scholarly journals AN SEIR MODEL WITH INFECTIOUS LATENT AND A PERIODIC VACCINATION STRATEGY

2021 ◽  
Vol 26 (2) ◽  
pp. 236-252
Author(s):  
Islam A. Moneim
Keyword(s):  
Infectious Diseases ◽  
Periodic Solutions ◽  
Disease Transmission ◽  
Vaccination Strategy ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
New Wave ◽  
Globally Asymptotically Stable ◽  
Seir Model ◽  
The Impact

An SEIR epidemic model with a nonconstant vaccination strategy is studied. This SEIR model has two disease transmission rates β1 and β2 which imitate the fact that, for some infectious diseases, a latent person can pass the disease into a susceptible one. Here we study the spread of some childhood infectious diseases as good examples of diseases with infectious latent. We found that our SEIR model has a unique disease free solution (DFS). A lower bound and an upper bound of the basic reproductive number, R0 are estimated. We show that, the DFS is globally asymptotically stable when and unstable if Computer simulations have been conducted to show that non trivial periodic solutions are possible. Moreover the impact of the contact rate between the latent and the susceptibles is simulated. Different periodic solutions with different periods including one, two and three years, are obtained. These results give a clearer view for the decision makers to know how and when they should take action against a possible new wave of these infectious diseases. This action is mainly, applying a suitable dose of vaccination just before a severe peak of infection occurs.

scholarly journals A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model

2020 ◽  
Vol 9 (4) ◽  
pp. 944 ◽  
Author(s):  
Kentaro Iwata ◽  
Chisato Miyakoshi
Keyword(s):  
Healthcare Professionals ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asian Countries ◽  
Hospital Visit ◽  
Seir Model ◽  
Stochastic Epidemic ◽  
Novel Coronavirus ◽  
The Impact ◽  
Multiple Scenarios

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. Even though it began to spread to many other parts of the world, such as other Asian countries, the Americas, Europe, and the Middle East, the impact of secondary outbreaks caused by exported cases outside China remains unclear. We conducted simulations to estimate the impact of potential secondary outbreaks in a community outside China. Simulations using stochastic SEIR model were conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in the total number of persons recovered or removed to be 997 (95% CrI 990–1000) at day 100 and a maximum number of symptomatic infectious patients per day of 335 (95% CrI 232–478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6–7.2). However, better case scenarios with different parameters led to no secondary cases. Altering parameters, especially time to hospital visit. could change the impact of a secondary outbreak. With these multiple scenarios with different parameters, healthcare professionals might be able to better prepare for this viral infection.

scholarly journals A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model

2020 ◽  
Author(s):  
Kentaro Iwata ◽  
Chisato Miyakoshi
Keyword(s):  
Healthcare Professionals ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Secondary Case ◽  
Hospital Visit ◽  
Seir Model ◽  
Stochastic Epidemic ◽  
Novel Coronavirus ◽  
The Impact ◽  
Multiple Scenarios

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. On the contrary to ongoing outbreak in China, however, there are limited secondary outbreaks caused by exported case outside the country. We here conducted simulations to estimate the impact of potential secondary outbreaks at a community outside China. Simulations using stochastic SEIR model was conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in total number of persons recovered or removed to be 997 (95% CrI 990-1,000) at day 100 and maximum number of symptomatic infectious patients per day of 335 (95% CrI 232-478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6-7.2). However, with good case scenarios with different parameter led to no secondary case. Altering parameters, especially time to hospital visit could change the impact of secondary outbreak. With this multiple scenarios with different parameters, healthcare professionals might be able to prepare for this viral infection better.

THRESHOLD AND STABILITY RESULTS FOR AN SIRS EPIDEMIC MODEL WITH A GENERAL PERIODIC VACCINATION STRATEGY

2005 ◽  
Vol 13 (02) ◽  
pp. 131-150 ◽  
Author(s):  
I. A. MONEIM ◽  
D. GREENHALGH
Keyword(s):  
Epidemic Model ◽  
Vaccination Strategy ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Contact Rate ◽  
Globally Asymptotically Stable ◽  
Epidemic Dynamics ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Periodic Disease

An SIRS epidemic model with general periodic vaccination strategy is analyzed. This periodic vaccination strategy is discussed first for an SIRS model with seasonal variation in the contact rate of period T = 1 year. We start with the case where the vaccination strategy and the contact rate have the same period and then discuss the case where the period of the vaccination strategy is LT, where L is an integer. We investigate whether a periodic vaccination strategy may force the epidemic dynamics to have periodic behavior. We prove that our SIRS model has a unique periodic disease free solution (DFS) whose period is the same as that of the vaccination strategy, which is globally asymptotically stable when the basic reproductive number R0 is less than or equal to one in value. When R0 > 1, we prove that there exists a non-trivial periodic solution of period the same as that of the vaccination strategy. Some persistence results are also discussed. Threshold conditions for these periodic vaccination strategies to ensure that R0 ≤ 1 are derived.

INTRINSIC TRANSMISSION GLOBAL DYNAMICS OF TUBERCULOSIS WITH AGE STRUCTURE

2011 ◽  
Vol 04 (03) ◽  
pp. 329-346 ◽  
Author(s):  
JUN-YUAN YANG ◽  
XIAO-YAN WANG ◽  
XUE-ZHI LI ◽  
FENG-QIN ZHANG
Keyword(s):  
Steady State ◽  
Disease Transmission ◽  
Death Rate ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured

An age-structured epidemiological model for the disease transmission dynamics of TB is studied. We show that the infection-free steady state is locally and globally asymptotically stable if the basic reproductive number is below one, and in this case, the disease always dies out. We prove that the endemic steady state exists when the basic reproductive number is above one. In addition, the endemic steady state is globally asymptotically stable if the basic reproductive number is above one and death rate due to TB is zero.

scholarly journals Rich Dynamics of an Epidemic Model with Saturation Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hui Wan ◽  
Jing-an Cui
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Medical Resource ◽  
Sir Epidemic Model ◽  
The Impact ◽  
The Basic Reproduction Number

A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction numberℝ0is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.

scholarly journals Pesticide application, educational treatment and infectious respiratory diseases: A mechanistic model with two impulsive controls

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243048
Author(s):  
Juan Pablo Gutiérrez-Jara ◽  
Fernando Córdova-Lepe ◽  
María Teresa Muñoz-Quezada ◽  
Gerardo Chowell
Keyword(s):  
Respiratory Disease ◽  
Disease Transmission ◽  
Pesticide Exposure ◽  
Transmission Rate ◽  
Toxic Substance ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Pesticide Use ◽  
Educational Treatment ◽  
The Impact

In this paper, we develop and analyze an SIS-type epidemiological-mathematical model of the interaction between pesticide use and infectious respiratory disease transmission for investigating the impact of pesticide intoxication on the spread of these types of diseases. We further investigate the role of educational treatment for appropriate pesticide use on the transmission dynamics. Two impulsive control events are proposed: pesticide use and educational treatment. From the proposed model, it was obtained that the rate of forgetfulness towards educational treatment is a determining factor for the reduction of intoxicated people, as well as for the reduction of costs associated with educational interventions. To get reduced intoxications, the population’s fraction to which is necessary to apply the educational treatment depends on its individual effectiveness level and the educational treatments’ forgetfulness rate. In addition, the turnover of agricultural workers plays a fundamental role in the dynamics of agrotoxic use, particularly in the application of educational treatment. For illustration, a flu-like disease with a basic reproductive number below the epidemic threshold of 1.0 is shown can acquire epidemic potential in a population at risk of pesticide exposure. Hence, our findings suggest that educational treatment targeting pesticide exposure is an effective tool to reduce the transmission rate of an infectious respiratory disease in a population exposed to the toxic substance.

scholarly journals Modeling the health impact of water and sanitation service deficits on waterborne disease transmission

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rujira Chaysiri ◽  
Garrick E. Louis ◽  
Wirawan Chinviriyasit
Keyword(s):  
Public Health ◽  
Disease Transmission ◽  
Health Impact ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Waterborne Disease ◽  
Water And Sanitation ◽  
Globally Asymptotically Stable

AbstractCholera is a waterborne disease that continues to pose serious public health problems in many developing countries. Increasing water and sanitation coverage is a goal for local authorities in these countries, as it can eliminate one of the root causes of cholera transmission. The SIWDR (susceptible–infected–water–dumpsite–recovered) model is proposed here to evaluate the effects of the improved coverage of water and sanitation services in a community at risk of a cholera outbreak. This paper provides a mathematical study of the dynamics of the water and sanitation (WatSan) deficits and their public health impact in a community. The theoretical analysis of the SIWDR model gave a certain threshold value (known as the basic reproductive number and denoted $\mathcal{R}_{0}$ R 0 ) to stop the transmission of cholera. It was found that the disease-free equilibrium was globally asymptotically stable whenever $\mathcal{R}_{0} \leq 1$ R 0 ≤ 1 . The unique endemic equilibrium was globally asymptotically stable whenever $\mathcal{R}_{0} >1$ R 0 > 1 . Sensitivity analysis was performed to determine the relative importance of model parameters to disease transmission and prevention. The numerical simulation results, using realistic parameter values in describing cholera transmission in Haiti, showed that improving the drinking water supply, wastewater and sewage treatment, and solid waste disposal services would be effective strategies for controlling the transmission pathways of this waterborne disease.

scholarly journals Assessing the Impact of Prophylactic Vaccines on HPV Prevalence

2019 ◽  
Vol 20 (2) ◽  
pp. 305
Author(s):  
F. Azevedo ◽  
L. Esteva ◽  
Claudia P. Ferreira
Keyword(s):  
Vaccine Coverage ◽  
Transmission Rate ◽  
Geometric Mean ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Health Politics ◽  
Vaccination Strategies ◽  
The Impact

A mathematical model considering female and male individuals is proposed to evaluate vaccination strategies applied to control of HPV transmission in human population. The basic reproductive number of the disease, $R_0$, is given by the geometric mean of the basic reproductive number of female and male populations. The model has a globally asymptotically stable disease-free equilibrium whenever $R_0 <1$. Furthermore, it has an unique endemic state when $R_0$ exceeds unity which is globally asymptotically stable. Numerical simulations were done to compare several different vaccination schedules. The results showed that the vaccination strategies that do not include vaccination of men can only control the disease if more than 90\% of women are vaccinated. The sensitivity analysis indicated that the relevant parameters to control HPV transmission, in order of importance, are vaccine efficacy times the fraction of population that is vaccinated, disease recovery-rate, and disease transmission rate. Therefore, health politics that promoting the increase of vaccine coverage, and screening for the disease in both population can improve disease control.

scholarly journals A realistic model for the periodic dynamics of the hand-foot-and-mouth disease

2021 ◽  
Vol 7 (2) ◽  
pp. 2585-2601
Author(s):  
I. A. Moneim ◽  
◽  
G. A. Mosa
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Foot And Mouth Disease ◽  
Vaccination Strategy ◽  
Mouth Disease ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Good Prediction ◽  
Foot And Mouth ◽  
Simulation Results

<abstract><p>In this paper, an SEIQRS model with a periodic vaccination strategy is studied for the dynamics of the Hand-Foot-and-Mouth Disease (HFMD). This model incorporates a seasonal variation in the disease transmission rate $ \beta (t) $. Our model has a unique disease free periodic solution (DFPS). The basic reproductive number $ R_{0} $ and its lower and upper bounds, $ R_{0}^{inf} $ and $ R_{0}^{sup} $ respectively, are defined. We show that the DFPS is globally asymptotically stable when $ R_{0}^{sup} &lt; 1 $ and unstable if $ R_{0}^{inf} &gt; 1 $. Computer simulations of our model have been conducted using a novel periodic function of the contact rate. This novel function imitates the seasonality in the observed, multi-peaks pattern, data. Clear and good matching between real data and the obtained simulation results are shown. The obtained simulation results give a good prediction and possible control of the disease dynamics.</p></abstract>

scholarly journals The Impact of Vaccination on Covid-19 Disease Transmission Patterns in a Human Population: A Theoretical Analysis

2021 ◽  
pp. 1-14
Author(s):  
A. B. Okrinya ◽  
C. N. Timinibife
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Human Population ◽  
Index Case ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Disease Eradication ◽  
Free Region ◽  
The Impact ◽  
Disease Free

We construct a Mathematical model that describes the effect of vaccination on the dynamics of the transmission of COVID-19 disease in a human population. The model is a system of ordinary differential equations that describes the evolution of humans in a range of Covid-19 states due to emergence of an index case in a disease free region. The analysis of the model shows that effective vaccination can lead to disease eradication, where in the disease free state is locally asymptomatically stable if the basic reproductive number, and unstable when The numerical simulations suggests the use of other social measures alongside  vaccination in order to avert the possibility of the disease  becoming endemic.

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