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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 3 Documents
 1 
Search results for , issue "Vol. 5 No. 2 (2022)" : 3 Documents clear
A Fractional-Order Food Chain Model with Omnivore and Anti-Predator Adin Lazuardy Firdiansyah
Communication in Biomathematical Sciences Vol. 5 No. 2 (2022)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2022.5.2.2

Abstract

A fractional-order food chain model is proposed in this article. The model is built by prey, intermediate predator, and omnivore. It is assumed that intermediate predator only eat prey and omnivore can consume prey and intermediate predator. But, prey has the ability called as anti-predator behavior to escape from both predators. For the first discussion, it is found that all solutions are existential, uniqueness, boundedness, and non-negative. Further, we analyze the existence condition and local stability of all points, that is point for the extinction of all populations, both predators, intermediate predator, omnivore, and point for the existence of all populations. We also investigate the global stability of all points, except point for the extinction of all populations and both predators. Finally, we preform several numerical solutions by using the nonstandard Grunwald-Letnikov approximation to demonstrate the our analytical results.
Control Design for Dengue Fever Model with Disturbance Hanna Hilyati Aulia; Roberd Saragih; Dewi Handayani
Communication in Biomathematical Sciences Vol. 5 No. 2 (2022)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2022.5.2.3

Abstract

A mathematical model has become a useful tool to predict and control dengue fever dynamics. In reality, the dynamic of dengue fever transmission can be disturbed by uncertainty measurements, so it is needed to consider the disturbance in the model. Then, dengue fever model with disturbance is constructed by using a gain matrix consisting a covariance matrix and random vector. As dengue vaccine has been challenging to reduce the pandemic, a dengue model with vaccination as control is constructed. The aim is to propose a feedback controller that can reduces the infected human (H2 control problem) and the uncertainty measurements (H∞ control problem). The control u denotes the proportion of susceptible humans that one decides to vaccinate at time t. A random mass vaccination with wanning immunity is chosen because vaccine still on development process. A Design of mixed H2 - H∞ control with State-dependent Riccati Equation (SDRE) approach is applied. The SDRE has been an effective method to solve for synthesizing nonlinear feedback controller by transforming the system to an State-dependent coefficient (SDC) form. By comparing the mixed scheme with basic H∞, numerical simulation shows that the control application effectively decreases the number of infected humans and reduces the disturbance.
Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission P. Muthu; Bikash Modak
Communication in Biomathematical Sciences Vol. 5 No. 2 (2022)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2022.5.2.1

Abstract

During the process of immune response to the infection caused by dengue virus, antibodies are generated by plasma cells which are produced by B-cells. In some cases, it is observed that there is a delay in the production of plasma cells from B-cells which causes a delay in the immune response. We propose a SIVA within-host model of the virus transmission with delayed immune response to articulate the dynamics of the cell and virus population. The stability analysis of different equilibrium states is also studied. The basic reproduction number (BRN) of the model is computed using next generation matrix (NGM) method. The local stability analysis is discussed using the method of linearisation. The stability conditions of the equilibrium states are validated using the Li´enard - Chipart criterion. Hopf bifurcation analysis is carried out as the system has time lag in the immune response. Three equilibrium states, namely, virus free equilibrium state, endemic equilibrium state with and without immune response, have been observed. It has been found that the virus free equilibrium state is locally asymptotically stable if BRN is less than or equal to 1. Additionally, the conditions for the stability of the endemic equilibrium points are derived and elaborated. Numerical simulations for different values of time delay parameter τ are presented and illustrated using graphs. A Hopf bifurcation is observed if the delay parameter τ crosses a threshold value and then the system becomes unstable with periodic solution. To determine the relative importance of the model parameters to the virus transmission and prevalence, sensitivity analysis of the parameters is illustrated using graphs. Due to the time lag in the immune response, an increase in the virus growth is observed in large quantity. As a result, the infection spreads more quickly within the host.

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