scholarly journals A mathematical model to investigate the transmission of COVID-19 in the Kingdom of Saudi Arabia

2020 ◽  
Author(s):  
Fehaid Salem Alshammari
Keyword(s):  
Mathematical Model ◽  
Saudi Arabia ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
European Countries ◽  
Dynamical Model ◽  
Kingdom Of Saudi Arabia ◽  
Ministry Of Health ◽  
Reported Data ◽  
The Basic Reproduction Number

AbstractSince the first confirmed case of SARS-CoV-2 coronavirus (COVID-19) in the 2nd day of March, Saudi Arabia has not report a quite rapid COVD-19 spread compared to America and many European countries. Possible causes include the spread of asymptomatic cases. To characterize the transmission of COVID-19 in Saudi Arabia, this paper applies a susceptible, exposed, symptomatic, asymptomatic, hospitalized, and recovered dynamical model, along with the official COVID-19 reported data by the Ministry of Health in Saudi Arabia. The basic reproduction number R0 is estimated to range from 2.87 to 4.9.

scholarly journals A Mathematical Model to Investigate the Transmission of COVID-19 in the Kingdom of Saudi Arabia

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Fehaid Salem Alshammari
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Saudi Arabia ◽  
Reproduction Number ◽  
Real Data ◽  
Kingdom Of Saudi Arabia ◽  
Globally Stable ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Good Agreement

Since the first confirmed case of SARS-CoV-2 coronavirus (COVID-19) on March 02, 2020, Saudi Arabia has not reported quite a rapid COVD-19 spread as seen in America and many European countries. Possible causes include the spread of asymptomatic COVID-19 cases. To characterize the transmission of COVID-19 in Saudi Arabia, a susceptible, exposed, symptomatic, asymptomatic, hospitalized, and recovered dynamical model was formulated, and a basic analysis of the model is presented including model positivity, boundedness, and stability around the disease-free equilibrium. It is found that the model is locally and globally stable around the disease-free equilibrium when R 0 < 1 . The model parameterized from COVID-19 confirmed cases reported by the Ministry of Health in Saudi Arabia (MOH) from March 02 till April 14, while some parameters are estimated from the literature. The numerical simulation showed that the model predicted infected curve is in good agreement with the real data of COVID-19-infected cases. An analytical expression of the basic reproduction number R 0 is obtained, and the numerical value is estimated as R 0 ≈ 2.7 .

scholarly journals Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Strategy ◽  
Vaccination Rate ◽  
Rapid Testing ◽  
Social Distancing ◽  
Rapid Spread ◽  
Vaccine Potential ◽  
The Basic Reproduction Number

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

scholarly journals Simple MSEIR Model for Measles Transmission

2019 ◽  
pp. 1-11
Author(s):  
Mojeeb Al-Rahman EL-Nor Osman ◽  
Appiagyei Ebenezer ◽  
Isaac Kwasi Adu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Birth Rate ◽  
Reproduction Number ◽  
Progression Rate ◽  
Asymptotically Stable ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria.  The basic reproduction number  is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out.  The disease was locally asymptotically stable if  and unstable if  . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

GLOBAL DYNAMICS OF A MATHEMATICAL MODEL OF TUBERCULOSIS WITH AGE-DEPENDENT LATENCY AND ACTIVE INFECTION

2019 ◽  
Vol 27 (04) ◽  
pp. 503-530
Author(s):  
RUI XU ◽  
NING BAI ◽  
XIAOHONG TIAN
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Feasible Region ◽  
Global Dynamics ◽  
Active Infection ◽  
Age Dependent ◽  
Latent Tb ◽  
Latent Tb Infection ◽  
The Basic Reproduction Number

In this paper, mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) with age-dependent latency and active infection. The model divides latent TB infection into two stages: an early stage of high risk of developing active TB and a late stage of lower risk for developing active TB. Infected persons initially progress through the early latent TB stage and then can either progress to active TB infection or progress to late latent TB infection. The model is formulated by incorporating the duration that an individual has spent in the stages of the early latent TB, the late latent TB and the active TB infection as variables. By constructing suitable Lyapunov functionals and using LaSalle’s invariance principle, it is shown that the global dynamics of the disease is completely determined by the basic reproduction number: if the basic reproduction number is less than unity, the TB always dies out; if the basic reproduction number is greater than unity, a unique endemic steady state exists and is globally asymptotically stable in the interior of the feasible region and therefore the TB becomes endemic. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Global Stability and Sensitivity Assessment of COVID-19 with Timely and Delayed Diagnosis in Ghana

2021 ◽  
Author(s):  
Stephen E. Moore ◽  
Hetsron L. Nyandjo Bamen ◽  
Joshua Kiddy K. Asamoah ◽  
Olivier Menoukeu-Pamen ◽  
Zhen Jin
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Delayed Diagnosis ◽  
Rank Correlation ◽  
Health Benefit ◽  
Recruitment Rate ◽  
Susceptible Population ◽  
Sensitivity Assessment ◽  
Reported Data ◽  
The Basic Reproduction Number

Abstract In this paper, we present the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana, using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, R_0, for the proposed model is 1.04. One of the main focus of this study is stability results and senesitity assessment of the parameters. We show both theoretically and numerically that, the disease can be eliminated when the basic reproduction number is less or equal to a unity. Furthermore, we show that the disease persist whenever R_0>1 or whenever there is a delay in the diagnoses of infected individuals in the community. To assess the most influential parameters in the basic reproduction number, we carried out global sensitivity analysis. The scatter plots and the partial rank correlation coefficient reveal that, the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility of exposed individuals; and that the most negative sensitive parameters are the proportion of the infectious with timely diagnosis, and the transition rate of self-quarantined individuals to the susceptible population. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection).

scholarly journals Mathematical model of transmission dynamics with mitigation and health measures for SARS-CoV-2 infection in European countries

2020 ◽  
Author(s):  
Shweta Sankhwar ◽  
Narender Kumar ◽  
Ravins Dohare
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
European Countries ◽  
Transmission Dynamics ◽  
Second Phase ◽  
Geographical Regions ◽  
Two Phases ◽  
Spread Of Infection ◽  
And Control

Abstract The pandemic of Severe Acute Respiratory Syndrome Coronavirus (SARS-CoV-2) continue to pose a serious threat to global health resulting in disease COVID-19. No specific drug or vaccine is available against this infection. Therefore, the prevention is only way to reduce the spread of infection. The pandemic needs an enhanced mathematical model, therefore, we propose a SEIAJR compartmental mathematical model to estimate the basic reproduction number (R0 ) and the transmission dynamics of four European countries (Germany, United Kingdom, Switzerland and Spain). The proposed mathematical model incorporates mitigation and healthcare measures as recommended by ECDC (European Centre for Disease Prevention and Control). The simulation of proposed model is done in two phases. First-phase simulation estimates basic reproduction number and mitigation rate according to active infected cases in all four European countries. R0 estimate 2.82 - 3.3 for considered European countries. Second-phase simulation predicts the dynamics of infection on the estimated R0 with varying mitigation rate and constant healthcare rate. This study predicts that no more mitigation is required to invade the infection. The current mitigation and healthcare measures are enough to stop the propogation of infection, however, infection would last by end of July 2020. The developed mathematical model would also be applicable to portray the infection trasmission dynamics for other geographical regions with varying parameters.

scholarly journals Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

2020 ◽  
Author(s):  
Tamer Sanlidag ◽  
Nazife Sultanoglu ◽  
Bilgen Kaymakamzade ◽  
Evren Hincal ◽  
Murat Sayan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Real Data ◽  
Northern Cyprus ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

scholarly journals COVID-19 disease transmission model considering direct and indirect transmission

2020 ◽  
Vol 202 ◽  
pp. 12008
Author(s):  
Dipo Aldila
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Model ◽  
Indirect Transmission ◽  
Variation Of Parameters ◽  
The Media ◽  
Disease Transmission Model ◽  
The Basic Reproduction Number

A mathematical model for understanding the COVID-19 transmission mechanism proposed in this article considering two important factors: the path of transmission (direct-indirect) and human awareness. Mathematical model constructed using a four-dimensional ordinary differential equation. We find that the Covid-19 free state is locally asymptotically stable if the basic reproduction number is less than one, and unstable otherwise. Unique endemic states occur when the basic reproduction number is larger than one. From sensitivity analysis on the basic reproduction number, we find that the media campaign succeeds in suppressing the endemicity of COVID-19. Some numerical experiments conducted to show the dynamic of our model respect to the variation of parameters value.

scholarly journals Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

2020 ◽  
Author(s):  
Tamer Sanlidag ◽  
Nazife Sultanoglu ◽  
Bilgen Kaymakamzade ◽  
Evren Hincal ◽  
Murat Sayan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Real Data ◽  
Northern Cyprus ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2epidemic.

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.

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