scholarly journals Basic Reproduction Ratio for a Fishery Model in a Patchy Environment

2012 ◽  
Vol 60 (1-2) ◽  
pp. 167-188 ◽  
Author(s):  
Pierre Auger ◽  
Ali Moussaoui ◽  
Gauthier Sallet
Keyword(s):  
Patchy Environment ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Fishery Model

scholarly journals Mathematical analysis of a within-host model of SARS-CoV-2

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bhagya Jyoti Nath ◽  
Kaushik Dehingia ◽  
Vishnu Narayan Mishra ◽  
Yu-Ming Chu ◽  
Hemanta Kumar Sarmah
Keyword(s):  
Stability Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Basic Reproduction Ratio ◽  
Viral Kinetics ◽  
Reproduction Ratio ◽  
Biological Implication ◽  
Infection Models ◽  
Kinetics Of ◽  
The Basic Reproduction Number

AbstractIn this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper “The within-host viral kinetics of SARS-CoV-2” published in (Math. Biosci. Eng. 17(4):2853–2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number $(\chi _{0})$ ( χ 0 ) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection.

scholarly journals The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

scholarly journals Transmission of bovine herpesvirus 1 within and between herds on an island with a BHV1 control programme

2003 ◽  
Vol 130 (3) ◽  
pp. 541-552 ◽  
Author(s):  
J. J. HAGE ◽  
Y. H. SCHUKKEN ◽  
H. SCHOLS ◽  
M. A. MARIS-VELDHUIS ◽  
F. A. M. RIJSEWIJK ◽  
...  
Keyword(s):  
The Netherlands ◽  
Bovine Herpesvirus ◽  
Control Programme ◽  
Basic Reproduction Ratio ◽  
Bovine Herpesvirus 1 ◽  
Reproduction Ratio ◽  
Animal Contact ◽  
Major Outbreak ◽  
Herpesvirus 1

Transmission of bovine herpesvirus 1 (BHV1) within and between herds was studied on the island of Ameland, The Netherlands. There were 50 herds with 3300 head of cattle on the island. Herds were divided into three groups: (1) only containing seronegative cattle, (2) containing seronegative cattle and vaccinated seropositive cattle, and (3) containing only vaccinated cattle. All 23 herds in groups 1 and 2 were monitored. Three major outbreaks of BHV1 infections were observed due to the introduction of infectious cattle. Another major outbreak was most likely induced by reactivation of latent BHV1 in seropositive cattle. The basic reproduction ratio within these herds was estimated at least 4. Only one of these outbreaks led to three secondary outbreaks in susceptible herds in which all cattle were seronegative. These outbreaks were most likely due to respectively, direct animal contact, human transmission, and aerogenic transmission. The basic reproduction ratio between herds in this study was estimated to be 0·6.

scholarly journals Optimal Control of the Lost to Follow Up in a Tuberculosis Model

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yves Emvudu ◽  
Ramsès Demasse ◽  
Dany Djeudeu
Keyword(s):  
Optimal Control ◽  
Optimization Strategy ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Tb Control ◽  
New Class ◽  
Tuberculosis Model ◽  
African Context ◽  
Lost To Follow Up

This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A TB model that considers the existence of a new class (mainly in the African context) is considered: the lost to follow up individuals. Based on the model formulated and studied in the work of Plaire Tchinda Mouofo, (2009), the TB control is formulated and solved as an optimal control theory problem using the Pontryagin's maximum principle (Pontryagin et al., 1992). This control strategy indicates how the control of the lost to follow up class can considerably influence the basic reproduction ratio so as to reduce the number of lost to follow up. Numerical results show the performance of the optimization strategy.

scholarly journals The size of a major epidemic of a vector-borne disease

2011 ◽  
Vol 48 (A) ◽  
pp. 235-247
Author(s):  
Daryl J. Daley ◽  
Randall J. Swift
Keyword(s):  
Simple Model ◽  
Population Parameters ◽  
Basic Reproduction Ratio ◽  
Total Size ◽  
Reproduction Ratio ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
Almost All ◽  
Transmission Of Disease

Based on a simple model due to Dietz, it is shown that the size of a major epidemic of a vector-borne disease with basic reproduction ratio R 0&gt;1 is dominated by the size of a standard SIR (susceptible–infected–removed) epidemic with direct host-to-host transmission of disease and the same R 0. Further bounds and numerical illustrations are provided, broadly spanning situations where the size of the epidemic is short of infecting almost all those susceptible. The total size is moderately sensitive to changes in the population parameters that contribute to R 0, so that the fluctuating behaviour in ‘annual’ epidemics is not surprising.

scholarly journals Genetic parameters and genomic breeding values for digital dermatitis in Holstein Friesian dairy cattle: host susceptibility, infectivity and the basic reproduction ratio

2019 ◽  
Vol 51 (1) ◽  
Author(s):  
Floor Biemans ◽  
Mart C. M. de Jong ◽  
Piter Bijma
Keyword(s):  
Standard Deviation ◽  
Dairy Cattle ◽  
Genetic Effect ◽  
Host Susceptibility ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Genomic Breeding ◽  
Holstein Friesian ◽  
The Mean ◽  
Genetic Standard Deviation

Abstract Background For infectious diseases, the probability that an animal gets infected depends on its own susceptibility, and on the number of infectious herd mates and their infectivity. Together with the duration of the infectious period, susceptibility and infectivity determine the basic reproduction ratio of the disease ($$ R_{0} $$R0). $$ R_{0} $$R0 is the average number of secondary cases caused by a typical infectious individual in an otherwise uninfected population. An infectious disease dies out when $$ R_{0} $$R0 is lower than 1. Thus, breeding strategies that aim at reducing disease prevalence should focus on reducing $$ R_{0} $$R0, preferably to a value lower than 1. In animal breeding, however, $$ R_{0} $$R0 has received little attention. Here, we estimate the additive genetic variance in host susceptibility, host infectivity, and $$ R_{0} $$R0 for the endemic claw disease digital dermatitis (DD) in Holstein Friesian dairy cattle, and estimate genomic breeding values (GEBV) for these traits. We recorded DD disease status of both hind claws of 1513 cows from 12 Dutch dairy farms, every 2 weeks, 11 times. The genotype data consisted of 75,904 single nucleotide polymorphisms (SNPs) for 1401 of the cows. We modelled the probability that a cow got infected between recordings, and compared four generalized linear mixed models. All models included a genetic effect for susceptibility; Models 2 and 4 also included a genetic effect for infectivity, while Models 1 and 2 included a farm*period interaction. We corrected for variation in exposure to infectious herd mates via an offset. Results GEBV for $$ R_{0} $$R0 from the model that included genetic effects for susceptibility only had an accuracy of ~ 0.39 based on cross-validation between farms, which is very high given the limited amount of data and the complexity of the trait. Models with a genetic effect for infectivity showed a larger bias, but also a slightly higher accuracy of GEBV. Additive genetic standard deviation for $$ R_{0} $$R0 was large, i.e. ~ 1.17, while the mean $$ R_{0} $$R0 was 2.36. Conclusions GEBV for $$ R_{0} $$R0 showed substantial variation. The mean $$ R_{0} $$R0 was only about one genetic standard deviation greater than 1. These results suggest that lowering DD prevalence by selective breeding is promising.

Modelling the Dynamics of Leishmaniasis Considering Human, Animal Host and Vector Populations

1998 ◽  
Vol 06 (04) ◽  
pp. 337-356 ◽  
Author(s):  
Marcelo N. Burattini ◽  
Francisco A. B. Coutinho ◽  
Luis F. Lopez ◽  
Eduardo Massad
Keyword(s):  
Human Population ◽  
Control Strategies ◽  
Domestic Dog ◽  
Basic Reproduction Ratio ◽  
Public Health Importance ◽  
Animal Reservoir ◽  
Reproduction Ratio ◽  
Extrinsic Incubation Period ◽  
Vector Borne ◽  
Human Animal

Some of the vector-borne infections with public health importance involve an animal reservoir. This work describes, through a compartimental model, the dynamics of leishmaniasis considering the interactions between the three populations involved, namely the sandfly, the domestic dog (as the principal intermediate host), and the human population. An expression for the Basic Reproduction Ratio (R0), which takes into account the time delay representing the extrinsic incubation period of the parasite in the vector, is presented. Numerical simulation, equilibrium and stability analysis provided insights into the transmission dynamics of the infection that can help in the design of control strategies.

The quasi-stationary distribution of the closed endemic sis model

1996 ◽  
Vol 28 (3) ◽  
pp. 895-932 ◽  
Author(s):  
Ingemar Nåsell
Keyword(s):  
Stationary Distribution ◽  
Geometric Distribution ◽  
Threshold Value ◽  
Basic Reproduction Ratio ◽  
Sis Model ◽  
Reproduction Ratio ◽  
Time To Extinction ◽  
Extreme Distributions ◽  
Stochastic Sis Model ◽  
Quasi Stationary Distribution

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R0 distinctly below 1 and by a normal distribution (continuous!) for R0 distinctly above 1. Uniformity of the approximation with respect to R0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

GLOBAL DYNAMICS OF A DELAYED HIV-1 INFECTION MODEL WITH ABSORPTION AND SATURATION INFECTION

2012 ◽  
Vol 05 (03) ◽  
pp. 1260012 ◽  
Author(s):  
RUI XU
Keyword(s):  
Viral Entry ◽  
Chronic Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Virus Particles ◽  
Hiv 1

In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle's invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.

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