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All Journal Jurnal Statistika Universitas Muhammadiyah Semarang Jurnal Sains Matematika dan Statistika BAREKENG: Jurnal Ilmu Matematika dan Terapan Communication in Biomathematical Sciences Limits: Journal of Mathematics and Its Applications Jambura Journal of Mathematics MONSU'ANI TANO Jurnal Pengabdian Masyarakat Jurnal Matematika UNAND Contemporary Mathematics and Applications (ConMathA) Jambura Journal of Mathematics Education Jambura Journal of Biomathematics (JJBM) Jurnal Diferensial MATHunesa: Jurnal Ilmiah Matematika Jurnal Pengabdian Papua Trigonometri: Jurnal Matematika dan Ilmu Pengetahuan Alam Journal of Mathematics, Computation and Statistics (JMATHCOS)
Hasan S. Panigoro
Universitas Negeri Gorontalo
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Journal : Communication in Biomathematical Sciences

 1 
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.
Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey Hasan S. Panigoro; Agus Suryanto; Wuryansari Muharini Kusumahwinahyu; Isnani Darti
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.2019.2.2.4

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.
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.
Co-Authors Agus Suryanto Agusyarif Rezka Nuha Ajiboye, Aminat Olabisi Amelia Tri Rahma Sidik Amelia Tri Rahma Sidik Anatasya Lahay Apon Ismail Armayani Arsal Asriadi Asriadi Asriadi Balogun, Ghaniyyat Bolanle Beay, Lazarus Kalvein Cabelita Husuna Darti, Isnani Datu, Pratiwi Ardin Daud, Sriwati M. Dewi Rahmawaty Isa DIAN SAVITRI Dian Savitri Djihad Wungguli Femy Mahmud Sahami Friansyah Gani G. S. Mahapatra Hadi Susanto Hamani, Mohamad Taufik Harto Malik Isnani Darti Isnani Darti Isran K Hasan K. Nasib, Salmun Kai, Ferawati Kusumahwinahyu, Wuryansari Muharini La Ode Nashar Lailany Yahya Lakoro, Tiara Lamuda, Zulfatra Lanto Ningrayati Amali Mahmud, Sri Lestari Muhammad Rezky F. Payu Ninik Wahju Hidajati NISKY IMANSYAH YAHYA Novianita Achmad Nurdia Walangadi Nurhayati Abbas Nurmardia Abdussamad, Siti Nurwan Nurwan Oguntolu, Festus Abiodun Omede, Benjamin Idoko P. K. Santra Perry Zakaria Peter, Olumuyiwa James Rahmi, Emli Rauf, Jayanti Resmawan Resmawan Revandi S. Pakaya Salmun K. Nasib Sarson W DJ Pomalato Sri Agustin Limalo Sri Lestari Mahmud Sri Lestari Mahmud Suaib A Siraj Suryanto, Agus Wuryansari Muharini Kusumahwinahyu Yayu Indriati Arifin