scholarly journals Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Wahidah Sanusi ◽  
Nasiah Badwi ◽  
Ahmad Zaki ◽  
Sahlan Sidjara ◽  
Nurwahidah Sari ◽  
...  
Keyword(s):  
Dengue Fever ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Dengue Case ◽  
Fever Case ◽  
South Sulawesi ◽  
Sirs Model ◽  
The Government ◽  
Case Data ◽  
The Basic Reproduction Number

This study is aimed at building and analysing a SIRS model and also simulating the model to predict the number of dengue fever cases. Methods applied for this model are building the SIRS model by modifying the SIR model, analysing the SIRS model using the Lyapunov function to prove three theorems (the existence, the free disease, and the endemic status of dengue fever), and simulating the SIRS model using the number of dengue case data in South Sulawesi by Maple. The results obtained are the SIRS model of dengue fever transmission, stability analysis, global stability, and the value of the basic reproduction number R 0 . The simulation done for the dengue fever case in South Sulawesi found the basic reproduction number R 0 = 26.47609 > 1 ; it means that South Sulawesi is in the endemic stage of transmission for dengue fever disease. Simulation of the SIRS model for dengue fever can predict the number of dengue cases in South Sulawesi that could be a recommendation for the government in an effort to prevent the number of dengue fever cases.

scholarly journals Global proprieties of a delayed epidemic model with partial susceptible protection

2021 ◽  
Vol 19 (1) ◽  
pp. 209-224
Author(s):  
Abdelheq Mezouaghi ◽  
◽  
Salih Djillali ◽  
Anwar Zeb ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Isolation Rate ◽  
Globally Asymptotically Stable ◽  
The Government ◽  
The Basic Reproduction Number

<abstract><p>In the case of an epidemic, the government (or population itself) can use protection for reducing the epidemic. This research investigates the global dynamics of a delayed epidemic model with partial susceptible protection. A threshold dynamics is obtained in terms of the basic reproduction number, where for $ R_0 &lt; 1 $ the infection will extinct from the population. But, for $ R_0 &gt; 1 $ it has been shown that the disease will persist, and the unique positive equilibrium is globally asymptotically stable. The principal purpose of this research is to determine a relation between the isolation rate and the basic reproduction number in such a way we can eliminate the infection from the population. Moreover, we will determine the minimal protection force to eliminate the infection for the population. A comparative analysis with the classical SIR model is provided. The results are supported by some numerical illustrations with their epidemiological relevance.</p></abstract>

scholarly journals Stability of a Mathematical Model of Malaria Transmission with Relapse

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Feng Huo ◽  
Guang-Ming Qiu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Next Generation Matrix ◽  
The Government ◽  
Disease Free ◽  
The Basic Reproduction Number

A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction numberR0is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable ifR0≤1, and the system is uniformly persistence ifR0>1. Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.

scholarly journals Mathematics Model Development Deployment of Dengue Fever Diseases by Involve Human and Vectors Exposed Components

2018 ◽  
Vol 8 (4) ◽  
Author(s):  
Flaviana Priscilla Persulessy ◽  
Paian Siantur ◽  
Jaharuddin .
Keyword(s):  
Dengue Virus ◽  
Equilibrium Point ◽  
Dengue Fever ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Development ◽  
Endemic Equilibrium ◽  
Mathematics Model ◽  
Sensitivity Index ◽  
The Basic Reproduction Number

Dengue virus is one of virus that cause deadly disease was dengue fever. This virus was transmitted through bite of Aedes aegypti female mosquitoes that gain virus infected by taking food from infected human blood, then mosquitoes transmited pathogen to susceptible humans. Suppressed the spread and growth of dengue fever was important to avoid and prevent the increase of dengue virus sufferer and casualties. This problem can be solved with studied important factors that affected the spread and equity of disease by sensitivity index. The purpose of this research were to modify mathematical model the spread of dengue fever be SEIRS-ASEI type, to determine of equilibrium point, to determined of basic reproduction number, stability analysis of equilibrium point, calculated sensitivity index, to analyze sensitivity, and to simulate numerical on modification model. Analysis of model obtained disease free equilibrium (DFE) point and endemic equilibrium point. The numerical simulation result had showed that DFE, stable if the basic reproduction number is less than one and endemic equilibrium point was stable if the basic reproduction number is more than one.

scholarly journals Pemodelan Matematika SIRI pada Penyebaran Penyakit Tifus di Sulawesi Selatan

2021 ◽  
Vol 4 (2) ◽  
pp. 55
Author(s):  
Syafruddin Side ◽  
Ahmad Zaki ◽  
S. Sartika
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
South Sulawesi ◽  
Research Procedure ◽  
The Stability ◽  
Siri Model ◽  
The Basic Reproduction Number

Penelitian ini bertujuan untuk membangun model penyebaran penyakit Tifus tipe SIRI (Susceptible-Infected-Recovered-Infected), dengan menambahkan asumsi bahwa manusia yang sembuh dapat kembali terinfeksi penyakit Tifus. Model ini di bagi menjadi 3 kelas yaitu rentan, terinfeksi dan sembuh. Adapun prosedur penelitian dilakukan melalui tahapan-tahapan: membangun model penyebaran penyakit Tifus tipe SIRI, Menguji Kestabilan titik kesetimbangan dan menentukan bilangan reproduksi dasar , kemudian menerapkannya pada kasus Penyakit Tifus di Provinsi Sulawesi Selatan. Data yang digunakan dalam membangun model adalah jumlah penderita penyakit Tifus tahun 2018 dari Dinas Kesehatan Provinsi Sulawesi Selatan. Model matematika tipe SIRI digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi model SIRI diperoleh bilangan reproduksi dasar (  sebesar 0,000903 yang menandakan bahwa penyebaran penyakit Tifus di Provinsi Sulawesi Selatan pada tahun 2018 bukan kejadian luar biasa atau dapat dikatakan bahwa seseorang yang terinfeksi penyakit Tifus ini tidak menyebabkan orang lain terkenapenyakit yang sama, dengan kata lain tidak terjadi wabah pada populasi tersebut.Kata kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Tifus, Model SIRI. The research aims to build a SIRI model of the Typhoid spread (Susceptible-Infected-Recovered-Infected) by adding assumption that people who are recovered might be infected again. This model is divided into three classes, namely, susceptible, infected and recovered. the research procedure is carried out through several stages: Building SIRI model for the spread of Typhoid, examining the stability of the equilibrium point and determining the basic reproduction number, and applying the model to Typhoid cases in South Sulawesi. The data is the number of Typhus patients in 2018 that was obtained from Health office of South Sulawesi Province. SIRI type mathematical models are used to determine the equilibrium point. Based on the simulation results of the SIRI model, the basic reproduction number is 0,000903 indicate that, indicating that the spread of Typhus in the Province of South Sulawesi in 2018 was not an extraordinary event or it can be said that someone who is infected with this Typhoid does not cause another person to contract the same disease, in other words there was no outbreak in that population.Keywords: equilibrium Point, Basic Reproductive Number, Typhoid, SIRI Model.

scholarly journals A Data Driven Analysis and Forecast of COVID-19 Dynamics during the Third Wave Using SIRD Model in Bangladesh

COVID ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 503-517
Author(s):  
Omar Faruk ◽  
Suman Kar
Keyword(s):  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Goodness Of Fit ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Third Wave ◽  
The Third ◽  
The Government ◽  
The Basic Reproduction Number

In this study, we developed a compartmental SIRD model to analyze and forecast the transmission dynamics of the COVID-19 pandemic in Bangladesh during the third wave caused by the Indian delta variant. With the help of the nonlinear system of differential equations, this model can analyze the trends and provide reliable predictions regarding how the epidemic would evolve. The basic reproduction number regarding the pandemic has been determined analytically. The parameters used in this model have been estimated by fitting our model to the reported data for the months of May, June, and July 2021 and the goodness of fit of the parameter’s value has been found by the respective regression coefficients. Further, we conducted a sensitivity analysis of the basic reproduction number and observed that decreasing the transmission rate is the most significant factor in disease prevention. Our proposed model’s appropriateness for the available COVID-19 data in Bangladesh has been demonstrated through numerical simulations. According to the numerical simulation, it is evident that a rise in the transmission rate leads to a significant increase in the infected number of the population. Numerical simulations have also been performed by using our proposed model to forecast the future transmission dynamics for COVID-19 over a longer period of time. Knowledge of these forecasts may help the government in adopting appropriate measures to prepare for unforeseen situations that may arise in Bangladesh as well as to minimize detrimental impacts during the outbreak.

scholarly journals Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever

2021 ◽  
Vol 4 (1) ◽  
pp. 1-13
Author(s):  
Glenn Lahodny Jr. ◽  
Mona Zevika
Keyword(s):  
Markov Chain ◽  
Dengue Fever ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Markov Chain Model ◽  
Chain Model ◽  
Multitype Branching Process ◽  
The Basic Reproduction Number

A Continuous-Time Markov Chain model is constructed based on the a deterministic model of dengue fever transmission including mosquito fogging and the use of repellent. The basic reproduction number (R0) for the corresponding deterministic model is obtained. This number indicates the possible occurrence of an endemic at the early stages of the infection period. A multitype branching process is used to approximate the Markov chain. The construction of offspring probability generating functions related to the infected states is used to calculate the probability of disease extinction and the probability of an outbreak (P0). Sensitivity analysis is shown for variation of control parameters and for indices of the basic reproduction number. These results allow for a better understanding of the relation of the basic reproduction number with other indicators of disease transmission.

scholarly journals Maximum Equilibrium Prevalence of Mosquito-Borne Microparasite Infections in Humans

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Marcos Amaku ◽  
Marcelo Nascimento Burattini ◽  
Francisco Antonio Bezerra Coutinho ◽  
Luis Fernandez Lopez ◽  
Eduardo Massad
Keyword(s):  
Dengue Fever ◽  
Basic Reproduction Number ◽  
General Model ◽  
Reproduction Number ◽  
Equilibrium Analysis ◽  
Force Of Infection ◽  
Maximum Value ◽  
Explicit Function ◽  
Vector Borne ◽  
The Basic Reproduction Number

To determine the maximum equilibrium prevalence of mosquito-borne microparasitic infections, this paper proposes a general model for vector-borne infections which is flexible enough to comprise the dynamics of a great number of the known diseases transmitted by arthropods. From equilibrium analysis, we determined the number of infected vectors as an explicit function of the model’s parameters and the prevalence of infection in the hosts. From the analysis, it is also possible to derive the basic reproduction number and the equilibrium force of infection as a function of those parameters and variables. From the force of infection, we were able to conclude that, depending on the disease’s structure and the model’s parameters, there is a maximum value of equilibrium prevalence for each of the mosquito-borne microparasitic infections. The analysis is exemplified by the cases of malaria and dengue fever. With the values of the parameters chosen to illustrate those calculations, the maximum equilibrium prevalence found was 31% and 0.02% for malaria and dengue, respectively. The equilibrium analysis demonstrated that there is a maximum prevalence for the mosquito-borne microparasitic infections.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

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