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INDONESIA
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 79 Documents
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Dynamical analysis of a predator-prey model arising from palm tree plantation Syukriyah, Yenie; Fakhruddin, Muhammad; Nuraini, Nuning; Kusdiantara, Rudy
Communication in Biomathematical Sciences Vol 2, No 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (919.846 KB) | 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.
Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey Panigoro, Hasan S.; Suryanto, Agus; Kusumahwinahyu, Wuryansari Muharini; Darti, Isnani
Communication in Biomathematical Sciences Vol 2, No 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2363.045 KB) | 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.
MODELING SIMULATION OF COVID-19 IN INDONESIA BASED ON EARLY ENDEMIC DATA Nuraini, Nuning; Khairudin, Kamal; Apri, Mochamad
Communication in Biomathematical Sciences Vol 3, No 1 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.1.1

Abstract

The COVID-19 pandemic has recently caused so much anxiety and speculation around the world. This phenomenon was mainly driven by the drastic increase in the number of infected people with the COVID-19 virus worldwide. Here we propose a simple model to predict the endemic in Indonesia. The model is based on the Richard?s Curve that represents a modified logistic equation. Based on the similar trends of initial data between Indonesia and South Korea, we use parameter values that are obtained through parameter estimation of the model to the data in South Korea. Further, we use a strict assumption that the implemented strategy in Indonesia is as effective as in South Korea. The results show that endemic will end in April 2020 with the total number of cases more than 8000.
ON THE ANALYSIS OF COVID-19 TRANSMISSION IN WUHAN, DIAMOND PRINCESS AND JAKARTA-CLUSTER Soewono, Edy
Communication in Biomathematical Sciences Vol 3, No 1 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.1.2

Abstract

The whole world has been recently shocked by the massive spread of Covid-19 without any sign of when it will end. This phenomenon of this scale is understood as a plague that has never been happening in a lifetime. Almost all countries do not have proper preparedness when positive cases are found in a region. In a relatively short time, cases then spread quickly, and panic broke out in the community. With the rapid human to human transmission, and there is no vaccine available, the only way to control the spread of the disease is by implementing a contact tracing and isolation policy. The fact indicated that health officials in many affecting countries have difficulty in detecting individuals who are potentially exposed to the virus. The success of controlling the disease is very much dependent on the ability of the health authority in tracking and isolating the infected and the suspected cases. A transmission model for Covid-19 transmission in the form of SEIR is chosen to fit with the cases in Wuhan, Diamond Princess, and Jakarta-cluster. These cases represent the transmission in a large city, a relatively restricted and dense area, and a small cluster, respectively. The basic reproductive ratio and the infection rate are obtained based on the cumulative data for each case. These indicators can be used for predicting the progress of transmission for similar cases. A simple model for estimating the completing time of contact tracing and isolation is constructed in the form of a differential operator on the cumulative case. This operator represents the number of daily new infected cases. It is shown that for the case of Wuhan, the completing time for contact tracing and isolation is 55 days. This result is important for analyzing the intervention strategy of Covid-19 in an affected region.
THE COVID-19 OUTBREAK IN GERMANY – MODELS AND PARAMETER ESTIMATION Heidrich, Peter; Schäfer, Moritz; Nikouei, Mostafa; Götz, Thomas
Communication in Biomathematical Sciences Vol 3, No 1 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.1.5

Abstract

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS?CoV?2, is reported from China and later also from other parts of the world. Since 21 January 2020, World Health Organization (WHO) reports daily data on confirmed cases and deaths from both China and other countries [1]. The Johns Hopkins University [2] collects those data from various sources worldwide on a daily basis. For Germany, the Robert?Koch?Institute (RKI) also issues daily reports on the current number of infections and infection related fatal cases and also provides estimates of several disease-related parameters [3]. In this work we present an extended SEIRD?model to describe these disease dynamics in Germany. The model takes into account the susceptible, exposed, infected, recovered and deceased fractions of the population. Epidemiological parameters like the transmission rate, lethality or the detection rate of infected individuals are estimated by fitting the model output to available data. For the parameter estimation itself we compare two methods: an adjoint based approach and a Monte?Carlo based Metropolis algorithm.
AN ANALYSIS OF COVID-19 TRANSMISSION IN INDONESIA AND SAUDI ARABIA Ndii, Meksianis Z.; Hadisoemarto, Panji; Agustian, Dwi; Supriatna, Asep K.
Communication in Biomathematical Sciences Vol 3, No 1 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (324.2 KB) | DOI: 10.5614/cbms.2020.3.1.3

Abstract

An outbreak of novel coronavirus has been happening in more than 200 countries and has shocked society. Several measures have been implemented to slowing down the epidemics while waiting for vaccine and pharmaceutical intervention. Using a deterministic and stochastic model, we assess the effectiveness of current strategies: reducing the transmission rate and speeding up the time to detect infected individuals. The reproductive ratio and the probability of extinction are determined. We found that the combination of both strategies is effective to slow down the epidemics. We also find that speeding up the time to detect infected individuals without reducing the transmission rate is not sufficient to slow down the epidemics.
HOW MANY CAN YOU INFECT? SIMPLE (AND NAIVE) METHODS OF ESTIMATING THE REPRODUCTION NUMBER Susanto, H.; Tjahjono, V.R.; Hasan, A.; Kasim, M.F.; Nuraini, N.; Putri, E.R.M.; Kusdiantara, R.; Kurniawan, H.
Communication in Biomathematical Sciences Vol 3, No 1 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.1.4

Abstract

This is a pedagogical paper on estimating the number of people that can be infected by one infectious person during an epidemic outbreak, known as the reproduction number. Knowing the number is crucial for developing policy responses. There are generally two types of such a number, i.e., basic and effective (or instantaneous). While basic reproduction number is the average expected number of cases directly generated by one case in a population where all individuals are susceptible, effective reproduction number is the number of cases generated in the current state of a population. In this paper, we exploit the deterministic susceptibleinfected-removed (SIR) model to estimate them through three different numerical approximations. We apply the methods to the pandemic COVID-19 in Italy to provide insights into the spread of the disease in the country. We see that the effect of the national lockdown in slowing down the disease exponential growth appearedabout two weeks after the implementation date. We also discuss available improvements to the simple (and naive) methods that have been made by researchers in the field. Authors of this paper are members of the SimcovID (Simulasi dan Pemodelan COVID-19 Indonesia) collaboration.
Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function Amit Kumar Chakraborty; M. A. Haque; M. A. Islam
Communication in Biomathematical Sciences Vol. 3 No. 2 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.2.2

Abstract

Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presented to describe the transmission of dengue. The equilibrium points and the basic reproduction number have been computed. The conditions which lead the disease free equilibrium and the endemic equilibrium have been determined. The local stability for the equilibrium points has been established based on the eigenvalues of the Jacobian matrix and the global stability has been analyzed by using the Lyapunov function theory. It is found that the stability of equilibrium points can be controlled by the reproduction number. In order to calculate the infection rate, data for infected human populations have been collected from several health institutions of Bangladesh. Numerical simulations of various compartments have been generated using MATLAB to investigate the influence of the key parameters for the transmission of the disease and to support the analytical results. The effect of treatment function over the infected compartment has been illustrated. The sensitivity of the reproduction number concerning the parameters of the model has been analyzed. Finally, the most sensitive parameter that has the highest effect over reproduction number has been identified.
Forecasting COVID-19 Epidemic in Spain and Italy Using A Generalized Richards Model with Quantified Uncertainty Isnani Darti; Agus Suryanto; Hasan S. Panigoro; Hadi Susanto
Communication in Biomathematical Sciences Vol. 3 No. 2 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.2.1

Abstract

The Richards model and its generalized version are deterministic models that are often implemented to fit and forecast the cumulative number of infective cases in an epidemic outbreak. In this paper we employ a generalized Richards model to predict the cumulative number of COVID-19 cases in Spain and Italy, based on available epidemiological data. To quantify uncertainty in the parameter estimation, we use a parametric bootstrapping approach to construct a 95% confidence interval estimation for the parameter model. Here we assume that the time series data follow a Poisson distribution. It is found that the 95% confidence interval of each parameter becomes narrow with the increasing number of data. All in all, the model predicts daily new cases of COVID-19 reasonably well during calibration periods. However, the model fails to produce good forecasts when the amount of data used for parameter estimations is not sufficient. Based on our parameter estimates, it is found that the early stages of COVID-19 epidemic, both in Spain and in Italy, followed an almost exponentially growth. The epidemic peak in Spain and Italy is respectively on 2 April 2020 and 28 March 2020. The final sizes of cumulative number of COVID-19 cases in Spain and Italy are forecasted to be at 293220 and 237010, respectively.
The Role of Mathematical Model in Curbing COVID-19 in Nigeria Chinwendu Emilian Madubueze; Nkiru Maria Akabuike; Sambo Dachollom
Communication in Biomathematical Sciences Vol. 3 No. 2 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.2.5

Abstract

COVID-19 is a viral disease that is caused by Severe Acute Respiratory Syndrome coronavirus 2 (SARSCoV-2) which has no approved vaccine. Based on the available non-pharmacological interventions like wearing of face masks, observing social distancing, and lockdown, this work assesses the impact of non-pharmaceutical control measures (social distancing and use of face-masks) and mass testing on the transmission of COVID-19 in Nigeria. A mathematical model for COVID-19 is formulated with intervention measures (observing social distancing and wearing of face masks) and mass testing. The basic reproduction number, R_0, is computed using next-generation method while the disease-free equilibrium is found to be locally and globally asymptotically stable when R_0< 1. The model is parameterized using Nigeria data on COVID-19 in Nigeria. The basic reproduction number is found to be less than unity (R_0 < 1) either when the compliance with intervention measures is moderate (50% <= alpha< 70%) and the testing rate per day is moderate (0,5 <=alpha_2 < 0,7) or when the compliance with intervention measures is strict (alpha>=70%) and the testing rate per day is poor (alpha_2 = 0,3). This implies that Nigeria will be able to halt the spread of COVID-19 under these two conditions. However, it will be easier to enforce strict compliance with intervention measures in the presence of poor testing rate due to the limited availability of testing facilities and manpower in Nigeria. Hence, this study advocates that Nigerian governments (Federal and States) should aim at achieving a testing rate of at least 0.3 per day while ensuring that all the citizens strictly comply with wearing face masks and observing social distancing in public.

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