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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
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Search results for , issue "Vol. 5 No. 1 (2022)" : 3 Documents clear
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

Abstract

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.
Optimal Control Strategy to Reduce the Infection of Pandemic HIV Associated with Tuberculosis M. Haider Ali Biswas; S. Abdus Samad; Tahera Parvin; M. Tusberul Islam; Asep K. Supriatna
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.2022.5.1.2

Abstract

Tuberculosis (TB) and HIV/AIDS has become hazardous among communicable diseases and so as their co-infection in present era. HIV virus gradually weakens immune system in human body, and then TB infects with the assist of HIV/AIDS at any stage of the total infectious period. Today, HIV and tuberculosis (TB) are the main causes of mortality from infectious and chronic diseases. In this Study, we manifest a compartmental co-infection model including HIV and TB on the basis of their characteristics of disease transmission. The model is divided into 10 compartments, each with its own set of nonlinear ordinary differential equations. Using the Pontryagin's Maximum Principle, we investigate the existence of state variables, objective functional and optimum control plans. Identifying the most effective ways for reducing infection among the individuals, the optimal control techniques like vaccination control and treatment control measures are applied. The goal of this study is to lower the rate of HIV-TB co-infection and the cost of treatment. Another objective is to find the better control strategy to prevent HIV/AIDS that invites other pathogen in human body by gradual loosing of immunity. We carried out the investigation both analytically and numerically to divulge the effectiveness of the vaccination and treatment control to lessen the HIV and TB infection among the individuals.
A Malaria Status Model: The Perspective of Mittag-Leffler Function with Stochastic Component Ebenezer Bonyah
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.2022.5.1.3

Abstract

Malaria continues to affect many individuals irrespective of the status or class particularly in Sub-Saharan Africa. In this work, an existing malaria status classical model is studied in fractionalized perspective. The positivity and boundedness of the malaria model is studied. The existence and uniqueness of solutions based on fractional derivative and stochastic perspective is established. The numerical simulation results depict that the infectious classes of humans and vector increase as the fractional order derivative increases. Susceptible classes humans and vector reduce as the fractional order derivative increases. This phenomenon is peculiar with epidemiological models. The implications of the results are that in managing the dynamics of the status model, the fractional order derivative as well as its associated operator is important. It is observed that fractional order derivative based on Mittag-Leffler function provides a better prediction because of its crossover property, its non-local and non-singular property.

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