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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 124 Documents
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How Many Can You Infect? Simple (and Naive) Methods of Estimating the Reproduction Number H. Susanto; V.R. Tjahjono; A. Hasan; M.F. Kasim; N. Nuraini; E.R.M. Putri; R. Kusdiantara; H. Kurniawan
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.2020.3.1.4

Abstract

This is a pedagogical paper on estimating the number of people that can be infected by one infectious person during an epidemic outbreak, known as the reproduction number. Knowing the number is crucial for developing policy responses. There are generally two types of such a number, i.e., basic and effective (or instantaneous). While basic reproduction number is the average expected number of cases directly generated by one case in a population where all individuals are susceptible, effective reproduction number is the number of cases generated in the current state of a population. In this paper, we exploit the deterministic susceptibleinfected-removed (SIR) model to estimate them through three different numerical approximations. We apply the methods to the pandemic COVID-19 in Italy to provide insights into the spread of the disease in the country. We see that the effect of the national lockdown in slowing down the disease exponential growth appearedabout two weeks after the implementation date. We also discuss available improvements to the simple (and naive) methods that have been made by researchers in the field. Authors of this paper are members of the SimcovID (Simulasi dan Pemodelan COVID-19 Indonesia) collaboration.
The COVID-19 outbreak in Germany – Models and Parameter Estimation Peter Heidrich; Moritz Schäfer; Mostafa Nikouei; Thomas Götz
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.2020.3.1.5

Abstract

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS–CoV–2, is reported from China and later also from other parts of the world. Since 21 January 2020, World Health Organization (WHO) reports daily data on confirmed cases and deaths from both China and other countries [1]. The Johns Hopkins University [2] collects those data from various sources worldwide on a daily basis. For Germany, the Robert–Koch–Institute (RKI) also issues daily reports on the current number of infections and infection related fatal cases and also provides estimates of several disease-related parameters [3]. In this work we present an extended SEIRD–model to describe these disease dynamics in Germany. The model takes into account the susceptible, exposed, infected, recovered and deceased fractions of the population. Epidemiological parameters like the transmission rate, lethality or the detection rate of infected individuals are estimated by fitting the model output to available data. For the parameter estimation itself we compare two methods: an adjoint based approach and a Monte–Carlo based Metropolis algorithm.
SHAR and effective SIR models: from dengue fever toy models to a COVID-19 fully parametrized SHARUCD framework Maira Aguiar; Nico Stollenwerk
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.2020.3.1.6

Abstract

We review basic models of severe/hospitalized and mild/asymptomatic infection spreading (with classes of susceptibles S, hopsitalized H, asymptomatic A and recovered R, hence SHAR-models) and develop the notion of comparing different models on the same data set as exemplified in the comparison of SHAR models with effective SIR models, where only the H-class of the SHAR model is taken into account in the SIR model. This is done via the so-called Bayes factor. A simpler pair of models with analytical expressions up to the Bayes factor will be briefly mentioned as well. The notions developed with respect to dengue fever epidemiology will then be used to analyze recently becoming available data on coronavirus disease 2019, COVID-19, where models can be fully parametrized including hospital admission and more extensions like intensive care unit (ICU) admission and deceased, always with a close look on as simple as possible models but not simpler, as exercised in Ocham's razor and analyzed by e.g. the Bayes factor. We present the resulting models of SHAR-type with additional classes of ICU admissions U, and deceased D, and for data analysis of cumulative disease data, also accounting the cumulative classes C, in the so-called SHARUCD framework. Besides a first basic version, SHARUCD model 1, we investigate also in detail a refined version, SHARUCD model 2, which could be achieved by a closer analysis of available data only obtained after the exponential growth phase of the epidemic, when lockdown control measures showed effects. Namely, the ICU admissions turned out to be more in synchrony with the hospitalized than with e.g. the deceased cases, such that we could adjust the transitions so that ICU admissions are modeled like hospitalizations in model 2, and not like recovery or disease induced death as assumed in model 1, explaining much better the empirical data, specially after the effects of the lockdown became visible. Special attention will be given here, for the first time, to the initial phase of the COVID-19 epidemics, before all variables entered into the exponential phase, and its interplay between asymptomatic and severe hospitalized cases, always in close check with the SIR-limiting case. Such improved understanding of the initial phase will help in the future analysis of re-emergent outbreaks of COVID-19, likely to happen in the next or a subsequent respiratory disease season in autumn or winter.
A Game Dynamic Modeling Framework to Understand the Influence of Human Choice to Vaccinate or to Reduce Contact with Mosquitoes on Dengue Transmission Dynamics Meksianis Z. Ndii
Communication in Biomathematical Sciences Vol. 4 No. 1 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.1.6

Abstract

Strategies for reducing dengue incidence are by minimizing the contact between mosquitoes and human or the use of vaccine. However, the candidate of dengue is not perfect and potentially results in more secondary infection cases.This leads to the question which strategy should be decided by individuals to reduce the chance for being infected by dengue. A game-dynamic modeling framework by coupling epidemic and behavior model has been constructed to study the effects of human decision making behavior on dengue transmission dynamics. We also consider strategies as time-dependent controls and estimate the parameter values against data of dengue incidence in Kupang city, Indonesia. Parameter estimation gives the reproduction number of 1.17 which indicates the possibility of outbreak occurrence. When the efficacy of reduced contact with mosquitoes is low, the use of vaccination is the best option to reduce dengue incidence. The efficacy of reduced contact with mosquitoes should be at high level to get higher reduction in dengue incidence if no vaccine is available yet. An optimal control approach suggests that a higher level of vaccination rate and the reduced contact with mosquitoes is required to reach optimal reduction in dengue incidence. However, solutions from epidemiological-behavior model showed that individuals are likely to choose one strategy only which has higher cost and the probability of perceived efficacy. The implementation of vaccination helps in reducing dengue incidence. However, understanding the effects of dengue vaccine on secondary infections is required before the delivery of such intervention.
Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model Muhammad Afief Balya; Bunga Oktaviani Dewi; Faza Indah Lestari; Gayatri Ratu; Hanna Rosuliyana; Tama Windyhani; Zawir Rifqa Fadhlia; Brenda M. Samiadji; Dipo Aldila; Sarbaz H. A. Khoshnaw; Muhammad Shahzad
Communication in Biomathematical Sciences Vol. 4 No. 1 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.1.5

Abstract

In this article, we propose and analyze a mathematical model of COVID-19 transmission among a closed population, with social awareness and rapid test intervention as the control variables. For this, we have constructed the model using a compartmental system of the ordinary differential equations. Dynamical analysis regarding the existence and local stability of equilibrium points is conducted rigorously. Our analysis shows that COVID-19 will disappear from the population if the basic reproduction number is less than one, and persist if the basic reproduction number is greater than one. In addition, we have shown a trans-critical bifurcation phenomenon based on our proposed model when the basic reproduction number equals one. From the elasticity analysis, we have observed that rapid testing is more promising in reducing the basic reproduction number as compared to a media campaign to improve social awareness on COVID-19. Using the Pontryagin Maximum Principle (PMP), the characterization of our optimal control problem is derived analytically and solved numerically using the forward-backward iterative algorithm. Our cost-effectiveness analysis shows that using rapid test and media campaigns partially are the best intervention strategy to reduce the number of infected humans with the minimum cost of intervention. If the intervention is to be implemented as a single intervention, then using solely the rapid test is a more promising and low-cost option in reducing the number of infected individuals vis-a-vis a media campaign to increase social awareness as a single intervention.
Mathematical Modelling and Control of COVID-19 Transmission in the Presence of Exposed Immigrants Reuben Iortyer Gweryina; Chinwendu Emilian Madubueze; Martins Afam Nwaokolo
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.2

Abstract

In this paper, a mathematical model for COVID-19 pandemic that spreads through horizontal transmission in the presence of exposed immigrants is studied. The model has equilibrium points, notably, COVID-19-free equilibrium and COVID-19-endemic equilibrium points. The model exhibits a basic reproduction number, R0 which determines the elimination and persistence of the disease. It was found that when R0 < 1, then the equilibrium becomes locally asymptotically stable and endemic equilibrium does not exists. However, when R0 > 1, the equilibrium is found to be stable globally. This implies that continuous mixing of exposed immigrants with the susceptible population will make the eradication of COVID-19 difficult and endemic in the community. The system is also proved qualitatively to experience transcritical bifurcation close to the COVID-19-free equilibrium at the point R0 = 1. Numerically, the model is used to investigate the impact of certain other relevant parameters on the spread of COVID-19 and how to curtail their effect.
Defining Causality in Covid-19 and Google Search Trends in Java, Indonesia Cases: A Retrospective Analysis Afrina Andriani br Sebayang; Enrico Antonius; Elisabeth Victoria Pravitama; Jonathan Irianto; Shannen Widijanto; Muhammad Syamsuddin
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.1

Abstract

The Coronavirus disease 2019 (Covid-19) has led all countries around the world to the unpredicted situation. It is such a crucial to investigate novel approaches in predicting the future behaviour of the outbreak. In this paper, Google trend analysis will be employed to analyse the seek pattern of Covid-19 cases. The first method to investigate the seek information behaviour related to Covid-19 outbreak is using lag-correlation between two time series data per regional data. The second method is used to encounter the cause-effect relation between time series data. We apply statistical methods for causal inference in epidemics. Our focus is on predicting the causal-effect relationship between information-seeking patterns and Google search in the Covid-19 pandemic. We propose the using of Granger Causality method to analyse the causal relation between incidence data and Google Trend Data.
Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination Raqqasyi Rahmatullah Musafir; Agus Suryanto; Isnani Darti
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.3

Abstract

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V ). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points.
Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model Dipo Aldila; Arthana Islamilova; Sarbaz H.A. Khosnaw; Bevina D. Handari; Hengki Tasman
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.4

Abstract

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.
Analysis of A Coendemic Model of COVID-19 and Dengue Disease Hilda Fahlena; Widya Oktaviana; Farida; Sudirman; Nuning Nuraini; Edy Soewono
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.5

Abstract

The coronavirus disease 2019 (COVID-19) pandemic continues to spread aggressively worldwide, infecting more than 170 million people with confirmed cases, including more than 3 million deaths. This pandemic is increasingly exacerbating the burden on tropical and subtropical regions of the world due to the pre-existing dengue fever, which has become endemic for a longer period in the same region. Co-circulation dengue and COVID-19 cases have been found and confirmed in several countries. In this paper, a deterministic model for the coendemic of COVID-19 and dengue is proposed. The basic reproduction ratio is obtained, which is related to the four equilibria, disease-free, endemic-COVID-19, endemic-dengue, and coendemic equilibria. Stability analysis is done for the first three equilibria. Furthermore, a condition for coexistence equilibrium is obtained, which gives a condition for bifurcation analysis. Numerical simulations were carried out to obtain a stable limit-cycle resulting from two Hopf bifurcation points with dengue transmission rate and COVID-19 transmission rate as the bifurcation parameter, representing a stable periodic coexistence of dengue and COVID-19 transmission. We identify the period of limit cycle decreases after reaching the maximum value.

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