Authors:Mona Zevika, Anita Triska, Nuning Nuraini, Glenn Lahodny Jr. Pages: 1 - 19 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. PubDate: 2022-04-15 DOI: 10.5614/cbms.2022.5.1.1 Issue No:Vol. 5, No. 1 (2022)

Authors:M. Haider Ali Biswas, S. Abdus Samad, Tahera Parvin, M. Tusberul Islam, Asep K. Supriatna Pages: 20 - 39 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. PubDate: 2022-07-03 DOI: 10.5614/cbms.2022.5.1.2 Issue No:Vol. 5, No. 1 (2022)

Authors:Ebenezer Bonyah Pages: 40 - 62 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. PubDate: 2022-07-03 DOI: 10.5614/cbms.2022.5.1.3 Issue No:Vol. 5, No. 1 (2022)

Authors:Tahmineh Azizi Pages: 63 - 77 Abstract: In this study, we present the application of fractional calculus (FC) in biomedicine. We present three different integer order pharmacokinetic models which are widely used in cancer therapy with two and three compartments and we solve them numerically and analytically to demonstrate the absorption, distribution, metabolism, and excretion (ADME) of drug in different tissues. Since tumor cells interactions are systems with memory, the fractional-order framework is a better approach to model the cancer phenomena rather than ordinary and delay differential equations. Therefore, the nonstandard finite difference analysis or NSFD method following the Grunwald-Letinkov discretization may be applied to discretize the model and obtain the fractional-order form to describe the fractal processes of drug movement in body. It will be of great significance to implement a simple and efficient numerical method to solve these fractional-order models. Therefore, numerical methods using finite difference scheme has been carried out to derive the numerical solution of fractional-order two and tri-compartmental pharmacokinetic models for oral drug administration. This study shows that the fractional-order modeling extends the capabilities of the integer order model into the generalized domain of fractional calculus. In addition, the fractional-order modeling gives more power to control the dynamical behaviors of (ADME) process in different tissues because the order of fractional derivative may be used as a new control parameter to extract the variety of governing classes on the non local behaviors of a model, however, the integer order operator only deals with the local and integer order domain. As a matter of fact, NSFD may be used as an effective and very easy method to implement for this type application, and it provides a convenient framework for solving the proposed fractional-order models. PubDate: 2022-08-02 DOI: 10.5614/cbms.2022.5.1.4 Issue No:Vol. 5, No. 1 (2022)

Authors:La Pimpi, Sapto Wahyu Indratno, Juni Wijayanti Puspita, Edi Cahyono Pages: 78 - 89 Abstract: Indonesia, a country in the tropics, is an area of distribution and an endemic area of dengue. The death rate caused by dengue is relatively high In Indonesia. Therefore, the health authority must prioritize preventing and controlling dengue disease for a long-term policy. This study proposes a method based on dynamic climate variables in estimating the proportion of infected human and infected mosquito. We focus on the dengue case in Bandung city, one of the big cities in Indonesia, which is classified as endemic dengue. We applied the Poisson regression method involving dynamic climate variables to estimate the average number of infected human population. We then use these estimation results as the basis for approximating the proportion of infected human and mosquito populations using a deterministic and stochastic model approach. Effective reproduction number is also obtained here. The simulation results show that the stochastic model looks better in capturing dengue incidence data than the deterministic model. Therefore, dengue transmission can be reduced by controlling the abundance of mosquito populations, considering climate conditions and the historical number of infected human. PubDate: 2022-08-02 DOI: 10.5614/cbms.2022.5.1.5 Issue No:Vol. 5, No. 1 (2022)

Authors:Agus Hasan, Yuki Nasution, Hadi Susanto, Endah Putri, Venansius Tjahjono, Dila Puspita, Kamal Sukandar, Nuning Nuraini, Widyastuti Pages: 90 - 100 Abstract: This paper presents mathematical modeling and quantitative evaluation of Large Scale Social Restriction (LSSR) in Jakarta between 10 April and 4 June 2020. The special capital region of Jakarta is the only province among 34 provinces in Indonesia with an average Testing Positivity Rate (TPR) below 5% recommended by the World Health Organization (WHO). The transmission model is based on a discrete-time compartmental epidemiological model incorporating suspected cases. The quantitative evaluation is measured based on the estimation of the time-varying effective reproduction number (Rt). Our results show the LSSR has been successfully suppressed the spread of COVID-19 in Jakarta, which was indicated by Rt < 1. However, once the LSSR was relaxed, the effective reproduction number increased significantly. The model is further used for short-term forecasting to mitigate the course of the pandemic. PubDate: 2022-08-02 DOI: 10.5614/cbms.2022.5.1.6 Issue No:Vol. 5, No. 1 (2022)