Communication in Biomathematical Sciences最新文献

{"title":"A Nonlinear Observer to Estimate the Effective Reproduction Number of Infectious Diseases","authors":"A. Hasan","doi":"10.1101/2021.03.02.21252730","DOIUrl":"https://doi.org/10.1101/2021.03.02.21252730","url":null,"abstract":"In this paper, we design a Nonlinear Observer (NLO) to estimate the effective reproduction number (Rt) of infectious diseases. The NLO is designed from a discrete-time augmented Susceptible-Infectious-Removed (SIR) model. The observer gain is obtained by solving a Linear Matrix Inequality (LMI). The method is used to estimate Rt in Jakarta using epidemiological data during COVID-19 pandemic. If the observer gain is tuned properly, this approach produces similar result compared to existing approach such as Extended Kalman filter (EKF).","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41717734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling COVID-19 Transmissions and Evaluation of Large Scale Social Restriction in Jakarta, Indonesia","authors":"A. Hasan, Y. Nasution, H. Susanto, E. Putri, V. Tjahjono, D. Puspita, K. Sukandar, N. Nuraini, W. Widyastuti","doi":"10.1101/2020.10.30.20222984","DOIUrl":"https://doi.org/10.1101/2020.10.30.20222984","url":null,"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.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42985930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SHAR and effective SIR models: from dengue fever toy models to a COVID-19 fully parametrized SHARUCD framework","authors":"M. Aguiar, N. Stollenwerk","doi":"10.5614/CBMS.2020.3.1.6","DOIUrl":"https://doi.org/10.5614/CBMS.2020.3.1.6","url":null,"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.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48644711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How Many Can You Infect? Simple (and Naive) Methods of Estimating the Reproduction Number","authors":"H. Susanto, V. Tjahjono, A. Hasan, M. F. Kasim, N. Nuraini, E. Putri, R. Kusdiantara, H. Kurniawan","doi":"10.5614/CBMS.2020.3.1.4","DOIUrl":"https://doi.org/10.5614/CBMS.2020.3.1.4","url":null,"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.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43372689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Analysis of Covid-19 Transmission in Indonesia and Saudi Arabia","authors":"M. Z. Ndii, P. Hadisoemarto, D. Agustian, Asep K. Supriatna","doi":"10.5614/CBMS.2020.3.1.3","DOIUrl":"https://doi.org/10.5614/CBMS.2020.3.1.3","url":null,"abstract":"An outbreak of novel coronavirus has been happening in more than 200 countries and has shocked society. Several measures have been implemented to slowing down the epidemics while waiting for vaccine and pharmaceutical intervention. Using a deterministic and stochastic model, we assess the effectiveness of current strategies: reducing the transmission rate and speeding up the time to detect infected individuals. The reproductive ratio and the probability of extinction are determined. We found that the combination of both strategies is effective to slow down the epidemics. We also find that speeding up the time to detect infected individuals without reducing the transmission rate is not sufficient to slow down the epidemics.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47232900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Reproduction Ratio of Dengue Incidence in Semarang, Indonesia 2015-2018","authors":"J. W. Puspita, M. Fakhruddin, Hilda Fahlena, Fatkhur Rohim, Sutimin Sutimin","doi":"10.5614/cbms.2019.2.2.5","DOIUrl":"https://doi.org/10.5614/cbms.2019.2.2.5","url":null,"abstract":"Dengue is one of the mosquito-borne diseases caused by dengue viruses (DENV), which has become endemic in most tropical and subtropical countries, including Indonesia. Since there is a lot of dengue incidence on children of age less than fourteen years old in Semarang, Indonesia, it is the interest here to analyze the different rates of infection among different age groups. A SIR-UV mathematical model with age structure in human the population is constructed to describe dengue transmission in Semarang from 2015 to 2018. In this study, we separated the human population into four age classes: children (0-4 years), youngster (5-14 years), productive adults (15-60 years) and non-productive adults (over 60 years). We use Particle Swarm  Optimization to obtain optimal parameters for the transmission rates based on the yearly incidence. The basic reproduction ratio (R0) is derived from the Next Generation Matrix and is evaluated by using the optimal parameters for data Semarang in 2015-2018. Numerical simulation results show that the number of dengue incidence is in a good agreement with the actual data in Semarang for 2015-2018.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41553621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical analysis of mathematical model for Bovine Tuberculosis among human and cattle population","authors":"D. Aldila, Siti Latifa, Putri A. Dumbela","doi":"10.5614/cbms.2019.2.1.6","DOIUrl":"https://doi.org/10.5614/cbms.2019.2.1.6","url":null,"abstract":"Bovine Tuberculosis (BTB) is a disease that can attack humans through cattle.The process of transmission can occur through the air and cattle products that are not treated properly. When humans are infected with BTB, reinfection, and relapse may occur. This phenomenon is modeled as an eleven-dimension dynamical system. Our aim is to gain insight into the effect of separation of human activity area into the transmission dynamics of BTB. The model incorporates (among many others features) the dynamics of BTB among human and cattle population, density-dependent infection rate, and reinfection, are rigorously analyzed and simulated. The trivial disease-free equilibrium of the model is shown to be locally asymptotically stable when the two associated basic reproduction number are less than unity. Although the non-trivial equilibrium cannot be shown explicitly, for a special case, this equilibrium is still possible to show and discuss further. Our results suggest that controlling BTB in cattle population may indirectly control the spread of BTB in human. An example of controlling the infected population of infected cattle can be done with the annihilation of infected cattle.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44046428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bottom-up and top-down control in a multitrophic system: the role of nutrient limitation and infochemical-mediated predation in a plankton food-web model","authors":"N. Walker, H. Susanto, M. Steinke, Edward A. Codling","doi":"10.5614/CBMS.2019.2.2.1","DOIUrl":"https://doi.org/10.5614/CBMS.2019.2.2.1","url":null,"abstract":"Chemicals released following herbivore grazing on primary producers can promote multitrophic interactions by influencing the foraging behaviour of higher order predators. In particular, chemicals released during microzooplankton grazing on phytoplankton can act as infochemical cues that elicit foraging responses and improve search efficiency in carnivorous copepods. Models investigating such infochemical-mediated multitrophic interactions in the plankton are typically based on top-down control, where phytoplankton concentrations are controlled through predation and grazing from higher trophic levels. However, in marine environments nutrient limitation is an important factor that influences a food-web from below, and earlier models of this system only indirectly account for this by assuming predator-free growth is logistic with a fixed carrying capacity. Here we consider the dynamics of infochemical-mediated interactions in a marine system where nutrient limitation is modelled directly through an extended NPZ-style model. We show the one-parameter bifurcation behavior of the top-down model to change when the total nutrient availability is changed, and hence demonstrate phytoplankton bloom formation to be a function of both top-down and bottom-up processes.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43391518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Model of an Interaction between Bears and Salmon; A Case in British Columbia","authors":"Hilda Fahlena, J. T. M. Sahetapy-Engel, Azhary Ramadhanty, D. Sutanto, Eduardus Axel Wijaya, Ambar Winarni","doi":"10.5614/CBMS.2019.2.1.4","DOIUrl":"https://doi.org/10.5614/CBMS.2019.2.1.4","url":null,"abstract":"An interaction model for the Pacific salmon and bear population in British Columbia is discussed here. The phenomenon is shown during the salmons period of migration back to their birthplace river at the end of their life. During this returning home, a large number of bears from the nearby state come and prey on them. This predation of salmon before spawning is suspected as the cause of the decline in Salmon production. Here a dynamical model involving a specific predator-prey type interaction between Salmon and Bears is constructed in the form of a non-autonomous dynamical system, in which the transition rate from the adult state of salmon to the spawning state is positive only in the month of migration. Dynamical analysis for the stability of the coexistence equilibrium for the autonomous case is shown and sensitivity analysis for the non-autonomous the case is done numerically.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49298898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Competition between Javan Rhino (Rhinoceros Sondaicus) and Javan Bull (Bos Javanicus) at Ujung Kulon National Park with Allee Effect","authors":"Eric Harjanto, Respati Mentari","doi":"10.5614/CBMS.2019.2.1.5","DOIUrl":"https://doi.org/10.5614/CBMS.2019.2.1.5","url":null,"abstract":"In the last few decades, it has been reported that the population of Rhino (Rhinoceros Sondaicus) at the Ujung Kulon National Park has been reaching a stagnation at the number 50s, despite the existing territory can support a much larger number of Rhinos. Here, we construct a dynamical model representing the interaction between Rhino and Bull (Bos Javanicus) with Allee effect for the Javan rhinos population. This Allee effect may occur in the field, among others, due to the solitary behaviour of Rhino within large territory, imbalance of age structure and gender and difficulty of finding mates in Javan rhinos population which causes inbreeding in the population. In this paper, we follow the previous paper on the territorial competition between Javan  rhino and Javan bull at Ujung Kulon National Park and add Allee effect factor on the Javan rhino’s population. We give a proof on the boundedness of the solution and explanation on the bifurcations that occur in the model. One of these bifurcations plays an important role in the system. Some simulations and suggestion on how to improve the survival of Javan rhino is also included.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44957855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}