scholarly journals A Mathematical Analysis of an In-vivo Ebola Virus Transmission Dynamics Model

2021 ◽  
Vol 47 (4) ◽  
pp. 1464-1477
Author(s):  
Seleman Ismail ◽  
Adeline Peter Mtunya
Keyword(s):  
Mathematical Model ◽  
Infection Rate ◽  
Ebola Virus ◽  
Virus Transmission ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Model Parameters ◽  
Sensitivity Index

Ebola virus (EBOV) infection is a hemorrhagic and hazardous disease, which is among the most shocking threats to human health causing a large number of deaths. Currently, there are no approved curative therapies for the disease. In this study, a mathematical model for in-vivo Ebola virus transmission dynamics was analyzed. The analysis of the model mainly focused on the sensitivity of basic reproductive number,  pertaining to the model parameters. Particularly, the sensitivity indices of all parameters of  were computed by using the forward normalized sensitivity index method. The results showed that a slight change in the infection rate immensely influences  while the same change in the production rate of the virus has the least impact on . Thus, , being a determining factor  of the disease progression, deliberate control measures targeting the infection rate, the most positively sensitive parameter, are required. This implies that reducing infection rate will redirect the disease to extinction. Keywords: Ebola virus infection, immune response, sensitivity index, mathematical model.

scholarly journals Mathematical Analysis of Epidemiological Model of Influenza a (H1N1) Virus Transmission Dynamics in Perspective of Bangladesh

2018 ◽  
Vol 37 ◽  
pp. 39-50 ◽  
Author(s):  
Rafiqul Islam ◽  
Md Haider Ali Biswas ◽  
ARM Jalal Uddin Jamali
Keyword(s):  
Influenza A ◽  
H1n1 Virus ◽  
Herd Immunity ◽  
Virus Transmission ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Numerical Result ◽  
Influenza A H1n1 ◽  
Novel Influenza A

This study deals with transmission dynamics of novel influenza A (H1N1) virus to understand the evolution of its epidemic in Bangladesh. For this purpose an SEIR model has been employed to study the dynamics of A (H1N1) virus relating to data of Bangladesh. To find threshold conditions, the equilibria and stability of the equilibria of the model have been determined and also analyzed. Basic Reproductive Number (R0) is determined relating to data of Bangladesh by which Herd Immunity Threshold has been estimated. Our numerical result suggests that vaccinating 12.69% population of Bangladesh can control spread of the pandemic novel A (H1N1) virus when outbreak occurs.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 39-50

scholarly journals TRANSMISSION DYNAMICS OF DENGUE IN COSTA RICA: THE ROLE OF HOSPITALIZATIONS

2019 ◽  
Vol 27 (1) ◽  
pp. 241-266
Author(s):  
FABIO SANCHEZ ◽  
JORGE ARROYO-ESQUIVEL ◽  
PAOLA VÁSQUEZ
Keyword(s):  
Costa Rica ◽  
Compartmental Model ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Specific Parameter ◽  
Public Health Officials ◽  
Disease Free

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, R0, is computed, as well as a sensitivity analysis on R0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.

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.

scholarly journals A MATHEMATICAL MODEL FOR EBOLA EPIDEMIC WITH SELF-PROTECTION MEASURES

2018 ◽  
Vol 26 (01) ◽  
pp. 107-131 ◽  
Author(s):  
T. BERGE ◽  
M. CHAPWANYA ◽  
J. M.-S. LUBUMA ◽  
Y. A. TEREFE
Keyword(s):  
Mathematical Model ◽  
Ebola Virus ◽  
Virus Disease ◽  
Mass Action ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Protection Measures ◽  
Globally Asymptotically Stable ◽  
New Formulation ◽  
Self Protection

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number [Formula: see text] is less than or equal to unity and unstable when [Formula: see text]. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.

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.

A MATHEMATICAL MODEL FOR HUMAN AND ANIMAL LEPTOSPIROSIS

2015 ◽  
Vol 23 (supp01) ◽  
pp. S55-S65 ◽  
Author(s):  
DAVID BACA-CARRASCO ◽  
DANIEL OLMOS ◽  
IGNACIO BARRADAS
Keyword(s):  
Mathematical Model ◽  
Original Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Si Model

In this paper, we propose a SI model for the study of human and animal leptospirosis. Unlike other models for leptospirosis which consider only rodents as infection vectors, we consider that humans can be infected not only through contact with rodents, but also through any other animal that serves as a reservoir for the bacteria, and through contact with bacteria that are free in the environment. We calculate the basic reproductive number for this model, which is given in terms of the basic reproductive numbers of simpler subsystems of the original model, and propose some intervention techniques for controlling the disease based on our results.

Transmission dynamics of primary pneumonic plague in the USA

2011 ◽  
Vol 140 (3) ◽  
pp. 554-560 ◽  
Author(s):  
A. F. HINCKLEY ◽  
B. J. BIGGERSTAFF ◽  
K. S. GRIFFITH ◽  
P. S. MEAD
Keyword(s):  
Severe Form ◽  
Antimicrobial Treatment ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Published Data ◽  
Pneumonic Plague ◽  
Transmission Potential ◽  
The Usa ◽  
Using Data

SUMMARYPlague is thought to have killed millions during three catastrophic pandemics. Primary pneumonic plague, the most severe form of the disease, is transmissible from person-to-person and has the potential for propagating epidemics. Efforts to quantify its transmission potential have relied on published data from large outbreaks, an approach that artificially inflates the basic reproductive number (R0) and skews the distribution of individual infectiousness. Using data for all primary pneumonic plague cases reported in the USA from 1900 to 2009, we determined that the majority of cases will fail to transmit, even in the absence of antimicrobial treatment or prophylaxis. Nevertheless, potential for sustained outbreaks still exists due to superspreading events. These findings challenge current concepts regarding primary pneumonic plague transmission.

scholarly journals Global Dynamics of an HTLV-1 Model with Cell-to-Cell Infection and Mitosis

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sumei Li ◽  
Yicang Zhou
Keyword(s):  
Chronic Infection ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Cell Infection ◽  
Globally Asymptotically Stable ◽  
Human T Cell

A mathematical model of human T-cell lymphotropic virus type 1 in vivo with cell-to-cell infection and mitosis is formulated and studied. The basic reproductive numberR0is derived. It is proved that the dynamics of the model can be determined completely by the magnitude ofR0. The infection-free equilibrium is globally asymptotically stable (unstable) ifR0<1  (R0>1). There exists a chronic infection equilibrium and it is globally asymptotically stable ifR0>1.

scholarly journals Quantitative Expression and Virus Transmission Analysis of DC-SIGN on Monocyte-Derived Dendritic Cells

2002 ◽  
Vol 76 (18) ◽  
pp. 9135-9142 ◽  
Author(s):  
Frédéric Baribaud ◽  
Stefan Pöhlmann ◽  
George Leslie ◽  
Frank Mortari ◽  
Robert W. Doms
Keyword(s):  
Dendritic Cells ◽  
Cell Lines ◽  
Ebola Virus ◽  
Virus Transmission ◽  
Virus Binding ◽  
Expression Levels ◽  
Quantitative Expression ◽  
Immunodeficiency Virus

ABSTRACT The C-type lectins DC-SIGN and DC-SIGNR efficiently bind human immunodeficiency virus (HIV) and simian immunodeficiency virus (SIV) strains and can transmit bound virus to adjacent CD4-positive cells. DC-SIGN also binds efficiently to the Ebola virus glycoprotein, enhancing Ebola virus infection. DC-SIGN is thought to be responsible for the ability of dendritic cells (DCs) to capture HIV and transmit it to T cells, thus promoting HIV dissemination in vitro and perhaps in vivo as well. To investigate DC-SIGN function and expression levels on DCs, we characterized a panel of monoclonal antibodies (MAbs) directed against the carbohydrate recognition domain of DC-SIGN. Using quantitative fluorescence-activated cell sorter technology, we found that DC-SIGN is highly expressed on immature monocyte-derived DCs, with at least 100,000 copies and often in excess of 250,000 copies per DC. There was modest variation (three- to fourfold) in DC-SIGN expression levels between individuals and between DCs isolated from the same individual at different times. Several MAbs efficiently blocked virus binding to cell lines expressing human or rhesus DC-SIGN, preventing HIV and SIV transmission. Interactions with Ebola virus pseudotypes were also blocked efficiently. Despite their ability to block virus-DC-SIGN interactions on cell lines, these antibodies only inhibited transmission of virus from DCs by approximately 50% or less. These results indicate that factors other than DC-SIGN may play important roles in the ability of DCs to capture and transmit HIV.

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