Note on determining the limiting susceptible population in an epidemic model

1970 ◽  
Vol 9 ◽  
pp. 161-163 ◽  
Author(s):  
Herbert W. Hethcote
Keyword(s):  
Epidemic Model ◽  
Susceptible Population

Deterministic and stochastic epidemics with several kinds of susceptibles

1985 ◽  
Vol 17 (01) ◽  
pp. 1-22 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Epidemic Model ◽  
Susceptible Population ◽  
Basic Model ◽  
Spread Of Infection

We consider the spread of a general epidemic amongst a population consisting of invididuals with differing susceptibilities to the disease. Deterministic and stochastic versions of the basic model are described and analysed. For both versions of the model we show that assuming a uniform susceptible population, with average susceptibility, leads to an increased spread of infection. We also show how our results can be extended to the carrier-borne epidemic model of Weiss (1965).

scholarly journals Pattern Dynamics of Nonlocal Delay SI Epidemic Model with the Growth of the Susceptible following Logistic Mode

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zun-Guang Guo ◽  
Jing Li ◽  
Can Li ◽  
Juan Liang ◽  
Yiwei Yan
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Turing Instability ◽  
Average Density ◽  
Linear Stability Theory ◽  
Susceptible Population ◽  
Nonlocal Delay ◽  
Pattern Dynamics ◽  
And Control ◽  
Theoretical Results

In this paper, we investigate pattern dynamics of a nonlocal delay SI epidemic model with the growth of susceptible population following logistic mode. Applying the linear stability theory, the condition that the model generates Turing instability at the endemic steady state is analyzed; then, the exact Turing domain is found in the parameter space. Additionally, numerical results show that the time delay has key effect on the spatial distribution of the infected, that is, time delay induces the system to generate stripe patterns with different spatial structures and affects the average density of the infected. The numerical simulation is consistent with the theoretical results, which provides a reference for disease prevention and control.

scholarly journals Analysis of a Chlamydia epidemic model with pulse vaccination strategy in a random environment

2018 ◽  
Vol 23 (4) ◽  
pp. 457-474 ◽  
Author(s):  
Guruprasad Samantaa ◽  
Shyam Pada Bera
Keyword(s):  
Random Environment ◽  
Epidemic Model ◽  
Vaccination Strategy ◽  
Point Of View ◽  
Susceptible Population ◽  
Pulse Vaccination ◽  
Exponentially Stable ◽  
Periodic Disease ◽  
The Mean ◽  
Varying Total Population Size

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate, and pulse vaccination strategy in a random environment. It has been shown that the Chlamydia epidemic model has global positive solutions and, under some conditions, it admits a unique positive periodic disease-free solution, which is globally exponentially stable in mean square. We have defined two positive numbers R1 and R2 (< R1). It is proved that the susceptible population will be persistent in the mean and the disease will be going to extinct if R1 < 1 and the susceptible population as well as the disease will be weakly persistent in the mean if R2 > 1. Our analytical findings are explained through numerical simulation, which show the reliability of our model from the epidemiological point of view.

Deterministic and stochastic epidemics with several kinds of susceptibles

1985 ◽  
Vol 17 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Epidemic Model ◽  
Susceptible Population ◽  
Basic Model ◽  
Spread Of Infection

We consider the spread of a general epidemic amongst a population consisting of invididuals with differing susceptibilities to the disease. Deterministic and stochastic versions of the basic model are described and analysed. For both versions of the model we show that assuming a uniform susceptible population, with average susceptibility, leads to an increased spread of infection. We also show how our results can be extended to the carrier-borne epidemic model of Weiss (1965).

scholarly journals Stability Analysis of an Epidemic Model with Infected Immigrants and Optimal Vaccination

2019 ◽  
Vol 8 (2) ◽  
pp. 3071-3077
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Epidemic Model ◽  
Susceptible Individual ◽  
Susceptible Population ◽  
Vaccination Strategies ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Impact ◽  
Disease Free

In this paper an SIR (Susceptible-infectious-recovered) epidemic model consisting of saturated incidence rate with vaccination to the susceptible individual in presence of infected immigrants is studied. Stabilities of disease free and endemic equilibrium are also analyzed. The impact of the infected immigrants in the spread of the illness in a populace is examined. A mathematical model has been used to investigate the inflow of the infected immigrants in a population who rapidly transmit the disease. By using appropriate vaccine level to the susceptible population, disease can be reduced. The main purpose of this work is minimizing the invectives and maximizes the recovered individuals. To attain this, apply optimal vaccination strategies by utilizing the pontryagin’s maximum principle (PMP). Speculative results are demonstrated through the numerical simulations

scholarly journals Improved Estimation of the Initial Number of Susceptible Individuals in the General Stochastic Epidemic Model Using Penalized Likelihood

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Changhyuck Oh
Keyword(s):  
Epidemic Model ◽  
Likelihood Function ◽  
Hessian Matrix ◽  
Short Note ◽  
Penalized Likelihood ◽  
Initial Number ◽  
Susceptible Population ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
General Stochastic

The initial size of a completely susceptible population in a group of individuals plays a key role in drawing inferences for epidemic models. However, this can be difficult to obtain in practice because, in any population, there might be individuals who may not transmit the disease during the epidemic. This short note describes how to improve the maximum likelihood estimators of the infection rate and the initial number of susceptible individuals and provides their approximate Hessian matrix for the general stochastic epidemic model by using the concept of the penalized likelihood function. The simulations of major epidemics show significant improvements in performance in averages and coverage ratios for the suggested estimator of the initial number in comparison to existing methods. We applied the proposed method to the Abakaliki smallpox data.

scholarly journals Inferring epidemic containment probability from non-pharmaceutical interventions using a Gillespie-based epidemic model

2021 ◽  
Author(s):  
Yasuhiko Kawato ◽  
Masatoshi Yamasaki ◽  
Tomomasa Matsuyama ◽  
Tohru Mekata ◽  
Takafumi Ito ◽  
...  
Keyword(s):  
Stochastic Simulation ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Model Parameters ◽  
Gillespie Algorithm ◽  
Susceptible Population ◽  
Markovian Processes ◽  
Pharmaceutical Interventions

The Gillespie algorithm, which is a stochastic numerical simulation of continuous-time Markovian processes, has been proposed for simulating epidemic dynamics. In the present study, using the Gillespie-based epidemic model, we focused on each single trajectory by the stochastic simulation to infer the probability of controlling an epidemic by non-pharmaceutical interventions (NPIs). The single trajectory analysis by the stochastic simulation suggested that a few infected people sometimes dissipated spontaneously without spreading of infection. The outbreak probability was affected by basic reproductive number but not by infectious duration and susceptible population size.　A comparative analysis suggested that the mean trajectory by the stochastic simulation has equivalent dynamics to a conventional deterministic model in terms of epidemic forecasting. The probability of outbreak containment by NPIs was inferred by trajectories derived from 1000 Monte Carlo simulation trials using model parameters assuming COVID-19 epidemic. The model-based analysis indicated that complete containment of the disease could be achieved by short-duration NPIs if performed early after the import of infected individuals. Under the correctness of the model assumptions, analysis of each trajectory by Gillespie-based stochastic model would provide a unique and valuable output such as the probabilities of outbreak containment by NPIs.

A TWO-STRAIN EPIDEMIC MODEL WITH DIFFERENTIAL SUSCEPTIBILITY AND MUTATION

2013 ◽  
Vol 21 (04) ◽  
pp. 1340009 ◽  
Author(s):  
XUE-ZHI LI ◽  
SHA-SHA GAO ◽  
SOUVIK BHATTACHARYA
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Differential Susceptibility ◽  
Complete Protection ◽  
Susceptible Population ◽  
Explicit Formulae ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Invasion Reproduction Number

A two-strain epidemic model with differential susceptibility and mutation is formulated and analyzed in this paper. The susceptible population is divided into two subgroups according to the vaccine that provides complete protection against one of the strains (strain two) but only partial against the other (strain one). The explicit formulae for the basic reproduction number and invasion reproduction number corresponding to each strain with and without mutation are derived, respectively. It is shown that there exist exclusive equilibria and coexistence equilibria, even if the reproduction number is below one. The stability of the disease-free equilibrium, strain dominance with or without mutation are investigated. The persistence of the disease is also briefly discussed. Numerical simulations are presented to illustrate the results.

scholarly journals STATIONARY DISTRIBUTION AND EXTINCTION OF STOCHASTIC CORONAVIRUS (COVID-19) EPIDEMIC MODEL

Fractals ◽  
2021 ◽  
Author(s):  
AMIR KHAN ◽  
HEDAYAT ULLAH ◽  
MOSTAFA ZAHRI ◽  
USA WANNASINGHA HUMPHRIES ◽  
TOURIA KARITE ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Unique Solution ◽  
Epidemic Model ◽  
Feasible Region ◽  
Random Perturbations ◽  
Suggested Model ◽  
Susceptible Population ◽  
Ergodic Distribution ◽  
Very High

The aim of this paper is to model corona-virus (COVID-19) taking into account random perturbations. The suggested model is composed of four different classes i.e. the susceptible population, the smart lockdown class, the infectious population, and the recovered population. We investigate the proposed problem for the derivation of at least one unique solution in the positive feasible region of nonlocal solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function and the condition for the extinction of the disease is also established. The obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been simulated numerically.

DISTRIBUSI DAN IDENTIFIKASI POPULASI SINTRONG (Crossocephalum crepidiodes.Benth) RESISTEN PARAKUAT PADA LAHAN JAGUNG (Zea mays) DI KABUPATEN DAIRI

2017 ◽  
Vol 4 (2) ◽  
pp. 149-161
Author(s):  
Berton Sianturi
Keyword(s):  
Zea Mays ◽  
Dose Response ◽  
High Resistance ◽  
Block Design ◽  
Recommended Dose ◽  
Second Step ◽  
Resistance Level ◽  
Susceptible Population ◽  
Randomized Complete Block Design ◽  
Susceptible Populations

Crassocephalum crepidioides on Cornfields in Dairi Regency had been reported tobecome more difficult to control using paraquat. The objective of the research was todetermine the characteristics and the distribution of C.crepidioides resistant to paraquatin cornfields. The experiment was carried out in two steps, the first step was screeningthe population of C. crepidioides with paraquat at the recommended dose, and the secondstep, dose-response experiment for the resistance level of C. crepidioides population withdose 0, 76, 152, 304,5, 609, 1218, and 2436 g.ai /ha. In the first step experiment, paraquatdichloride was applied at 280 g.ai/ha. The treatments were arranged in a randomized blockdesign with 3 replication. The second step experiment was that the resistant populationsconfirmed in the first experiment were sprayed for their dose-response. The treatmentswere arranged in a randomized complete block design (CRBD). The results showed thatof 30 populations of C. crepidiodes, 19 populations (63.3%) were categorized to beresistant with the mortality ranging from 10.84% to 52.08%, and 11 populations (36.7%),was categorized as high resistance with mortality of 0% to 9.21%. The level ofresistance (R/S) of R-C25, R-C27, and R-C30 populations of C. crepidioides were 12,3,14,86, and 24,83 times consecutively, compared with the susceptible population. Thenumber of C. crepidioides chlorophyl leaves in susceptible populations was significantlylower than that of a resistant populations.

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