scholarly journals Impact of reproduction number on the multiwave spreading dynamics of COVID-19 with temporary immunity: A mathematical model

2021 ◽  
Vol 104 ◽  
pp. 649-654 ◽  
Author(s):  
B. Shayak ◽  
Mohit M. Sharma ◽  
Manas Gaur ◽  
Anand Kumar Mishra
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Spreading Dynamics ◽  
Temporary Immunity

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.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

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 A Deterministic Analysis of the Effectiveness of Non-Clinical Approaches in the Control of Transimission of Schistosomiasis: Case Study of Mwea Irrigation Scheme, Kenya

2021 ◽  
Vol 2 (6) ◽  
pp. 40-49
Author(s):  
Jane N. Murungi ◽  
Stephen Karanja ◽  
Paul Wanjau
Keyword(s):  
Mathematical Model ◽  
Control Strategy ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Health Concern ◽  
Behavior Patterns ◽  
Sensitivity Index ◽  
Irrigation Scheme ◽  
Deterministic Analysis ◽  
Media Campaigns

Schistosomiasis commonly known as bilharzia is regarded by W.H.O as a neglected tropical disease. It affects the intestines and the urinary system preferentially, but can harm other systems in the body. The disease is a health concern among majority of the population in Mwea irrigation scheme in Kenya and indeed other tropical countries. This paper documents a deterministic analysis of the effectiveness of non-clinical approaches in the control of transmission of schistosomiasis in the region. A SIR based mathematical model that incorporates media campaigns as a control strategy of reducing transmission of the disease is used. The model considers behavior patterns of hosts as the main process of transmission of the disease. The dynamics of these processes is expressed in terms of ordinary differential equations deduced from the human behavior patterns that contribute to the spread of the disease. The reproduction number R0 and equilibrium points both DFE and EE are obtained. The stabilities of these equilibrium points are analyzed in reference to the reproduction number (R0). Secondary data is used in the mathematical model developed and in the prediction of the dynamics estimated in the model for a period of five years. Numerical simulation was carried out and results represented graphically. The results of the simulation show that the infection decreased from 75108 to about 35000 and the susceptible from 325142 to 50000 respectively in a period of five years. From the analysis, the DFE point is asymptotically stable when R_0<1.Sensitivity analysis of parameters was carried out using partial differentiation. The results show that the sensitivity index of most parameters are inversely proportional to R0 which will reduce schistosomiasis infection. From the results, incorporation of media campaigns as a control strategy significantly reduces transmission of the disease. The results will be useful to MOH to enhance media campaigns to prevent spread of schistosomiasis in Mwea Irrigation scheme and other endemic areas.

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.

scholarly journals Assessing countermeasures during a hepatitis A virus outbreak among men who have sex with men

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Ryohei Saito ◽  
Akifumi Imamura ◽  
Hiroshi Nishiura
Keyword(s):  
Mathematical Model ◽  
Situation Awareness ◽  
Hepatitis A ◽  
Hepatitis A Virus ◽  
Reproduction Number ◽  
Risky Behaviors ◽  
Extrinsic Factors ◽  
Environmental Transmission ◽  
Sex With Men ◽  
Epidemic Risk

Abstract Background A hepatitis A epidemic occurred among men who have sex with men (MSM) in Japan in 2017–2018. In this study, we employ a parsimonious mathematical model to epidemiologically investigate the dynamics of infection, aiming to evaluate the effectiveness of campaign-based interventions among MSM to raise awareness of the situation. Methods A mathematical model describing a mixture of human-to-human transmission and environmental transmission was fitted to surveillance data. Taking seasonally varying environmental transmission into account, we estimated the reproduction number of hepatitis A virus during the course of epidemic, and, especially, the abrupt decline in this reproduction number following campaign-based interventions. Results The reproduction number prior to the countermeasures ranged from 2.6 to 3.1 and then began to decrease following campaign-based interventions. After the first countermeasure, the reproduction number decreased, but the epidemic remained supercritical (i.e., Rt > 1). The value of Rt dropped well below one following the second countermeasure, which used web articles to widely disseminate information about the epidemic risk. Conclusions Although the effective reproduction number, Rt, changes because of both intrinsic and extrinsic factors, the timing of the examined countermeasures against hepatitis A in the MSM population was consistent with the abrupt declines observed in Rt. Even without vaccination, the epidemic was brought under control, and risky behaviors may have been changed by the increase in situation awareness reached through web articles.

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 A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

2020 ◽  
Vol 24 (5) ◽  
pp. 917-922
Author(s):  
J. Andrawus ◽  
F.Y. Eguda ◽  
I.G. Usman ◽  
S.I. Maiwa ◽  
I.M. Dibal ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Line Treatment ◽  
Second Line ◽  
Tuberculosis Transmission ◽  
Disease Free

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

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