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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
 1 
Search results for , issue "Vol. 2 No. 1 (2019)" : 6 Documents clear
On Competition between Javan Rhino (Rhinoceros Sondaicus) and Javan Bull (Bos Javanicus) at Ujung Kulon National Park with Allee Effect Eric Harjanto; Respati Mentari
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.5

Abstract

In the last few decades, it has been reported that the population of Rhino (Rhinoceros Sondaicus) at the Ujung Kulon National Park has been reaching a stagnation at the number 50s, despite the existing territory can support a much larger number of Rhinos. Here, we construct a dynamical model representing the interaction between Rhino and Bull (Bos Javanicus) with Allee effect for the Javan rhinos population. This Allee effect may occur in the field, among others, due to the solitary behaviour of Rhino within large territory, imbalance of age structure and gender and difficulty of finding mates in Javan rhinos population which causes inbreeding in the population. In this paper, we follow the previous paper on the territorial competition between Javan  rhino and Javan bull at Ujung Kulon National Park and add Allee effect factor on the Javan rhino's population. We give a proof on the boundedness of the solution and explanation on the bifurcations that occur in the model. One of these bifurcations plays an important role in the system. Some simulations and suggestion on how to improve the survival of Javan rhino is also included.
Dynamical Behavior of Secondary Dengue Infection Model Chai Jian Tay
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.1

Abstract

With the increase of dengue cases in the last decades, efforts on controlling the dengue disease have been carried out. Dengvaxia, the first dengue vaccine developed by Sanofi Pasteur, was recommended by WHO for trial. The long-term safety follow-up indicates that the vaccine efficacy is higher in seropositive human population and there is an increase risk of severe dengue in vaccinated seronegative human. It is important to understand the dynamical behavior of dengue that includes both the seronegative and seropositive human population before performing vaccination. For such purpose, a secondary dengue infection model is developed and investigated in this paper. The basic reproduction number, Ro is derived and sensitivity analysis is performed to determine the most sensitive parameter in the model. The results indicate that Ro is the most sensitive to the ratio of mosquito to human, dengue transmission from human to mosquito, dengue transmission from mosquito to human and natural mortality of mosquito. It is also found that the ratio of seropositive to seronegative human population is 1.52 for a given set of parameter values at dengue endemic state. This would assist the authorities in deciding the proportion of seropositive and seronegative human population to be vaccinated. Numerical simulation results show that a decline in primary dengue infection is not associated with a decrease in secondary dengue infection. Therefore, the dengue control strategies should produce high efficacy in transmissibility reduction and ultimately reduce the DHF.
Biological and Mechanical Transmission Models of Dengue Fever Laura Laura; Asep K. Supriatna; Mia Siti Khumaeroh; Nursanti Anggriani
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.2

Abstract

Dengue fever disease is caused by the dengue virus and transmitted primarily by the Aedes aegypti mosquitoes. There is no vaccine available to prevent transmission of the disease until recently which makes 30% of the worlds population is at risk of the disease. The Aedes aegypti mosquitoes are known as multiplebiters during their blood meal periods. There are two possible transmissions of the dengue virus from the mosquitoes to humans. First, infectious mosquitoes may transmit the virus through the bite to a susceptible human after the virus experiencing the extrinsic incubation period (EIP) in the body of the mosquitoes. Second, the transmission happens directly through the transfer of virus carried in the saliva of a mosquito to a susceptible human at the second bite without waiting for the EIP. The later is known as a mechanical transmission, which occurs when a susceptible mosquito bites an infectious human and almost at the same time it transmits the virus to a healthy human. Only a few literature consider this kind of dengue transmission. In this paper, we develop a mathematical model for dengue transmission by modifying the standard dengue transmission model with the presence of mechanical transmission. We show that the spreading behavior of the disease can be described by the basic reproduction number (BRN), R0. The disease will die out if R0 < 1, and it remains endemic if R0 > 1. The analysis shows that the ratio of the BRN in the presence and absence of the mechanical transmission increases as the mechanical transmission rate increases. There is also a significant change in the outbreak intensity especially when the mechanical transmission rate is greater than the biological transmission rate.
Comparison of Dengue Transmission in Lowland and Highland Area: Case Study in Semarang and Malang, Indonesia Ilham Saiful Fauzi; Muhammad Fakhruddin; Nuning Nuraini; Karunia Putra Wijaya
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.3

Abstract

Dengue is a potentially lethal mosquito-borne disease, regarded as the most dangerous disease in the world. It is also a major health issue in tropical and subtropical countries. Environmental characteristics and sociocultural are factors which play a role in the spread of dengue. Different landscape structure such as lowland and highland areas are possible to give different infection rate on dengue transmission. Semarang and Malang are densely populated areas in Java, which are selected to be our study areas. A mathematical model (SIR-UV) is adapted to describe dengue transmission. Spiral dynamic optimization is applied to convert monthly data to weekly in Malang and estimate the infection rate that minimized the deviation between dengue data and simulation. This method produces a good fitting to the data. We compare the pattern of dengue cases from the simulation in both cities. Furthermore, we identify seasonal variations of the cases via Fourier series of the infection rate. We also investigate the correlation between humidity, infection rate, and dengue cases in Semarang and Malang. It reveals that humidity influences infection rate in 1-3 weeks later and the infection rate produces dengue cases in the next four weeks.
Mathematical Model of an Interaction between Bears and Salmon; A Case in British Columbia Hilda Fahlena; Jane T. M. Sahetapy-Engel; Azhary Ramadhanty; Dancent Sutanto; Eduardus Axel Wijaya; Ambar Winarni
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.4

Abstract

An interaction model for the Pacific salmon and bear population in British Columbia is discussed here. The phenomenon is shown during the salmons period of migration back to their birthplace river at the end of their life. During this returning home, a large number of bears from the nearby state come and prey on them. This predation of salmon before spawning is suspected as the cause of the decline in Salmon production. Here a dynamical model involving a specific predator-prey type interaction between Salmon and Bears is constructed in the form of a non-autonomous dynamical system, in which the transition rate from the adult state of salmon to the spawning state is positive only in the month of migration. Dynamical analysis for the stability of the coexistence equilibrium for the autonomous case is shown and sensitivity analysis for the non-autonomous the case is done numerically.
Dynamical analysis of mathematical model for Bovine Tuberculosis among human and cattle population Dipo Aldila; Siti Leah Latifa; Putri A. Dumbela
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.6

Abstract

Bovine Tuberculosis (BTB) is a disease that can attack humans through cattle.The process of transmission can occur through the air and cattle products that are not treated properly. When humans are infected with BTB, reinfection, and relapse may occur. This phenomenon is modeled as an eleven-dimension dynamical system. Our aim is to gain insight into the effect of separation of human activity area into the transmission dynamics of BTB. The model incorporates (among many others features) the dynamics of BTB among human and cattle population, density-dependent infection rate, and reinfection, are rigorously analyzed and simulated. The trivial disease-free equilibrium of the model is shown to be locally asymptotically stable when the two associated basic reproduction number are less than unity. Although the non-trivial equilibrium cannot be shown explicitly, for a special case, this equilibrium is still possible to show and discuss further. Our results suggest that controlling BTB in cattle population may indirectly control the spread of BTB in human. An example of controlling the infected population of infected cattle can be done with the annihilation of infected cattle.

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