ABSTRACT
In this paper we develop a mathematical model of disease transmission dynamics. Although some vaccines for some infectious diseases are available, there are some cases where handling new emerging infectious diseases, such as COVID-19 pandemic, is still a difficult problem to handle. Preventive actions, such as wearing masks, distance guarding, frequent hand washing, and others are still the most important interventions in handling the transmission of this disease. Recently, several countries have allowed the use of convalescent plasma transfusion (CPT) in the management of moderate and severe COVID-19 patients. Several early studies of this use have yielded prospective results with reduced mortality rates. A recent work also shows that using a simple discrete mathematical model of CPT could reduce the outbreak of disease transmission, in the sense of reducing the peak number of active cases and the length of the outbreak itself. In this paper, we use a continuous SIR model applied to COVID-19 pandemic data in Indonesia to address an important question whether convalescent plasma transfusion may reduce the transmission of the disease. © Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
ABSTRACT
Recently there are some mathematical models of COVID-19 transmission have been developed in an attempt to understand the disease. Various approaches of modeling have been devised by many authors which broadly divided into two different methods, the mechanistic modeling method and the empiric modeling method. In empirical modeling process ones usually look at the available COVID-19 data such as the cumulative cases of insidence and the daily cases of incidence. The data of such cases are usually available from legit situs such as the Worldometer website. This website provides total confirmed cases, daily new cases, daily active cases, daily death, etc. Ones usually use the time series data of the total confirmed cases to fit with a certain growth model. In this paper we will model the COVID-19 disease transmission by looking at the growth of the confirmed and daily new cases data. The growth model we choose is the Morgan-Mercer-Flodin (MMF) equation. We use two methods depending on the minimization process of the RMSE. We used the equation to model the COVID-19 transmission of Indonesia data starting from 2 March 2020, the official first day of the reported pandemic cases in Indonesia, up to 30 November 2020. In applying the growth equations to the pandemic data we denoted that X(t) is the cumulative of confirmed case at time t. The calculation is done using Solver in the Microsoft Excel application by choosing the GRG Nonlinear (Generalized Reduced Gradient) for the oftimization to find the minimum root of the mean square error as the measure. The results show that both methods give relatively similar results and reveal the strongly dependence of prediction on the sufficiency number of data being used. © IEOM Society International.
ABSTRACT
With no vaccine available on the market, handling the COVID-19 pandemic is still a difficult problem to do. Preventive actions, such as wearing masks, distance guarding, frequent hand washing, and others are still the most important interventions in handling the transmission of this disease. Apart from disease transmission, the mortality rate is also an issue that has been widely studied in order to reduce its intensity. So far several countries have allowed the use of convalescent plasma transfusion (CPT) in the management of moderate and severe COVID-19 patients. Although this method is a fairly old method and is often used for other diseases, so far there have not been many studies on the impact of using CPT for COVID-19 on the population level. Several early studies of this use have yielded prospective results with reduced mortality rates. In this paper, we show by using a simple discrete mathematical model, that the uses of CPT for COVID-19 patients can also reduce the outbreak, in the sense of reducing the peak number of active cases and the length of the outbreak itself. The model used is the simplest discrete SIR and SEIR models. The completion of the model is done numerically through simulation on a spreadsheet to obtain general insight regarding the effect of the CPT application in COVID-19 management. © IEOM Society International.
ABSTRACT
The current outbreak of coronavirus disease (COVID-19) has become a global issue to its quick and widespread over the world, including in Indonesia. More than 60% of positive cases came from Java island, therefore the proposed model focused on six provinces in this area. We developed a discrete-time stochastic epidemic model, such as Spatial-SIRD model, associated with the mobility of people by public transportation (air and land). Model parameters were estimated by fitting the data of October 22nd – 28th, 2020 and November 8th-November 14th, 2020 with the model. At the beginning of the estimation process, we used the coefficient of regression from the observation to estimate the range of parameters. Afterward, the order statistics method was carried out to determine the best parameters so we could forecast the number of infectious of each province. The SIR model was created by applying the regression rate of infection parameters before and after the long holiday from October 28 to November 1, 2020. The effect of this long holiday was that it could increase the number of cases so that there was a difference in the rate of infection. © IEOM Society International.
ABSTRACT
The Verhulst logistic function is among the most popular function to describe a growth phenomenon. Initially the theory is applied in studying the growth of living organism populations. However now it finds the applications in any growth phenomenon, including social, education, and engineering. There is a huge number of applications of the logistic function in various field. One of the strength of the model is its capability in estimating the carrying capacity or the maximum level of the growth. This upper bound is very important to obtain and has many practical implication. However, in some circumstances the function may fail to estimate this upper bound, especially when the growth is still at the beginning phase. In pedagogical context of mathematical modeling this failure is regarded as a good example in explaining the modeling process, in which when a model fails to comply with the reality, one should proceed to refine the model following the full cycle of modeling process. In this paper we present a modified growth model of the Verhulst logistic function, since when it is applied to the COVID-19 pandemic data in Indonesia, it cannot estimate the carrying capacity satisfactory. The modification has improved the estimation performance in terms of the root of the mean square error measure (RMSE). © IEOM Society International.