scholarly journals Assessing the Impact of Vaccination on Controlling the Spread of Human Scabies

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
C. P. Bhunu ◽  
S. Mushayabasa ◽  
T. G. Monera
Keyword(s):  
Numerical Simulations ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Disadvantaged Communities ◽  
To Come ◽  
The Impact ◽  
Scabies Infestation ◽  
Poor Communities

Scabies is among the infestations almost forgotten due to its association with poor communities. We formulate a deterministic model to assess the possible impact vaccination will have on scabies control. The Descartes’s rule of signs is used to show the nature of the endemic equilibria. Analysis of the reproduction number and numerical simulations suggest that vaccination in addition to treatment will help greatly in reducing the spread of scabies infestation. This suggests there is a strong need for researchers to come up with a possible vaccine in that order to effectively control scabies especially among the disadvantaged communities.

Mathematical analysis of a two-sex Human Papillomavirus (HPV) model

2018 ◽  
Vol 11 (07) ◽  
pp. 1850092 ◽  
Author(s):  
A. Omame ◽  
R. A. Umana ◽  
D. Okuonghae ◽  
S. C. Inyama
Keyword(s):  
Human Papillomavirus ◽  
Numerical Simulations ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Effective Control ◽  
Male Population ◽  
Previous Infection ◽  
Males And Females ◽  
Parameter Values ◽  
The Impact

A two-sex deterministic model for Human Papillomavirus (HPV) that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigorously analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection, when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional, and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e. condom use and vaccination of both males and females). Numerical simulations of the model showed that, based on the parameter values used therein, a vaccine (with 75% efficacy) for male population with about 40% condom compliance by females will result in a significant reduction in the disease burden in the population. Also, the numerical simulations of the model reveal that with 70% condom compliance by the male population, administering female vaccine (with 45% efficacy) is sufficient for effective control of the disease.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

Reflective Evolution Under Strategic Uncertainty

2019 ◽  
Vol 29 (02) ◽  
pp. 1950018 ◽  
Author(s):  
Arnaud Z. Dragicevic
Keyword(s):  
Population Dynamics ◽  
Numerical Simulations ◽  
Evolutionary Model ◽  
Competition Strategy ◽  
Strategic Uncertainty ◽  
Bifurcation Diagrams ◽  
Structured Population ◽  
To Come ◽  
The Impact ◽  
Negative Strategy

We consider population dynamics of agents who can both play the cooperative strategy and the competition strategy but ignore whether the game to come will be cooperative or noncooperative. For that purpose, we propose an evolutionary model, built upon replicator(–mutator) dynamics under strategic uncertainty, and study the impact of update decay. In replicator–mutator dynamics, we find that the strategy replication under certain mutation in an unstructured population is equivalent to a negative strategy replication in a structured population. Likewise, in replicator–mutator dynamics with decay, the strategy replication under certain mutation in a structured population is equivalent to a negative replication issued from an unstructured population. Our theoretical statements are supported by numerical simulations performed on bifurcation diagrams.

scholarly journals Nonlinear Analysis of the Dynamics of Criminality and Victimisation: A Mathematical Model with Case Generation and Forwarding

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Chikodili Helen Ugwuishiwu ◽  
D. S. Sarki ◽  
G. C. E. Mbah
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Nonlinear Analysis ◽  
Deterministic Model ◽  
Positive Impact ◽  
Threshold Value ◽  
Dynamical Analysis ◽  
Viable Option ◽  
Effective Implementation ◽  
The Impact

In this paper, a system of deterministic model is presented for the dynamical analysis of the interactional consequence of criminals and criminality on victimisation under two distinguishable forms of rehabilitation—the behavioural reformation of criminals and the emotional psychotherapy of victims. A threshold value, R0=maxRK,RV, responsible for the persistence of crime/criminality and victimisation, is obtained and, using it, stability analyses on the model performed. The impact of an effective implementation of the two forms of rehabilitation was found to be substantial on crime and criminality, while an ineffective implementation of same was observed to have a detrimental consequence. The prevention of repeat victimisation was seen to present a more viable option for containing crime than the noncriminalisation of victims. Further, the removal of criminals, either through quitting or death, among others, was also found to have a huge positive impact. Numerical simulations were performed for a variety of mixing criminal scenarios to verify the analytical results obtained.

scholarly journals Analysis of the Model on the Effect of Seasonal Factors on Malaria Transmission Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Victor Yiga ◽  
Hasifa Nampala ◽  
Julius Tumwiine
Keyword(s):  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Current Control ◽  
Transmission Dynamics ◽  
Mosquito Vector ◽  
The Impact ◽  
The Basic Reproduction Number

Malaria is one of the world’s most prevalent epidemics. Current control and eradication efforts are being frustrated by rapid changes in climatic factors such as temperature and rainfall. This study is aimed at assessing the impact of temperature and rainfall abundance on the intensity of malaria transmission. A human host-mosquito vector deterministic model which incorporates temperature and rainfall dependent parameters is formulated. The model is analysed for steady states and their stability. The basic reproduction number is obtained using the next-generation method. It was established that the mosquito population depends on a threshold value θ , defined as the number of mosquitoes produced by a female Anopheles mosquito throughout its lifetime, which is governed by temperature and rainfall. The conditions for the stability of the equilibrium points are investigated, and it is shown that there exists a unique endemic equilibrium which is locally and globally asymptotically stable whenever the basic reproduction number exceeds unity. Numerical simulations show that both temperature and rainfall affect the transmission dynamics of malaria; however, temperature has more influence.

scholarly journals Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 518
Author(s):  
Christopher Saaha Bornaa ◽  
Baba Seidu ◽  
Yakubu Ibrahim Seini
Keyword(s):  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Probability ◽  
Transmission Dynamics ◽  
Early Interventions ◽  
Coronavirus Infection ◽  
The Impact ◽  
Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

scholarly journals Analysis of Effectiveness of Quarantine Measures in Controlling COVID-19

2020 ◽  
Author(s):  
Garima Kaushik ◽  
Shaney Mantri ◽  
Shrishti Kaushik ◽  
Dhananjay Kalbande ◽  
B. N. Chaudhari
Keyword(s):  
Preventive Measures ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Intervention Strategies ◽  
Control Measures ◽  
Transmission Rates ◽  
The People ◽  
The World ◽  
The Impact ◽  
Insight Into

AbstractCOVID-19 has created an interesting discourse among the people of the world particularly regarding preventive measures of infectious diseases. In this paper, the authors forecast the spread of the Coronavirus outbreak and study how the reduction of transmission rates influences its decline. The paper makes use of the SIR (Susceptible Infected Recovered) Model which is a deterministic model used in the field of epidemiology-based on differential equations derived from sections of the population. The Basic Reproduction Number (Ro) represents the criticality of the epidemic in numeric terms. Forecasting an epidemic provides insights about the geographic spreading of the disease and the case incidences required to better inform intervention strategists about situations that may occur during the outbreak. Through this research paper, the authors wish to provide an insight into the impact of control measures on the pandemic. By drawing a comparison of three countries and their quarantine measures, observations on the decline of the outbreak are made. Authors intend to guide the intervention strategies of under-resourced countries like India and aid in the overall containment of the outbreak.

scholarly journals The Diffusive Model for West Nile Virus on a Periodically Evolving Domain

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Abdelrazig K. Tarboush ◽  
Zhengdi Zhang
Keyword(s):  
West Nile Virus ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Evolution Rate ◽  
Time Behavior ◽  
The West ◽  
West Nile ◽  
West Nile Virus Transmission ◽  
The Impact

In this paper, we investigate the impact of a periodically evolving domain on the dynamics of the diffusive West Nile virus. A reaction-diffusion model on a periodically and isotropically evolving domain which describes the transmission of the West Nile virus is proposed. In addition to the classical basic reproduction number, the spatial-temporal basic reproduction number depending on the periodic evolution rate is introduced and its properties are discussed. Under some conditions, we explore the long-time behavior of the virus. The virus will go extinct if the spatial-temporal basic reproduction number is less than or equal to one. The persistence of the virus happens if the spatial-temporal basic reproduction number is greater than one. We consider special case when the periodic evolution rate is equivalent to one to better understand the impact of the periodic evolution rate on the persistence or extinction of the virus. Some numerical simulations are performed in order to illustrate our analytical results. Our theoretical analysis and numerical simulations show that the periodic change of the habitat range plays an important role in the West Nile virus transmission, in particular, the increase of periodic evolution rate has positive effect on the spread of the virus.

scholarly journals Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 518
Author(s):  
Christopher Saaha Bornaa ◽  
Baba Seidu ◽  
Yakubu Ibrahim Seini
Keyword(s):  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Probability ◽  
Transmission Dynamics ◽  
Early Interventions ◽  
Coronavirus Infection ◽  
The Impact ◽  
Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

scholarly journals An extended SEIARD model for COVID-19 vaccination in Mexico: analysis and forecast

2021 ◽  
Author(s):  
Ángel G. C. Pérez ◽  
David Adeyemi Oluyori
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Reproduction Number ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Stability Of Equilibria ◽  
The Stability ◽  
Reported Data ◽  
The Impact ◽  
Disease Free

In this study, we propose and analyze an extended SEIARD model with vaccination. We compute the control reproduction number Rc of our model and study the stability of equilibria. We show that the set of disease-free equilibria is locally asymptotically stable when Rc<1 and unstable when Rc>1, and we provide a sufficient condition for its global stability. Furthermore, we perform numerical simulations using the reported data of COVID-19 infections and vaccination in Mexico to study the impact of different vaccination, transmission and efficacy rates on the dynamics of the disease.

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