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.

CONVENTIONAL MODELLING APPROACH TO PREDICT THE DYNAMICS OF COVID-19

2021 ◽  
Vol 5 (2) ◽  
pp. 470-476
Author(s):  
S Bashir ◽  
I. Z. Shehu ◽  
N. Chinenye
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
The Stability ◽  
Modelling Approach

The study examined transmission dynamics of COVID-19 with conventional modelling approach. We developed a mathematical model for COVID-19 pandemic as SEQIR where I, the infected compartment is partitioned in to  and for reported and unreported group of infected individuals. Basic reproduction number has been obtained and the stability analysis was carried out. The results revealed that the disease may die out in time

scholarly journals Impact of Hygiene on Malaria Transmission Dynamics: A Mathematical Model

2021 ◽  
Author(s):  
Temidayo Oluwafemi ◽  
Emmanuel Azuaba
Keyword(s):  
Mathematical Model ◽  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Model System ◽  
Transmission Dynamics ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Malaria continues to pose a major public health challenge, especially in developing countries, 219 million cases of malaria were estimated in 89 countries. In this paper, a mathematical model using non-linear differential equations is formulated to describe the impact of hygiene on Malaria transmission dynamics, the model is analyzed. The model is divided into seven compartments which includes five human compartments namely; Unhygienic susceptible human population, Hygienic Susceptible Human population, Unhygienic infected human population , hygienic infected human population and the Recovered Human population  and the mosquito population is subdivided into susceptible mosquitoes  and infected mosquitoes . The positivity of the solution shows that there exists a domain where the model is biologically meaningful and mathematically well-posed. The Disease-Free Equilibrium (DFE) point of the model is obtained, we compute the Basic Reproduction Number using the next generation method and established the condition for Local stability of the disease-free equilibrium, and we thereafter obtained the global stability of the disease-free equilibrium by constructing the Lyapunov function of the model system. Also, sensitivity analysis of the model system was carried out to identify the influence of the parameters on the Basic Reproduction Number, the result shows that the natural death rate of the mosquitoes is most sensitive to the basic reproduction number.

scholarly journals Mathematical Model of the Transmission Dynamics of Corona Virus Disease (COVID-19) and Its Control

2021 ◽  
pp. 69-88
Author(s):  
Atokolo William ◽  
Omale David ◽  
Bashir Sezuo Tenuche ◽  
Olayemi Kehinde Samuel ◽  
Daniel Musa Alih ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Control Measure ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Corona Virus ◽  
The Basic Reproduction Number

This work is aimed at formulating a mathematical model for the transmission dynamics and control of corona virus disease in a population. The Disease Free Equilibrium state of the model was determined and shown to be locally asymptotically stable. The Endemic Equilibrium state of the model was also established and proved to be locally asymptotically stable using the trace and determinant method, after which we determined the basic reproduction number ( ) of the model using the next generation method. When ( ), the disease is wiped out of a population, but if ( ), the disease invades such population. Local sensitivity analysis result shows that the rate at which the exposed are quarantined ( ), the rate at which the infected are isolated ( ), the rate at which the quarantined are isolated ( ), and the treatment rate ( ) should be targeted by the control intervention strategies as an increase in the values of these parameters (  and ) will reduce the basic reproduction number  ( ) of the COVID-19 and as such will eliminate the disease from the population with time. Numerical simulation of the model shows that the disease will be eradicated with time when enlightenment control measure for the susceptible individuals to observe social distance, frequent use of hand sanitizers, covering of mouth when coughing or sneezing are properly observed. Moreso, increasing the rates at which the suspected and confirmed cases of COVID-19 are quarantined and isolated respectively reduce the spread of the global pandemic.

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 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 Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

scholarly journals Bioindicator demonstrates high persistence of sulfentrazone in dry soil1

2015 ◽  
Vol 45 (3) ◽  
pp. 326-332 ◽  
Author(s):  
Renato Coradello Lourenço ◽  
Saul Jorge Pinto de Carvalho
Keyword(s):  
Dose Response ◽  
Residual Effect ◽  
Second Phase ◽  
Response Curves ◽  
Sugarcane Crop ◽  
Phytotoxic Activity ◽  
Dry Soil ◽  
Two Phases ◽  
Preemergence Herbicides ◽  
And Control

ABSTRACTIn sugarcane crop areas, the application of preemergence herbicides with long residual effect in the soil has been frequently necessary. The herbicide persistence in the soil must be high especially because of applications during the dry season of the year, after sugarcane harvest. This study aimed at estimating the sulfentrazone persistence and dissipation in dry soil using bioindicator. Five experiments were carried out, divided into two phases. In the first phase, three dose-response curves were adjusted to select the best bioindicator to be adopted in the second phase. Niger was adopted due to its lower sensibility to sulfentrazone. In the second phase, a new dose-response curve was carried out, with six doses of sulfentrazone, in order to standardize the bioindicator sensibility to sulfentrazone. At the end, another experiment with six periods of sulfentrazone persistence in dry clay soil was developed. Persistence periods were: 182, 154, 125, 98 and 30 days. The bioindicator was seeded at the application day in treated plots and control. In this experiment, the sulfentrazone dose applied was 800 g ha-1. Niger was considered a good species to estimate the sulfentrazone persistence in dry soil. The sulfentrazone phytotoxic activity was identified up to 182 days after application, and its average dissipation rate was 2.15 g ha-1 day-1, with half-life higher than 182 days.

scholarly journals Estimasi Reproduction Number Model Matematika Penyebaran Malaria di Sumba Tengah, Indonesia

2021 ◽  
Vol 2 (1) ◽  
pp. 13-19
Author(s):  
Ervin Mawo Banni ◽  
Maria A Kleden ◽  
Maria Lobo ◽  
Meksianis Zadrak Ndii
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Health Center ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Awareness Program ◽  
Awareness Programs ◽  
Malaria Eradication

Malaria is transmitted via a bite of mosquitoes and it is dangerous if it is not properly treated. Mathematical modeling can be formulated to understand the disease transmission dynamics. In this paper, a mathematical model with an awareness program has been formulated and the reproduction number has been estimated against the data from Weeluri Health Center, Mamboro District, Central Sumba. The calculation showed that the reproduction number is R0 = 1.2562. Results showed that if the efficacy of the awareness program is lower than 20%, the reproduction number is still above unity. If the efficacy of the awareness program is higher than 20%, the reproduction number is lower than unity. This implies that the efficacy of awareness programs is the key to the success of Malaria eradication.

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.

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