scholarly journals Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population

2007 ◽  
Vol 69 (3) ◽  
pp. 1067-1091 ◽  
Author(s):  
Nicolas Bacaër
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vector Borne Diseases ◽  
Vector Population ◽  
Vector Borne ◽  
The Basic Reproduction Number

scholarly journals Mapping the basic reproduction number (R0) for vector-borne diseases: A case study on bluetongue virus

Epidemics ◽  
2009 ◽  
Vol 1 (3) ◽  
pp. 153-161 ◽  
Author(s):  
N.A. Hartemink ◽  
B.V. Purse ◽  
R. Meiswinkel ◽  
H.E. Brown ◽  
A. de Koeijer ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Bluetongue Virus ◽  
Reproduction Number ◽  
Vector Borne Diseases ◽  
Vector Borne ◽  
The Basic Reproduction Number

scholarly journals On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Stanislas Ouaro ◽  
Ali Traoré
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Mass Action ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Vector Borne Disease ◽  
Special Cases ◽  
Vector Borne ◽  
The Basic Reproduction Number

We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination.

A MODEL OF THE TRANSMISSION DYNAMICS OF LEISHMANIASIS

2011 ◽  
Vol 19 (02) ◽  
pp. 237-250 ◽  
Author(s):  
EPHRAIM O. AGYINGI ◽  
DAVID S. ROSS ◽  
KARTHIK BATHENA
Keyword(s):  
Global Attractor ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Sis Model ◽  
Vector Population ◽  
Single Animal ◽  
Reservoir Hosts ◽  
The Basic Reproduction Number

In this paper we present a susceptible–infectious–susceptible (SIS) model that describes the transmission dynamics of cutaneous Leishmaniasis. The model treats a vector population and several populations of different mammals. Members of the human population serve as the incidental hosts, and members of the various animals populations serve as reservoir hosts. We establish the basic reproduction number and the equilibrium conditions of the system. We use a generalization of the Lyapunov function approach to show that when the basic reproduction number is less than or equal to one, the diseases-free equilibrium is a global attractor, and that when it is greater than one the endemic equilibrium is a global attractor. We present numerical simulations that demonstrate the dynamics of the model for a system containing a human population and a single animal population.

scholarly journals Practical unidentifiability of a simple vector-borne disease model: implications for parameter estimation and intervention assessment

2017 ◽  
Author(s):  
Yu-Han Kao ◽  
Marisa C. Eisenberg
Keyword(s):  
Parameter Estimation ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Environmental Drivers ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Basic Reproduction Number

AbstractBackgroundMathematical modeling has an extensive history in vector-borne disease epidemiology, and is increasingly used for prediction, intervention design, and understanding mechanisms. Many of these studies rely on parameter estimation to link models and data, and to tailor predictions and counterfactuals to specific settings. However, few studies have formally evaluated whether vector-borne disease models can properly estimate the parameters of interest given the constraints of a particular dataset.Methodology/Principle FindingsIdentifiability methods allow us to examine whether model parameters can be estimated uniquely—a lack of consideration of such issues can result in misleading or incorrect parameter estimates and model predictions. Here, we evaluate both structural (theoretical) and practical identifiability of a commonly used compartmental model of mosquitoborne disease, using 2010 dengue epidemic in Taiwan as a case study. We show that while the model is structurally identifiable, it is practically unidentifiable under a range of human and mosquito time series measurement scenarios. In particular, the transmission parameters form a practically identifiable combination and thus cannot be estimated separately, which can lead to incorrect predictions of the effects of interventions. However, in spite of unidentifiability of the individual parameters, the basic reproduction number was successfully estimated across the unidentifiable parameter ranges. These identifiability issues can be resolved by directly measuring several additional human and mosquito life-cycle parameters both experimentally and in the field.ConclusionsWhile we only consider the simplest case for the model, without explicit environmental drivers, we show that a commonly used model of vector-borne disease is unidentifiable from human and mosquito incidence data, making it difficult or impossible to estimate parameters or assess intervention strategies. This work illustrates the importance of examining identifiability when linking models with data to make predictions, and particularly highlights the importance of combining experimental, field, and case data if we are to successfully estimate epidemiological and ecological parameters using models.Author SummaryMathematical models have seen increasing use in understanding transmission processes, developing interventions, and predicting disease incidence and prevalence. Vector-borne diseases in particular present both a challenge and an opportunity for modeling, due to the complex interactions between host and vector species. A key step in many of these studies is connecting transmission models with data to infer parameters and make useful predictions, which requires careful consideration of identifiability and uncertainty of the model parameters. Whether due to intrinsic limitations of the model structure, or practical limitations of the data collected, is common that many different parameter values may yield the same or very similar fits to the data, making it impossible to successfully estimate the parameters. This issue of parameter unidentifiability can have broad implications for our ability to draw conclusions from mechanistic models—in some cases making it difficult or impossible to generate specific predictions, forecasts, or parameter estimates from a given model and data. Here, we evaluate these questions for a commonly-used model of vectorborne disease, examining how parameter uncertainty and unidentifiability can affect intervention predictions, estimation of the basic reproduction number, and other public health conclusions drawn from the model.

scholarly journals Dynamics of a vector-borne model with direct transmission and age of infection.

2021 ◽  
Author(s):  
Necibe Tuncer ◽  
Sunil Giri
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Direct Transmission ◽  
Globally Asymptotically Stable ◽  
Born Model ◽  
Age Of Infection ◽  
Vector Borne ◽  
The Basic Reproduction Number

In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial di erential equation and obtain an explicit formula for the basic reproduction number R0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, R0 < 1. Endemic equilibrium exists and is locally asymptotically stable when R0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one.

scholarly journals Maximum Equilibrium Prevalence of Mosquito-Borne Microparasite Infections in Humans

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Marcos Amaku ◽  
Marcelo Nascimento Burattini ◽  
Francisco Antonio Bezerra Coutinho ◽  
Luis Fernandez Lopez ◽  
Eduardo Massad
Keyword(s):  
Dengue Fever ◽  
Basic Reproduction Number ◽  
General Model ◽  
Reproduction Number ◽  
Equilibrium Analysis ◽  
Force Of Infection ◽  
Maximum Value ◽  
Explicit Function ◽  
Vector Borne ◽  
The Basic Reproduction Number

To determine the maximum equilibrium prevalence of mosquito-borne microparasitic infections, this paper proposes a general model for vector-borne infections which is flexible enough to comprise the dynamics of a great number of the known diseases transmitted by arthropods. From equilibrium analysis, we determined the number of infected vectors as an explicit function of the model’s parameters and the prevalence of infection in the hosts. From the analysis, it is also possible to derive the basic reproduction number and the equilibrium force of infection as a function of those parameters and variables. From the force of infection, we were able to conclude that, depending on the disease’s structure and the model’s parameters, there is a maximum value of equilibrium prevalence for each of the mosquito-borne microparasitic infections. The analysis is exemplified by the cases of malaria and dengue fever. With the values of the parameters chosen to illustrate those calculations, the maximum equilibrium prevalence found was 31% and 0.02% for malaria and dengue, respectively. The equilibrium analysis demonstrated that there is a maximum prevalence for the mosquito-borne microparasitic infections.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

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