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

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.

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

International Journal of Biomathematics ◽

10.1142/s1793524511001726 ◽

2012 ◽

Vol 05 (04) ◽

pp. 1250029 ◽

Cited By ~ 3

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.

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

ISRN Computational Biology ◽

10.1155/2013/362973 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 4

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.

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Modeling and reviewing analysis of the COVID-19 epidemic in Algeria with diagnostic shadow

10.1101/2021.06.09.21258668 ◽

2021 ◽

Author(s):

Jiwei Jia ◽

Siyu Liu ◽

Yawen Liu ◽

Ruitong Shan ◽

Khaled Zennir ◽

...

Keyword(s):

Numerical Simulations ◽

Reproduction Number ◽

Control Strategies ◽

Control Measures ◽

Effective Control ◽

Reproduction Numbers ◽

Epidemic Dynamic ◽

Reported Data ◽

Parameter Values ◽

Research Period

In this paper, we formulate a special epidemic dynamic model to describe the transmission of COVID-19 in Algeria. We derive the threshold parameter control reproduction number (R0c ), and present the effective control reproduction number (Rc(t)) as a real-time index for evaluating the epidemic under different control strategies. Due to the limitation of the reported data, we redefine the number of accumulative confirmed cases with diagnostic shadow and then use the processed data to do the optimal numerical simulations. According to the control measures, we divide the whole research period into six stages. And then the corresponding medical resource estimations and the average effective control reproduction numbers for each stage are given. Meanwhile, we use the parameter values which are obtained from the optimal numerical simulations to forecast the whole epidemic tendency under different control strategies.

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Transmission Dynamics of Lymphatic Filariasis: A Mathematical Approach

ISRN Biomathematics ◽

10.5402/2012/930130 ◽

2012 ◽

Vol 2012 ◽

pp. 1-9 ◽

Cited By ~ 4

Author(s):

C. P. Bhunu ◽

S. Mushayabasa

Keyword(s):

Numerical Simulations ◽

Lymphatic Filariasis ◽

Reproduction Number ◽

Epidemiological Model ◽

Transmission Dynamics ◽

Effective Control ◽

Mathematical Approach

An epidemiological model for the spread of lymphatic filariasis, a mosquito-borne infection, is developed and analysed. The epidemic thresholds known as the reproduction number and equilibria for the model are determined and stabilities analysed. Results from the analysis of the reproduction number suggest that treatment will somehow contribute to a reduction in lymphatic filariasis cases, but what it does not show is the magnitude of the reduction, a part answered by the numerical simulations. Numerical simulations show that even when all lymphatic filariasis cases displaying elephantiasis symptoms are put on treatment it will not be able to eradicate the disease. This result suggests that effective control of lymphatic filariasis may lie in treatment for those displaying symptoms as well as chemoprophylaxis for the exposed.

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

Journal of Applied Mathematics ◽

10.1155/2019/9891503 ◽

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.

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Dynamics of High-Risk Nonvaccine Human Papillomavirus Types after Actual Vaccination Scheme

Computational and Mathematical Methods in Medicine ◽

10.1155/2014/542923 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Raúl Peralta ◽

Cruz Vargas-De-León ◽

Augusto Cabrera ◽

Pedro Miramontes

Keyword(s):

Cervical Cancer ◽

Human Papillomavirus ◽

High Risk ◽

Numerical Simulations ◽

Protective Immunity ◽

Type Model ◽

Vaccination Scheme ◽

Hpv Types ◽

High Risk Hpv ◽

The Impact

Human papillomavirus (HPV) has been identified as the main etiological factor in the developing of cervical cancer (CC). This finding has propitiated the development of vaccines that help to prevent the HPVs 16 and 18 infection. Both genotypes are associated with 70% of CC worldwide. In the present study, we aimed to determine the emergence of high-risk nonvaccine HPV after actual vaccination scheme to estimate the impact of the current HPV vaccines. A SIR-type model was used to study the HPV dynamics after vaccination. According to the results, our model indicates that the application of the vaccine reduces infection by target or vaccine genotypes as expected. However, numerical simulations of the model suggest the presence of the phenomenon called vaccine—induced pathogen strain replacement. Here, we report the following replacement mechanism: if the effectiveness of cross-protective immunity is not larger than the effectiveness of the vaccine, then the high-risk nonvaccine genotypes emerge. In this scenario, further studies of infection dispersion by HPV are necessary to ascertain the real impact of the current vaccines, primarily because of the different high-risk HPV types that are found in CC.

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

Journal of Applied Mathematics ◽

10.1155/2020/8885558 ◽

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.

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

F1000Research ◽

10.12688/f1000research.54268.1 ◽

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.

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Flattening the curve is not enough, we need to squash it: An explainer using a simple model

10.1101/2020.03.30.20048009 ◽

2020 ◽

Cited By ~ 1

Author(s):

ES McBryde ◽

MT Meehan ◽

JM Trauer

Keyword(s):

Deterministic Model ◽

Reproduction Number ◽

Herd Immunity ◽

International Travel ◽

Effective Control ◽

Curve Versus ◽

Successful Control ◽

The Difference ◽

The Uk ◽

Local Transmission

AbstractBackgroundAround the world there are examples of both effective control (e.g., South Korea, Japan) and less successful control (e.g., Italy, Spain, United States) of COVID-19 with dramatic differences in the consequent epidemic curves. Models agree that flattening the curve without controlling the epidemic completely is insufficient and will lead to an overwhelmed health service. A recent model, calibrated for the UK and US, demonstrated this starkly.MethodsWe used a simple compartmental deterministic model of COVID-19 transmission in Australia, to illustrate the dynamics resulting from shifting or flattening the curve versus completely squashing it.ResultsWe find that when the reproduction number is close to one, a small decrease in transmission leads to a large reduction in burden (i.e., cases, deaths and hospitalisations), but achieving this early in the epidemic through social distancing interventions also implies that the community will not reach herd immunity.ConclusionsAustralia needs not just to shift and flatten the curve, but to squash it by getting the reproduction number below one. This will require Australia to achieve transmission rates at least two thirds lower than those seen in the most severely affected countries.The knownCOVID-19 has been diagnosed in over 4,000 Australians. Up until mid-March, most were from international travel, but now we are seeing a rise in locally acquired cases.The newThis study uses a simple transmission dynamic model to demonstrate the difference between moderate changes to the reproduction number and forcing the reproduction number below one.The implicationsLowering local transmission is becoming important in reducing the transmission of COVID-19. To maintain control of the epidemic, the focus should be on those in the community who do not regard themselves as at risk.

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Analysis of Effectiveness of Quarantine Measures in Controlling COVID-19

10.1101/2020.04.21.20074245 ◽

2020 ◽

Cited By ~ 1

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.

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