents clear
Bottom-up and top-down control in a multitrophic system: the role of nutrient limitation and infochemical-mediated predation in a plankton food-web model Nicola D Walker; Hadi Susanto; Michael Steinke; Edward A. Codling
Communication in Biomathematical Sciences Vol. 2 No. 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.2.1

Abstract

Chemicals released following herbivore grazing on primary producers can promote multitrophic interactions by influencing the foraging behaviour of higher order predators. In particular, chemicals released during microzooplankton grazing on phytoplankton can act as infochemical cues that elicit foraging responses and improve search efficiency in carnivorous copepods. Models investigating such infochemical-mediated multitrophic interactions in the plankton are typically based on top-down control, where phytoplankton concentrations are controlled through predation and grazing from higher trophic levels. However, in marine environments nutrient limitation is an important factor that influences a food-web from below, and earlier models of this system only indirectly account for this by assuming predator-free growth is logistic with a fixed carrying capacity. Here we consider the dynamics of infochemical-mediated interactions in a marine system where nutrient limitation is modelled directly through an extended NPZ-style model. We show the one-parameter bifurcation behavior of the top-down model to change when the total nutrient availability is changed, and hence demonstrate phytoplankton bloom formation to be a function of both top-down and bottom-up processes.
Mathematical Modeling and Sensitivity Analysis of the Existence of Male Calico Cats Population Based on Cross Breeding of All Coat Colour Types Dani Suandi; Ira Prapti Ningrum; Amalia Nur Alifah; Nurul Izzah; Mazi Prima Reza; Imroatul Khoiriyah Muwahidah
Communication in Biomathematical Sciences Vol. 2 No. 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.2.3

Abstract

The coat color of cats is normally governed by genes found on the X chromosome in both male chromosome XY and female chromosome XX. The meiosis failure in the process of gametogenesis leads to the birth of three-colored male cats caused by an excess of the X chromosome in the male chromosome type XY. The chromosome structure of three-color male cats, called male calico cats, appeared similar to the XXY Klinefelter's syndrome in human. Mathematical modeling and investigation of the factors that influence the infrequency of male calico cats are our main objectives of this paper. In addition, we also discuss the possible contributions and strategies to overcome the scarcity of these cats. We construct a mathematical model based on a combination of genes in the chromosome that regulates the color of cat coat on the fertilization process. The mathematical model is given as a six-dimensional system of differential equations. Sensitivity analysis is used to investigate the important parameters in the existence of male calico cats. Our finding states that the probability of normal male cats meiosis is a crucial parameter in the maintenance of the existence of male calico cats. Furthermore, one of the strategies that we could recommend in maintaining the existence of male calico cats is minimizing the value of the successful meiosis probability of normal male cats.
Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey Hasan S. Panigoro; Agus Suryanto; Wuryansari Muharini Kusumahwinahyu; Isnani Darti
Communication in Biomathematical Sciences Vol. 2 No. 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.2.4

Abstract

In this paper, a dynamical analysis of a fractional-order predator-prey model with infectious diseases in prey is performed. First, we prove the existence, uniqueness, non-negativity, and boundedness of the solution. We also show that the model has at most five equilibrium points, namely the origin, the infected prey and predator extinction point, the infected prey extinction point, the predator extinction point, and the co-existence point. For the first four equilibrium points, we show that the local stability properties of the fractional-order system are the same as the first-order system, but for the co-existence point, we have different local stability properties.We also present the global stability of each equilibrium points except for the origin point. We observe an interesting phenomenon, namely the occurrence of Hopf bifurcation around the co-existence equilibrium point driven by the order of fractional derivative. Moreover, we show some numerical simulations based on a predictor-corrector scheme to illustrate the result of our dynamical analysis.
Continuous Monocyclic and Polycyclic Age Structured Models of Population Dynamics Vitalii V Akimenko
Communication in Biomathematical Sciences Vol. 2 No. 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.2.2

Abstract

This paper focuses on the study of continuous age-structured models, or more general, physiologically structured models, which used for detailed and accurate study of population dynamics in many ecological, biological applications and medicine. In contrast to simpler unstructured models, these models allow us to relate the individual life-histories described as fertility and mortality rates of an individual at a given age with population dynamics. Depending from the particularity of reproduction mechanism continuous age-structured models are divided into monocyclic (reproduction occurs only at the one fixed age of individuals) and polycyclic (reproduction occurs with age-dependent probability at some age reproductive window) models. The linear monocyclic age-structured models are used often in cell cycles modelling, in population dynamics of plants, etc. In this case continuous age-structured models allow for obtaining the exact analytical solution. Since the linear and non-linear polycyclic age-structured models are more general then monocyclic models, they coverwider  range of applications in life science. But in this case solution of model can be obtained only in the form of recurrent formulae and can be used only in numerical algorithms. Both solutions obtained in this work allow us to study numerically the important dynamical regimes population outbreaks of three types: oscillations with large magnitude, pulse sequence and single pulse. Thus, analysis of continuous age-structured models of population dynamics provides insight into features and particularities of complex dynamical regimes of populations in many applications in biology, ecology and medicine.
On the Reproduction Ratio of Dengue Incidence in Semarang, Indonesia 2015-2018 Juni Wijayanti Puspita; Muhammad Fakhruddin; Hilda Fahlena; Fatkhur Rohim; Sutimin Sutimin
Communication in Biomathematical Sciences Vol. 2 No. 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.2.5

Abstract

Dengue is one of the mosquito-borne diseases caused by dengue viruses (DENV), which has become endemic in most tropical and subtropical countries, including Indonesia. Since there is a lot of dengue incidence on children of age less than fourteen years old in Semarang, Indonesia, it is the interest here to analyze the different rates of infection among different age groups. A SIR-UV mathematical model with age structure in human the population is constructed to describe dengue transmission in Semarang from 2015 to 2018. In this study, we separated the human population into four age classes: children (0-4 years), youngster (5-14 years), productive adults (15-60 years) and non-productive adults (over 60 years). We use Particle Swarm  Optimization to obtain optimal parameters for the transmission rates based on the yearly incidence. The basic reproduction ratio (R0) is derived from the Next Generation Matrix and is evaluated by using the optimal parameters for data Semarang in 2015-2018. Numerical simulation results show that the number of dengue incidence is in a good agreement with the actual data in Semarang for 2015-2018.
Dynamical analysis of a predator-prey model arising from palm tree plantation Yenie Syukriyah; Muhammad Fakhruddin; Nuning Nuraini; Rudy Kusdiantara
Communication in Biomathematical Sciences Vol. 2 No. 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.2.6

Abstract

Palm oil industry has become an issue that has caught the attention of the world community in recent years. From an economic point of view, this industry is very influential in developing and spurring economic growth in rural areas. In this paper, a predator-prey dynamical model representing the interaction between palm leaf, caterpillar and predator is discussed here. The caterpillar life-cycle starts from eggs, larvae, pupas and the adult moths, and only the larvae interact with the predator. With a given threshold level of the leaves for survival and productivity, the critical level of predators is shown. Further, the dynamical analysis is discussed analytically and numerically. Bifurcation diagrams and sensitivity analysis of each compartment were also obtained to see the effect of changing parameters on the dynamics. The results explain that the increase of larvae predators can reduce the number of larvae pests that eat palm oil leaves, but they need to be controlled to maintain the balance of the ecosystem.

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