scholarly journals A final size relation for epidemic models

2007 ◽  
Vol 4 (2) ◽  
pp. 159-175 ◽  
Keyword(s):  
Epidemic Models ◽  
Final Size ◽  
Final Size Relation ◽  
Size Relation

scholarly journals Computational and Mathematical Methods to Estimate the Basic Reproduction Number and Final Size for Single-Stage and Multistage Progression Disease Models for Zika with Preventative Measures

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
P. Padmanabhan ◽  
P. Seshaiyer
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Single Stage ◽  
Final Size ◽  
Multistage Model ◽  
Preventative Measures ◽  
Final Size Relation ◽  
The Impact ◽  
Size Relation ◽  
The Basic Reproduction Number

We present new mathematical models that include the impact of using selected preventative measures such as insecticide treated nets (ITN) in controlling or ameliorating the spread of the Zika virus. For these models, we derive the basic reproduction number and sharp estimates for the final size relation. We first present a single-stage model which is later extended to a new multistage model for Zika that incorporates more realistic incubation stages for both the humans and vectors. For each of these models, we derive a basic reproduction number and a final size relation estimate. We observe that the basic reproduction number for the multistage model converges to expected values for a standard Zika epidemic model with fixed incubation periods in both hosts and vectors. Finally, we also perform several computational experiments to validate the theoretical results obtained in this work and study the influence of various parameters on the models.

scholarly journals A model assessing potential benefits of isolation and mass testing on COVID-19: the case of Nigeria

2020 ◽  
Author(s):  
Faraimunashe Chirove ◽  
Chinwendu Emilian Madubueze ◽  
Zviiteyi Chazuka ◽  
Sunday Casmir Madubueze
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Mathematical Analysis ◽  
Final Size ◽  
Global Stability Analysis ◽  
Potential Benefits ◽  
Final Size Relation ◽  
Isolation Facilities ◽  
Size Relation ◽  
Disease Free

We consider a model with mass testing and isolation mimicking the current policies implemented in Nigeria and use the Nigerian daily cumulative cases to calibrate the model to obtain the optimal mass testing and isolation levels. Mathematical analysis was done and important thresholds such the peak size relation and final size relation were obtained. Global stability analysis of the disease-free equilibrium indicated that COVID-19 can be eradicated provided that $\mathcal{R}_0<1$ and unstable otherwise. Results from simulations revealed that an increase in mass testing and reduction of transmission from isolated individuals are associated with benefits of increasing detected cases, lowering peaks of symptomatic cases, increase in self-isolating cases, decrease in cumulative deaths and decrease in admissions into monitored isolation facilities in the case of Nigeria

scholarly journals SPATIAL HETEROGENEITY IN SIMPLE DETERMINISTIC SIR MODELS ASSESSED ECOLOGICALLY

2012 ◽  
Vol 54 (1-2) ◽  
pp. 23-36 ◽  
Author(s):  
E. K. WATERS ◽  
H. S. SIDHU ◽  
G. N. MERCER
Keyword(s):  
Infectious Disease ◽  
Spatial Heterogeneity ◽  
Disease Transmission ◽  
Herd Immunity ◽  
Epidemic Models ◽  
Final Size ◽  
Infectious Disease Transmission ◽  
Epidemic Dynamics ◽  
Mean Crowding ◽  
Rate Of Movement

AbstractPatchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.

scholarly journals Coupling of Two SIR Epidemic Models with Variable Susceptibilities and Infectivities

2007 ◽  
Vol 44 (01) ◽  
pp. 41-57 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Size Distribution ◽  
Random Graph ◽  
Epidemic Model ◽  
Epidemic Models ◽  
Final Size ◽  
Sir Epidemic ◽  
Novel Approach ◽  
Stochastic Epidemic ◽  
Sir Epidemic Models ◽  
Variable Susceptibility

The variable generalised stochastic epidemic model, which allows for variability in both the susceptibilities and infectivities of individuals, is analysed. A very different epidemic model which exhibits variable susceptibility and infectivity is the random-graph epidemic model. A suitable coupling of the two epidemic models is derived which enables us to show that, whilst the epidemics are very different in appearance, they have the same asymptotic final size distribution. The coupling provides a novel approach to studying random-graph epidemic models.

The distribution of general final state random variables for stochastic epidemic models

1999 ◽  
Vol 36 (2) ◽  
pp. 473-491 ◽  
Author(s):  
Frank Ball ◽  
Philip O'Neill
Keyword(s):  
Random Variables ◽  
Epidemic Models ◽  
Exact Results ◽  
Final Size ◽  
Single Population ◽  
Final State ◽  
Stochastic Epidemic Models ◽  
Basic Model ◽  
Stochastic Epidemic ◽  
Quantities Of Interest

In this paper we introduce the notion of general final state random variables for generalized epidemic models. These random variables are defined as sums over all ultimately infected individuals of random quantities of interest associated with an individual; examples include final severity. By exploiting a construction originally due to Sellke (1983), exact results concerning the final size and general final state random variables are obtained in terms of Gontcharoff polynomials. In particular, our approach highlights the way in which these polynomials arise via simple probabilistic arguments. For ease of exposition we focus initially upon the single-population case before extending our arguments to multi-population epidemics and other variants of our basic model.

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