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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

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.

A Dynamical Model of â€™Invisible Wallâ€™ in Mosquito Control Khumaeroh, Mia Siti; Soewono, Edy; Nuraini, Nuning
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

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.

Comparison of Dengue Transmission in Lowland and Highland Area: Case Study in Semarang and Malang, Indonesia Fauzi, Ilham Saiful; Fakhruddin, Muhammad; Nuraini, Nuning; Wijaya, Karunia Putra
Communication in Biomathematical Sciences Vol 2, No 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

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.

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

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.

A Dynamical Model of âInvisible Wallâ in Mosquito Control Mia Siti Khumaeroh; Edy Soewono; Nuning Nuraini
Communication in Biomathematical Sciences Vol. 1 No. 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2018.1.2.2

A concept of an âinvisible wallâ 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.

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

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.

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

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.

Modeling Simulation of COVID-19 in Indonesia based on Early Endemic Data Nuning Nuraini; Kamal Khairudin; Mochamad Apri
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

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.

An Entomological Model for Estimating the Post-Mortem Interval Vania Mene Risriani; Tjandra Anggraeni; Nuning Nuraini
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.2020.3.2.6

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.

On The Study of Covid-19 Transmission Using Deterministic and Stochastic Models with Vaccination Treatment and Quarantine Mona Zevika; Anita Triska; Nuning Nuraini; Glenn Lahodny Jr.
Communication in Biomathematical Sciences Vol. 5 No. 1 (2022)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2022.5.1.1

In this study, we propose deterministic and stochastic models of the spread of Covid-19 with vaccination and quarantine programs. The model considers the facts that vaccines do not provide full protection, the efficacy of current vaccines only lasts for a limited time, and recovered people could be reinfected. The routine analysis was carried out for the deterministic model, including calculating an expression for the basic reproduction number. The stochastic formulation makes use of a Continuous-Time Markov Chain (CTMC) model. The basic reproduction number from the deterministic model relates to the stochastic model's analysis in producing a formula for the probability of extinction of Covid-19. Furthermore, numerical simulations are carried out to analyze the sensitivity of the dynamical states and the basic reproduction number to the model parameters. An expression for the probability of disease extinction in terms of the model parameters and initial conditions is given. The results of this study suggest that current conditions in Indonesia will lead to a longterm Covid-19 epidemic. One of the efforts to overcome the Covid-19 epidemic is by increasing the provision of vaccines to the susceptible population. However, the number of vaccinated people in the population is not always an ideal control for dealing with the spread of the disease. The vaccine efficacy is also important to reduce the infection. As long as the efficacy is not sufficient to give a good protection to the human population and it lasts only for a short period of time, quarantine is still needed.

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