scholarly journals Transmission dynamic and backward bifurcation of Middle Eastern respiratory syndrome coronavirus

2022 ◽  
Vol 27 (1) ◽  
pp. 54-69
Author(s):  
Bibi Fatima ◽  
Gul Zaman ◽  
Fahd Jarad
Keyword(s):  
Deterministic Model ◽  
Middle Eastern ◽  
Primary Source ◽  
Backward Bifurcation ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Source Of Infection ◽  
Proposed Model ◽  
The Stability ◽  
The Impact

Middle East respiratory syndrome coronavirus (MERS-CoV) remains an emerging disease threat with regular human cases on the Arabian Peninsula driven by recurring camels to human transmission events. In this paper, we present a new deterministic model for the transmission dynamics of (MERS-CoV). In order to do this, we develop a model formulation and analyze the stability of the proposed model. The stability conditions are obtained in term of R0, we find those conditions for which the model become stable. We discuss basic reproductive number R0 along with sensitivity analysis to show the impact of every epidemic parameter. We show that the proposed model exhibits the phenomena of backward bifurcation. Finally, we show the numerical simulation of our proposed model for supporting our analytical work. The aim of this work is to show via mathematical model the transmission of MERS-CoV between humans and camels, which are suspected to be the primary source of infection.

THE DELAYED BARBOUR'S MODEL FOR SCHISTOSOMIASIS

2012 ◽  
Vol 05 (02) ◽  
pp. 1250024 ◽  
Author(s):  
LONGXING QI ◽  
JING-AN CUI
Keyword(s):  
Sensitivity Analysis ◽  
Time Delays ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Stability Of Equilibria ◽  
The Stability ◽  
The Impact

The transmission of schistosomiasis involves latent periods of infected hosts. In this paper, considering the latent periods of infected human, infected bovines and infected snails, we propose a delayed Barbour's model with two definitive hosts and define basic reproductive number. The stability of equilibria for the systems with and without time delays are both investigated. To study the impact of the latent periods on the transmission of schistosomiasis, some sensitivity analysis of the basic reproductive number on the three time delays are carried out. It is shown that the basic reproductive number decreases as the three time delays increase. Furthermore, the impact of the latent periods of infected snails on the system is stronger than that of the latent periods of infected human and infected bovines. Thus, to reduce the prevalence of schistosomiasis infection, prolonging the latent periods of infected snails by some measures could achieve better results than prolonging the latent periods of infected definitive hosts.

Fractional-order COVID-19 pandemic outbreak: Modeling and stability analysis

2021 ◽  
Author(s):  
Iqbal M. Batiha ◽  
Shaher Momani ◽  
Adel Ouannas ◽  
Zaid Momani ◽  
Samir B. Hadid
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Differential Operators ◽  
Euler Method ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Established Disease ◽  
Acute Infectious Disease ◽  
The Stability ◽  
The Impact

Today, the entire world is witnessing an enormous upsurge in coronavirus pandemic (COVID-19 pandemic). Confronting such acute infectious disease, which has taken multiple victims around the world, requires all specialists in all fields to devote their efforts to seek effective treatment or even control its disseminate. In the light of this aspect, this work proposes two new fractional-order versions for one of the recently extended forms of the SEIR model. These two versions, which are established in view of two fractional-order differential operators, namely, the Caputo and the Caputo–Fabrizio operators, are numerically solved based on the Generalized Euler Method (GEM) that considers Caputo sense, and the Adams–Bashforth Method (ABM) that considers Caputo–Fabrizio sense. Several numerical results reveal the impact of the fractional-order values on the two established disease models, and the continuation of the COVID-19 pandemic outbreak to this moment. In the meantime, some novel results related to the stability analysis and the basic reproductive number are addressed for the proposed fractional-order Caputo COVID-19 model. For declining the total of individuals infected by such pandemic, a new compartment is added to the proposed model, namely the disease prevention compartment that includes the use of face masks, gloves and sterilizers. In view of such modification, it is turned out that the performed addition to the fractional-order Caputo COVID-19 model yields a significant improvement in reducing the risk of COVID-19 spreading.

Impact of climate factors on contact rate of vector-borne diseases: Case study of malaria

2016 ◽  
Vol 10 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Ezekiel Dangbé ◽  
Antoine Perasso ◽  
Damakoa Irépran ◽  
David Békollé
Keyword(s):  
Environmental Changes ◽  
Temporal Distribution ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Contact Rate ◽  
Vector Borne Diseases ◽  
Transmission Period ◽  
Vector Borne ◽  
The Stability ◽  
The Impact

Climate change influences more and more of our activities. These changes led to environmental changes which has in turn affected the spatial and temporal distribution of the incidence of vector-borne diseases. To establish the impact of climate on contact rate of vector-borne diseases, we examine the variation of prevalence of diseases according to season. In this paper, the goal is to establish that the basic reproductive number [Formula: see text] depends on the duration of transmission period and the date of the first conta-mination case that was declared ([Formula: see text]) in the specific case of malaria. We described the dynamics of transmission of malaria by using non-autonomous differential equations. We analyzed the stability of endemic equilibrium (EE) and disease-free equilibrium (DFE). We prove that the persistence of disease depends on minimum and maximum values of contact rate of vector-borne diseases.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

2020 ◽  
pp. 8-19
Author(s):  
Laid Chahrazed
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability ◽  
Disease Free ◽  
Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

scholarly journals Stability and Hopf Bifurcation of a Vector-Borne Disease Model with Saturated Infection Rate and Reinfection

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zhixing Hu ◽  
Shanshan Yin ◽  
Hui Wang
Keyword(s):  
Hopf Bifurcation ◽  
Infection Rate ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Cure Rate ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Stability

This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number R0, we determined the disease-free equilibrium E0 and the endemic equilibrium E1. Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium E1 by delay was studied, the existence of Hopf bifurcations of this system in E1 was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.

SE2IR Invest Market Rumor Spreading Model Considering Hesitating Mechanism

2019 ◽  
Vol 7 (1) ◽  
pp. 54-69 ◽  
Author(s):  
Hongxing Yao ◽  
Xiangyang Gao
Keyword(s):  
Mean Field ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Field Equations ◽  
Rumor Spreading ◽  
Immunization Strategy ◽  
Scale Free ◽  
Spreading Model ◽  
Mean Field Equations ◽  
The Impact

Abstract According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-field equations is obtained on scale-free network. In this paper, we first combine the theory of spreading dynamics and find out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the final rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions: Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.

scholarly journals Impact of Awareness to Control Malaria Disease: A Mathematical Modeling Approach

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Malik Muhammad Ibrahim ◽  
Muhammad Ahmad Kamran ◽  
Malik Muhammad Naeem Mannan ◽  
Sangil Kim ◽  
Il Hyo Jung
Keyword(s):  
Mathematical Modeling ◽  
Numerical Technique ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Awareness Campaign ◽  
Runge Kutta Method ◽  
Proposed Model ◽  
Awareness Programs ◽  
Disease Free ◽  
Differential Process

The mathematical modeling of malaria disease has a crucial role in understanding the insights of the transmission dynamics and corresponding appropriate prevention strategies. In this study, a novel nonlinear mathematical model for malaria disease has been proposed. To prevent the disease, we divided the infected population into two groups, unaware and aware infected individuals. The growth rate of awareness programs impacting the population is assumed to be proportional to the unaware infected individuals. It is further assumed that, due to the effect of awareness campaign, the aware infected individuals avoid contact with mosquitoes. The positivity and the boundedness of solutions have been derived through the completing differential process. Local and global stability analysis of disease-free equilibrium has been investigated via basic reproductive number R0, if R0 < 1, the system is stable otherwise unstable. The existence of the unique endemic equilibrium has been also determined under certain conditions. The solution to the proposed model is derived through an iterative numerical technique, the Runge–Kutta method. The proposed model is simulated for different numeric values of the population of humans and anopheles in each class. The results show that a significant increase in the population of susceptible humans is achieved in addition to the decrease in the population of the infected mosquitoes.

HEPATITIS C VIRUS AND INTRAVENOUS DRUG MISUSE: A MODELING APPROACH

2014 ◽  
Vol 07 (01) ◽  
pp. 1450006 ◽  
Author(s):  
STEADY MUSHAYABASA ◽  
CLAVER P. BHUNU
Keyword(s):  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Steady States ◽  
Transmission Dynamics ◽  
Intravenous Drug ◽  
Basic Reproductive Number ◽  
Drug Misuse ◽  
Dynamical Analysis ◽  
Reproductive Number ◽  
The Impact

Hepatitis C virus (HCV) is a blood-borne infection that can lead to progressive liver failure, cirrhosis, hepatocellular carcinoma and death. A deterministic mathematical model for assessing the impact of daily intravenous drug misuse on the transmission dynamics of HCV is presented and analyzed. A threshold quantity known as the reproductive number has been computed. Stability of the steady states has been investigated. The dynamical analysis reveals that the model has globally asymptotically stable steady states. The impact of daily intravenous drug misuse on the transmission dynamics of HCV has been discussed through the basic reproductive number and numerical simulations.

scholarly journals A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model

2020 ◽  
Vol 9 (4) ◽  
pp. 944 ◽  
Author(s):  
Kentaro Iwata ◽  
Chisato Miyakoshi
Keyword(s):  
Healthcare Professionals ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asian Countries ◽  
Hospital Visit ◽  
Seir Model ◽  
Stochastic Epidemic ◽  
Novel Coronavirus ◽  
The Impact ◽  
Multiple Scenarios

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. Even though it began to spread to many other parts of the world, such as other Asian countries, the Americas, Europe, and the Middle East, the impact of secondary outbreaks caused by exported cases outside China remains unclear. We conducted simulations to estimate the impact of potential secondary outbreaks in a community outside China. Simulations using stochastic SEIR model were conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in the total number of persons recovered or removed to be 997 (95% CrI 990–1000) at day 100 and a maximum number of symptomatic infectious patients per day of 335 (95% CrI 232–478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6–7.2). However, better case scenarios with different parameters led to no secondary cases. Altering parameters, especially time to hospital visit. could change the impact of a secondary outbreak. With these multiple scenarios with different parameters, healthcare professionals might be able to better prepare for this viral infection.

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