Articles
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<![CDATA[The Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever ]]>
<![CDATA[Glenn Lahodny Jr.]]>;
<![CDATA[Mona Zevika]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 4 No. 1 (2021) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2021.4.1.1
<![CDATA[A Continuous-Time Markov Chain model is constructed based on the a deterministic model of dengue fever transmission including mosquito fogging and the use of repellent. The basic reproduction number (R0) for the corresponding deterministic model is obtained. This number indicates the possible occurrence of an endemic at the early stages of the infection period. A multitype branching process is used to approximate the Markov chain. The construction of offspring probability generating functions related to the infected states is used to calculate the probability of disease extinction and the probability of an outbreak (P0). Sensitivity analysis is shown for variation of control parameters and for indices of the basic reproduction number. These results allow for a better understanding of the relation of the basic reproduction number with other indicators of disease transmission.]]>
<![CDATA[Measles Transmission Model with Vaccination and Hospitalization Treatments ]]>
<![CDATA[Abadi Abadi]]>;
<![CDATA[Muhammad Fakhruddin]]>;
<![CDATA[Rudianto Artiono]]>;
<![CDATA[Budi Priyo Prawoto]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 3 No. 2 (2020) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2020.3.2.4
<![CDATA[Measles (Rubeola) as one of notifiable diseases gets serious concern worldwide since it was first found in ninth century. The implementation of vaccines for controlling measles transmission since 1963 up to nowadays requires various studies regarding the effectiveness of the vaccines. Studies in the area of mathematical modeling of measles virus transmission has been done by many authors. This study intended to propose a model of measles virus transmission that also considered hospitalization as a complementary treatment for vaccination implementation program. The model is an SIHR model that divided the population into Susceptibles (S), Infectives (I), Hospitalized (H), and Recovered (R). The analysis started with determining the the equilibria and their stability based on the value of Basic Reproduction Ratio (R0). The analitical results were implemented to recorded data of measles of Jakarta, Indonesia in 2017 for numerical simulation. The simulation result said that hospitalization for measles patients in Jakarta escalates the effectiveness of vaccination program being implemented in the city. This can be considered by the city policy makers for giving more concern on hospitalizing measles-infected patients.]]>
<![CDATA[Successive Approximation, Variational Iteration, and Multistage-Analytical Methods for a SEIR Model of Infectious Disease Involving Vaccination Strategy ]]>
<![CDATA[Sudi Mungkasi]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 3 No. 2 (2020) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2020.3.2.3
<![CDATA[We consider a SEIR model for the spread (transmission) of an infectious disease. The model has played an important role due to world pandemic disease spread cases. Our contributions in this paper are three folds. Our first contribution is to provide successive approximation and variational iteration methods to obtain analytical approximate solutions to the SEIR model. Our second contribution is to prove that for solving the SEIR model, the variational iteration and successive approximation methods are identical when we have some particular values of Lagrange multipliers in the variational iteration formulation. Third, we propose a new multistage-analytical method for solving the SEIR model. Computational experiments show that the successive approximation and variational iteration methods are accurate for small size of time domain. In contrast, our proposed multistage-analytical method is successful to solve the SEIR model very accurately for large size of time domain. Furthermore, the order of accuracy of the multistage-analytical method can be made higher simply by taking more number of successive iterations in the multistage evolution.]]>
<![CDATA[Quantitative Measure to Differentiate Wicket Spike from Interictal Epileptiform Discharges ]]>
<![CDATA[Suryani Gunadharma]]>;
<![CDATA[Ahmad Rizal]]>;
<![CDATA[Rovina Ruslami]]>;
<![CDATA[Tri Hanggono Achmad]]>;
<![CDATA[See Siew Ju]]>;
<![CDATA[Juni Wijayanti Puspita]]>;
<![CDATA[Sapto Wahyu Indratno]]>;
<![CDATA[Edy Soewono]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 4 No. 1 (2021) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2021.4.1.2
<![CDATA[A number of benign EEG patterns are often misinterpreted as interictal epileptiform discharges (IEDs) because of their epileptiform appearances, one of them is wicket spike. Differentiating wicket spike from IEDs may help in preventing epilepsy misdiagnosis. The temporal location of IEDs and wicket spike were chosen from 143 EEG recordings. Amplitude, duration and angles were measured from the wave triangles and were used as the variables. In this study, linear discriminant analysis is used to create the formula to differentiate wicket spike from IEDs consisting spike and sharp waves. We obtained a formula with excellent accuracy. This study emphasizes the need for objective criteria to distinguish wicket spike from IEDs to avoid misreading of the EEG and misdiagnosis of epilepsy.]]>
<![CDATA[An Entomological Model for Estimating the Post-Mortem Interval ]]>
<![CDATA[Vania Mene Risriani]]>;
<![CDATA[Tjandra Anggraeni]]>;
<![CDATA[Nuning Nuraini]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 3 No. 2 (2020) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2020.3.2.6
<![CDATA[Identification of post-mortem interval started from the time when the dead body was found. The main question is to identify the time of death. In reality, the task is complicated since many local factors are involved in the process of decomposition. In most cases, the decomposition process is done by certain local insects that consume the biomass completely. This study uses a mathematical model for the post-mortem interval involving diptera and rabbit corpses as the biomass, based on experimental data from references. We formulate a type of logistic model with decaying carrying capacity only with diptera. The post-mortem interval is shown as the end period of consumption when larvae have entirely consumed the biomass. It is shown from the simulation that the decomposition lasts for 235 hours. The diptera are shown to disappear completely, leaving the remaining corpse after 120 hours.]]>
<![CDATA[Peristaltic-Ciliary Flow of A Casson Fluid through An Inclined Tube ]]>
<![CDATA[Saravana Ramachandran]]>;
<![CDATA[Kuppalapalle Vajravelu]]>;
<![CDATA[K.V. Prasad]]>;
<![CDATA[S. Sreenadh]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 4 No. 1 (2021) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2021.4.1.3
<![CDATA[The paper is concerned with the peristaltic-ciliary transport of a viscoplastic fluid (Casson fluid) through an inclined cylindrical tube. The peristalsis-cilia induced motion is analysed in the moving frame of reference under the lubrication approximations. Solutions to the flow characteristics petering to yielded and unyielded regions are obtained. The effects of various physical parameters on the axial velocity, the pumping characteristics, the pressure rise, and the frictional force over one wavelength, along with the trapping phenomenon are presented through graphs. Further, the peristaltic flow and peristaltic-ciliary flow results are compared. It is noticed that the axial velocity and the size of trapping bolus in the unplug flow region decrease with an increase in the yield stress. In addition, the axial velocity and the axial pressure gradient in the peristaltic-ciliary pumping are higher than those in the peristaltic pumping.]]>
<![CDATA[A Nonlinear Observer to Estimate the Effective Reproduction Number of Infectious Diseases ]]>
<![CDATA[Agus Hasan]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 4 No. 1 (2021) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2021.4.1.4
<![CDATA[In this paper, we design a Nonlinear Observer (NLO) to estimate the effective reproduction number (Rt) of infectious diseases. The NLO is designed from a discrete-time augmented Susceptible-Infectious-Removed (SIR) model. The observer gain is obtained by solving a Linear Matrix Inequality (LMI). The method is used to estimate Rt in Jakarta using epidemiological data during COVID-19 pandemic. If the observer gain is tuned properly, this approach produces similar result compared to existing approach such as Extended Kalman filter (EKF).]]>
<![CDATA[Modeling Simulation of COVID-19 in Indonesia based on Early Endemic Data ]]>
<![CDATA[Nuning Nuraini]]>;
<![CDATA[Kamal Khairudin]]>;
<![CDATA[Mochamad Apri]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 3 No. 1 (2020) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2020.3.1.1
<![CDATA[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.]]>
<![CDATA[On the Analysis of Covid-19 Transmission in Wuhan, Diamond Princess and Jakarta-cluster ]]>
<![CDATA[Edy Soewono]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 3 No. 1 (2020) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2020.3.1.2
<![CDATA[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.]]>
<![CDATA[An Analysis of Covid-19 Transmission in Indonesia and Saudi Arabia ]]>
<![CDATA[Meksianis Z. Ndii]]>;
<![CDATA[Panji Hadisoemarto]]>;
<![CDATA[Dwi Agustian]]>;
<![CDATA[Asep K. Supriatna]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 3 No. 1 (2020) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2020.3.1.3
<![CDATA[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.]]>
