scholarly journals SEIR Mathematical Model of Convalescent Plasma Transfusion to Reduce COVID-19 Disease Transmission

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2857
Author(s):  
Hennie Husniah ◽  
Ruhanda Ruhanda ◽  
Asep K. Supriatna ◽  
Md. H. A. Biswas
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Patient Survival ◽  
Equilibrium Points ◽  
Population Level ◽  
Infectious Period ◽  
Plasma Transfusion ◽  
Standard Procedures ◽  
Reproduction Numbers ◽  
Trivial Equilibrium

In some diseases, due to the restrictive availability of vaccines on the market (e.g., during the early emergence of a new disease that may cause a pandemic such as COVID-19), the use of plasma transfusion is among the available options for handling such a disease. In this study, we developed an SEIR mathematical model of disease transmission dynamics, considering the use of convalescent plasma transfusion (CPT). In this model, we assumed that the effect of CPT increases patient survival or, equivalently, leads to a reduction in the length of stay during an infectious period. We attempted to answer the question of what the effects are of different rates of CPT applications in decreasing the number of infectives at the population level. Herein, we analyzed the model using standard procedures in mathematical epidemiology, i.e., finding the trivial and non-trivial equilibrium points of the system including their stability and their relation to basic and effective reproduction numbers. We showed that, in general, the effects of the application of CPT resulted in a lower peak of infection cases and other epidemiological measures. As a consequence, in the presence of CPT, lowering the height of an infective peak can be regarded as an increase in the number of remaining healthy individuals; thus, the use of CPT may decrease the burden of COVID-19 transmission.

scholarly journals Investigating the Role of Environmental Transmission in COVID-19 Dynamics: A Mathematical Model Based Study

2020 ◽  
Author(s):  
Ibrahim M. ELmojtaba ◽  
Fatma Al-Musalhi ◽  
Asma Al-Ghassani ◽  
Nasser Al-Salti
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Environmental Transmission ◽  
Estimated Parameters ◽  
Existence And Stability

Abstract A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to two datasets. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Existence and stability analysis of disease free and endemic equilibrium points have been presented in relation with the obtained expressions of R0. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically.

scholarly journals SIR Mathematical Model of Convalescent Plasma Transfusion Applied to the COVID-19 Pandemic Data in Indonesia to Control the Spread of the Disease

2021 ◽  
Vol 2084 (1) ◽  
pp. 012022
Author(s):  
Hennie Husniah ◽  
Ruhanda ◽  
Asep Kuswandi Supriatna
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Disease Transmission ◽  
Emerging Infectious Diseases ◽  
Mortality Rates ◽  
Sir Model ◽  
Difficult Problem ◽  
Plasma Transfusion ◽  
Preventive Actions ◽  
Discrete Mathematical Model

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.

scholarly journals Characterizing super-spreaders using population-level weighted social networks in rural communities

2021 ◽  
Vol 380 (2214) ◽  
Author(s):  
Shivkumar Vishnempet Shridhar ◽  
Marcus Alexander ◽  
Nicholas A. Christakis
Keyword(s):  
Rural Communities ◽  
Disease Transmission ◽  
Data Science ◽  
Population Level ◽  
Respiratory Illness ◽  
Individual Characteristics ◽  
Contact Tracing ◽  
Transmission Model ◽  
Infectious Period ◽  
Interaction Patterns

Sociocentric network maps of entire populations, when combined with data on the nature of constituent dyadic relationships, offer the dual promise of advancing understanding of the relevance of networks for disease transmission and of improving epidemic forecasts. Here, using detailed sociocentric data collected over 4 years in a population of 24 702 people in 176 villages in Honduras, along with diarrhoeal and respiratory disease prevalence, we create a social-network-powered transmission model and identify super-spreading nodes as well as the nodes most vulnerable to infection, using agent-based Monte Carlo network simulations. We predict the extent of outbreaks for communicable diseases based on detailed social interaction patterns. Evidence from three waves of population-level surveys of diarrhoeal and respiratory illness indicates a meaningful positive correlation with the computed super-spreading capability and relative vulnerability of individual nodes. Previous research has identified super-spreaders through retrospective contact tracing or simulated networks. By contrast, our simulations predict that a node’s super-spreading capability and its vulnerability in real communities are significantly affected by their connections, the nature of the interaction across these connections, individual characteristics (e.g. age and sex) that affect a person’s ability to disperse a pathogen, and also the intrinsic characteristics of the pathogen (e.g. infectious period and latency). This article is part of the theme issue ‘Data science approach to infectious disease surveillance’.

scholarly journals Development of Compartmental Mathematical Model of Disease Transmission of Basal Stem Rot in Oil Palm Plantation

2020 ◽  
Vol 9 (6) ◽  
pp. 191-194
Keyword(s):  
Mathematical Model ◽  
Oil Palm ◽  
Disease Transmission ◽  
Plant Disease ◽  
Model Simulation ◽  
Equilibrium Points ◽  
Crop Protection ◽  
Stem Rot ◽  
Basal Stem Rot ◽  
Oil Palm Plantation

The mathematical modelling is one of the major research areas for mathematician and biologist in understanding the dynamics of transmissible infections. There might also be a mathematical model used to research the dynamics of plant disease and estimate the number of cases of outbreaks. In this research, we developed the compartmental mathematical model of the dynamical spread of transmission of plant disease with reference to basal stem rot (BSR) disease in oil palm plantation. The dynamics of the BSR disease were studied by a prone-contagious-sustained (PCS) compartmental mathematical model involving ordinary differential equations for three classes of hosts; prone, contagious and sustained. The equilibrium points and epidemic threshold conditions were analytically determined and numerical simulations were analyzed to support analytical results. From the numerical results, the solutions converge to each equilibrium state and PCS model simulation indicated that BSR disease has not become endemic. In particular, the threshold parameters that summarize the dynamics of the system will help to choose strategies for crop protection.

scholarly journals Pemodelan Matematika SEIR Penyebaran Penyakit Pneumonia pada Balita dengan Pengaruh Vaksinasi di Kota Makassar

2021 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Syafruddin Side ◽  
Wahidah Sanusi ◽  
Nurul Aulia Bohari
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Ordinary Differential Equation ◽  
Equilibrium Points ◽  
Seir Model ◽  
Reproduction Numbers ◽  
Ordinary Differential Equation Systems

Abstrak. Penelitian ini bertujuan untuk membangun model penyebaran penyakit pneumonia pada balita tipe SEIR (Susceptible- Exposed- Infected- Recovered-), menganalisis model, dan menentukan proporsi minimum vaksinasi. Data yang digunakan adalah data jumlah penderita pneumonia pada balita di Kota Makassar tahun 2019. Hasil penelitian diperoleh model matematika SEIR penyakit pneumonia dalam bentuk sistem persamaan diferensial biasa; titik keseimbangan bebas kecanduan dan titik keseimbangan kecanduan yang keduanya bersifat stabil; bilangan reproduksi dasar untuk simulasi tanpa vaksinasi lebih besar dari 1 yang artinya penyakit masih tetap ada dalam populasi, sedangkan bilangan reproduksi dasar untuk simulasi dengan vasksinasi kurang dari 1 yang artinya penyakit akan menghilang dan tidak meluas dari populasi.Kata Kunci: Titik Ekuilibrium, Bilangan Reproduksi Dasar, Pneumonia, Model SEIR.Abstract.This study aims to build a model of the spread of pneumonia in SEIR (Susceptible-Exposed-Infected-Recovered) toddlers, analyze the model, and determine the minimum proportion of vaccinations. The data used are data on the number of pneumonia sufferers in toddlers in Makassar City in 2019.The results obtained by the SEIR mathematical model of pneumonia in the form of ordinary differential equation systems; addiction free balance points and addiction balance points which are both stable; basic reproduction numbers for simulations without vaccination greater than 1, which means that the disease still exists in the population, while basic reproduction numbers for simulations with vasksination less than 1, which means the disease will disappear and not spread from the population.Keywords: Equilibrium Points, Basic Reproductive Numbers, Pneumonia, SEIR Model.

scholarly journals Model Epidemik Penyebaran Malaria

2020 ◽  
Author(s):  
Resmawan Resmawan
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Human Population ◽  
Medication Treatment ◽  
Reproduction Numbers ◽  
Effect Of Treatment ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Transmission Of Disease

This article discusses the mathematical model of SEIRS-SEI type malaria spread. Modification of themodel is done by giving the treatment in humans, in the form of vaccination and medication treatment. In thismodel, the human population is divided into four classes, namely susceptible, exposed, infected, and recovered.The mosquito population is divided into three classes, namely susceptible, exposed, and infected. Furthermore,the analysis of the model show the effect of treatment given to disease transmission. At the end of this article isprovided numerical simulations to show the effectiveness of vaccination and treatment in humans to suppressthe rate of transmission of disease. The simulation results show that the increase of vaccination effectiveness andmedication treatment in humans can reduce the reproduction numbers so that within a certain time the disease will disappear from the population.

scholarly journals Qualitative properties of mathematical model of English language education

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Atena Ghasemabadi ◽  
Nahid Soltanian
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Equilibrium Point ◽  
English Language ◽  
Language Education ◽  
Qualitative Properties ◽  
English Language Education ◽  
Compound Matrices ◽  
Reproduction Numbers ◽  
Coexistence Equilibrium

AbstractThis paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence equilibrium point using compound matrices.

scholarly journals Addressing the COVID-19 transmission in inner Brazil by a mathematical model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
G. B. Almeida ◽  
T. N. Vilches ◽  
C. P. Ferreira ◽  
C. M. C. B. Fortaleza
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Abiotic Factors ◽  
Severe Pneumonia ◽  
Mitigation Strategies ◽  
Social Distancing ◽  
Control Disease ◽  
Set Up ◽  
Novel Coronavirus ◽  
Public Health Strategies

AbstractIn 2020, the world experienced its very first pandemic of the globalized era. A novel coronavirus, SARS-CoV-2, is the causative agent of severe pneumonia and has rapidly spread through many nations, crashing health systems and leading a large number of people to death. In Brazil, the emergence of local epidemics in major metropolitan areas has always been a concern. In a vast and heterogeneous country, with regional disparities and climate diversity, several factors can modulate the dynamics of COVID-19. What should be the scenario for inner Brazil, and what can we do to control infection transmission in each of these locations? Here, a mathematical model is proposed to simulate disease transmission among individuals in several scenarios, differing by abiotic factors, social-economic factors, and effectiveness of mitigation strategies. The disease control relies on keeping all individuals’ social distancing and detecting, followed by isolating, infected ones. The model reinforces social distancing as the most efficient method to control disease transmission. Moreover, it also shows that improving the detection and isolation of infected individuals can loosen this mitigation strategy. Finally, the effectiveness of control may be different across the country, and understanding it can help set up public health strategies.

scholarly journals Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Woldegebriel Assefa Woldegerima ◽  
Aychew Wondifraw
Keyword(s):  
Mathematical Model ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Invariant Solution ◽  
Stochastic Approach ◽  
Disease Dynamics ◽  
Treatment Rate ◽  
Invariant Region ◽  
Contact Transmission

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

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