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Communication in Biomathematical Sciences
ISSN : -     EISSN : 25492896     DOI : 10.5614/cbms
Core Subject : Social,
Full research articles in the area of Applications of Mathematics in biological processes and phenomena
Articles 27 Documents
Mathematical models of dengue fever epidemiology: multi-strain dynamics, immunological aspects associated to disease severity and vaccines Aguiar, Maira; Stollenwerk, Nico
Communication in Biomathematical Sciences Vol 1, No 1 (2017)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2291.527 KB) | DOI: 10.5614/cbms.2017.1.1.1

Abstract

Epidemiological models formulated to describe the transmission of the disease and to predict future outbreaks, can become an interesting tool able to address specific public health questions, guiding public health authorities during implementation of disease control measures such as vector control and vaccination. In this paper, we survey a model framework for dengue fever epidemiology, the most important viral mosquitoborne disease in the world. Here, we discuss the role of number of subsequent infections versus detailed number of dengue serotypes included in the model framework and the human immunological aspects associated to disease severity, identifying the implications for model dynamics and its impact for vaccine implementation.
Estimation of time-space-varying parameters in dengue epidemic models Wijaya, Karunia Putra
Communication in Biomathematical Sciences Vol 1, No 1 (2017)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1147.319 KB) | DOI: 10.5614/cbms.2017.1.1.2

Abstract

There are nowadays a huge load of publications about dengue epidemic models, which mostly employ deterministic differential equations. The analytical properties of deterministic models are always of particular interest by many experts, but their validity ? if they can indeed track some empirical data ? is an increasing demand by many practitioners. In this view, the data can tell to which figure the solutions yielded from the models should be; they drift all the involving parameters towards the most appropriate values. By prior understanding of the population dynamics, some parameters with inherently constant values can be estimated forthwith; some others can sensibly be guessed. However, solutions from such models using sets of constant parameters most likely exhibit, if not smoothness, at least noise-free behavior; whereas the data appear very random in nature. Therefore, some parameters cannot be constant as the solutions to seemingly appear in a high correlation with the data. We were aware of impracticality to solve a deterministic model many times that exhaust all trials of the parameters, or to run its stochastic version with Monte Carlo strategy that also appeals for a high number of solving processes. We were also aware that those aforementioned non-constant parameters can potentially have particular relationships with several extrinsic factors, such as meteorology and socioeconomics of the human population. We then study an estimation of time-space-varying parameters within the framework of variational calculus and investigate how some parameters are related to some extrinsic factors. Here, a metric between the aggregated solution of the model and the empirical data serves as the objective function, where all the involving state variables are kept satisfying the physical constraint described by the model. Numerical results for some examples with real data are shown and discussed in details.
A Particle System Model for Dengue Transmission Zevika, Mona; Soewono, Edy; Tse, Oliver T.C.
Communication in Biomathematical Sciences Vol 1, No 1 (2017)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1120.11 KB) | DOI: 10.5614/cbms.2017.1.1.3

Abstract

Dengue disease has been known for decades as a vector-borne disease which is rapidly spreading in many tropical and subtropical countries. The disease is transmitted mostly by female Aedes aegypty mosquitoes. Although detailed biological properties of the infection process are already known, in the field applications the disease transmission of dengue is still far from being successfully controlled. The complexity surrounding the transmission is contributed by various factors such as climate, mobility and human-mosquito behavior. Many deterministic models have been developed to investigate the spread of dengue. However, in a deterministic model, spatial heterogeneity factor is not considered. In fact, distances between people and mosquitoes greatly influence the spread of dengue. This paper discusses a microscopic model of the spread of dengue based on spatial heterogeneity. In this microscopic model, every human and mosquito is regarded as a particle and the corresponding human and mosquito populations with their health status are considered as a system of particles. Three important dynamical factors and processes are constructed for each particle, i.e., position and health status of each particle, natural birth and death, infection and transition processes. An estimate of the corresponding basic reproductive ratio is introduced to accommodate the variation of health status and spatial spread of particles
The role of top-predator in the preservation of coral reefs ecosystem Ratianingsih, Rina; Ismawati, Nurul; Puspita, Juni Wijayanti; Jaya, Agus Indra
Communication in Biomathematical Sciences Vol 1, No 1 (2017)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (265.337 KB) | DOI: 10.5614/cbms.2017.1.1.5

Abstract

The coral reef ecosystem in Indonesian as part of Coral Triangle Region has been significantly decreasing in the last decades. This damage has been known widely due to coastal development, pollution, and uncontrolled fishing and harvesting. Among other many living species in the environment, the existence of coral reefs is directly related to the existence of Drupella sp. and Acanthaster planci as the coral predators, while the existence of the predators also related to the Napoleon wrasse and Giant triton/ Trumpet shell as the top predator. This study discusses the interaction among the coral reefs, the predators and the top predators, which is represented in a dynamical model of predator-prey-top predator. In the absence of top predators, the system is reduced as a two-predator-prey model with only one surviving predator, Acanthaster planci, which has more effective predation behavior. The role of Napoleon wrasse as a top predator of both Acanthaster planci and Drupella sp. is significantly important to protect the coral reef from the excessive predation from Acanthaster planci and Drupella sp. A stable co-existence is shown between coral reef, Acanthaster planci and Napoleon wrasse. With the appearance of Giant tritons which predate only Acanthaster planci, a co-existence between five species may occur with abundant species of Giant triton.
A Dynamical Model of ’Invisible Wall’ in Mosquito Control Khumaeroh, Mia Siti; Soewono, Edy; Nuraini, Nuning
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (392.149 KB) | DOI: 10.5614/cbms.2018.1.2.2

Abstract

A concept of an ?invisible wall? is used here as a control mechanism to separate the human population from mosquitoes in the hope that mosquitoes gradually change their preference to other blood resources. Although mosquitoes carry inherent traits in host preference, in a situation in which regular blood resource is less available, and there are abundant other blood resources, mosquitoes may adapt to the existing new blood resource. Here we construct a model of mosquitoes preference alteration involving anthropophilic, opportunistic, and zoophilic, based on the application of repellent clothing usage and the effects of fumigation. The coexistence equilibrium is shown to be stable when the rate of mosquito ovulation, which is successfully hatching into larvae, is greater than the total of mosquito natural death rate and mosquito death rate due to fumigation. Numerical simulation is performed after the reduction of unobservable parameters is done with Human Blood Index (HBI) data. Global sensitivity analysis is then performed to determine the parameters that provide the dominant alteration effect on the mosquito population. The simulation results show that a proper selection of the fumigation rate and repellent clothing rate should be carefully done in order to reduce the mosquito population as well as to increase the zoophilic ratio.
Modeling CD4+ T cells and CTL response in HIV-1 infection with antiretroviral therapy Sutimin, Sutimin; Sunarsih, Sunarsih; Tjahjana, R. Heru
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (278.074 KB) | DOI: 10.5614/cbms.2018.1.2.3

Abstract

The majority of an immune system infected by HIV (Human Immunodeficiency Virus) is CD4+ T cells. The HIV-1 transmission through cell to cell of CD4+ T cells supports the productive infection. On the other hand, infected CD4+ T cells stimulate cytotoxic T-lymphocytes cells to control HIV-1 infection. We develop and analyze a mathematical model incorporating the infection process through cell to cell contact of CD4+ T cells, CTL compartment and the combination of RTI and PI treatments. By means of the alternative reproduction ratio, it is analyzed the stability criteria and the existence of endemic equilibrium. Numerical simulations are presented to study the implication of the combination of RTI and PI therapy. The results indicate that RTI drug shows more significant effect in reducing HIV-1 infection compared to PI drug.
Comparison of the differential transformation method and non standard finite difference scheme for solving plant disease mathematical model Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (599.511 KB) | DOI: 10.5614/cbms.2018.1.2.4

Abstract

The Differential Transformation Method (DTM) and the Non Standard Finite Difference Scheme (NSFDS) are alternative numerical techniques used to solve a system of linear and nonlinear differential equations. In this paper, we construct the DTM and NSFDS for a mathematical model of plant disease transmission dynamics and compare their solutions to that generated by MATLAB ode45 routine, which is the well-established numerical routine. The solutions of the DTM and NSFDS are in good agreement with MATLAB ode45 routine in the small time step. However, when the time step is larger, the NSFDS performs better than the DTM.
On Territorial Competition between Rhinoceros Sondaicus and Bos Javanicus at Ujung Kulon National Park Harjanto, Eric
Communication in Biomathematical Sciences Vol 1, No 1 (2017)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (266.028 KB) | DOI: 10.5614/cbms.2017.1.1.4

Abstract

In this paper, we consider the interaction between Rhinoceros Sondaicus, known as Javan Rhino, and Bos Javanicus, known as Javan Bull, at Ujung Kulon National Park. For years, the population of Javan Rhinos never exceeds their estimated carrying capacity, despite their vast habitat and there is no natural predator in the area. Both species naturally consume different food resources, hence there is no direct competition on food resource between the two species. This stagnant growth of Javan Rhino is suspected due to the territorial competition between the two species, in which the rapid growth of Javan Bull may reduce the territory of Javan Rhino and consequently reduce the carrying capacity of Javan Rhino. We construct a mathematical model ofterritorial competition between two species and show that domination of one species can lower the carrying capacity of the second species.
A new modified logistic growth model for empirical use Windarto, Windarto; Eridani, Eridani; Purwati, Utami Dyah
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (263.141 KB) | DOI: 10.5614/cbms.2018.1.2.5

Abstract

Richards model, Gompertz model, and logistic model are widely used to describe growth model of a population. The Richards growth model is a modification of the logistic growth model. In this paper, we present a new modified logistic growth model. The proposed model was derived from a modification of the classical logistic differential equation. From the solution of the differential equation, we present a new mathematical growth model so called a WEP-modified logistic growth model for describing growth function of a living organism. We also extend the proposed model into couple WEP-modified logistic growth model. We further simulated and verified the proposed model by using chicken weight data cited from the literature. It was found that the proposed model gave more accurate predicted results compared to Richard, Gompertz, and logistic model. Therefore the proposed model could be used as an alternative model to describe individual growth.
A multiscale approach for spatially inhomogeneous disease dynamics Schmidtchen, Markus; Tse, Oliver T.C.; Wackerle, Stephan
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1849.524 KB) | DOI: 10.5614/cbms.2018.1.2.1

Abstract

In this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field limit. The chain of equations acquired via the multiscale approach is investigated, analytically as well as numerically. The outcome of these results provides strong evidence of the models? robustness and justifies their practicality in describing disease dynamics, in particularly when mobility is involved. The numerical results provide further insights into the applicability of the different scaling limits.

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