A Mathematical Model of Human Papillomavirus (HPV) in the United States and its Impact on Cervical Cancer

Modeling and analysis of a human papilloma virus transmission model with impact of media

The human papillomavirus (HPV) is threatening human health as it spreads globally in varying degrees. On the other hand, the speed and scope of information transmission continues to increase, as well as the significant increase in the number of HPV-related news reports, it has never been more important to explore the role of media news coverage in the spread and control of the virus. Using a decreasing factor that captures the impact of media on the actions of people, this paper develops a model that characterizes the dynamics of HPV transmission with media impact, vaccination and recovery. We obtain global stability of equilibrium points employing geometric method, and further yield effective methods to contain the HPV pandemic by sensitivity analysis. With the center manifold theory, we show that there is a forward bifurcation when R0=1. Our study suggested that, besides controlling contact between infected and susceptible populations and improving effective vaccine coverage, a better intervention would be to strengthen media coverage. In addition, we demonstrated that contact rate and the effect of media coverage result in multiple epidemics of infection when certain conditions are met, implying that interventions need to be tailored to specific situations.

Structured Literature Review to Identify Human Papillomavirus's Natural History Parameters for Dynamic Population Models of Vaccine Impacts

Human papillomavirus (HPV) is a common sexually transmitted virus that can cause cervical cancer and other diseases. Dynamic transmission models (DTMs) have been developed to evaluate the health and economic impacts of HPV vaccination. These models typically include many parameters, such as natural history of the disease, transmission, demographic, behavioral, and screening. To ensure the accuracy of DTM projections, it is important to parameterize them with the best available evidence. This study aimed to identify and synthesize data needed to parametrize DTMs on the natural history of HPV infection and related diseases. Parameters describing data of interest were grouped by their anatomical location (genital warts, recurrent respiratory papillomatosis, and cervical, anal, vaginal, vulvar, head and neck, and penile cancers), and natural history (progression, regression, death, cure, recurrence, detection), and were identified through a systematic literature review (SLR) and complementary targeted literature reviews (TLRs). The extracted data were then synthesized by pooling parameter values across publications, and summarized using the range of values across studies reporting each parameter and the median value from the most relevant study. Data were extracted and synthesized from 223 studies identified in the SLR and TLRs. Parameters frequently reported pertained to cervical cancer outcomes, while data for other anatomical locations were less available. The synthesis of the data provides a large volume of parameter values to inform HPV DTMs, such as annual progression rates from cervical intraepithelial neoplasia (CIN) 1 to CIN 2+ (median of highest quality estimate 0.0836), CIN 2 to CIN 3+ (0.0418), carcinoma in situ (CIS) 2 to local cancer+ (0.0396), and regional to distant cancer (0.0474). Our findings suggest that while there is a large body of evidence on cervical cancer, parameter values featured substantial heterogeneity across studies, and further studies are needed to better parametrize the non-cervical components of HPV DTMs.

Fractional view analysis of sexual transmitted human papilloma virus infection for public health

The infection of human papilloma virus (HPV) poses a global public health challenge, particularly in regions with limited access to health care and preventive measures, contributing to health disparities and increased disease burden. In this research work, we present a new model to explore the transmission dynamics of HPV infection, incorporating the impact of vaccination through the Atangana-Baleanu derivative. We establish the positivity and uniqueness of the solution for the proposed model HPV infection. The threshold parameter is determined through the next-generation matrix method, symbolized by [Formula: see text]. Moreover, we investigate the local asymptotic stability of the infection-free steady-state of the system. The existence of the solutions of the recommended model is determined through fixed-point theory. A numerical scheme is presented to visualize the dynamical behavior of the system with variation of input factors. We have shown the impact of input parameters on the dynamics of the system through numerical simulations. The findings of our investigation delineated the principal parameters exerting significant influence for the control and prevention of HPV infection.

Stochastic dynamics of human papillomavirus delineates cervical cancer progression

Starting from a deterministic model, we propose and study a stochastic model for human papillomavirus infection and cervical cancer progression. Our analysis shows that the chronic infection state as random variables which have the ergodic invariant probability measure is necessary for progression from infected cell population to cervical cancer cells. It is shown that small progression rate from infected cells to precancerous cells and small microenvironmental noises associated with the progression rate and viral infection help to establish such chronic infection states. It implicates that large environmental noises associated with viral infection and the progression rate in vivo can reduce chronic infection. We further show that there will be a cervical cancer if the noise associated with precancerous cell growth is large enough. In addition, comparable numerical studies for the deterministic model and stochastic model, together with Hopf bifurcations in both deterministic and stochastic systems, highlight our analytical results.

Epidemiological characteristics and transmissibility of HPV infection: A long-term retrospective study in Hokkien Golden Triangle, China, 2013-2021

OBJECTIVE

Multiple human papillomavirus (HPV)-associated diseases have put a significant disease burden on the world. Therefore, we conducted a study to explore the epidemiological characteristics of HPV and the transmissibility of its genotypes.

METHODS

HPV testing data was collected from Hospital. A transmission dynamics model of HPV was constructed to simulate and compare the transmissibility of different HPV genotypes, which was quantitatively described by the basic reproduction number (R0).

RESULTS

The collected HPV subjects were mainly from Xiamen City, Zhangzhou City and Quanzhou City, together, they are known as the Hokkien golden triangle. There were variations in the distribution of HPV infections by age groups. Among all HPV genotypes, 13 of them had R0 > 1, with 10 of them being high-risk types. The top five were HPV56, 18, 58, 52 and 53, among which, HPV56, 18, 58 and 42 were of high risk, whereas HPV53 was not, and the R0 values for the five were 3.35 (CI: 0.00-9.99), 3.20 (CI: 0.00-6.46), 3.19 (CI: 1.27-6.94), 3.19 (CI: 1.01-8.42) and 2.99 (CI: 0.00-9.39), respectively. In addition, HPV52 had R0 > 1 for about 51 months, which had the longest duration.

CONCLUSION

Most high-risk HPV types in the Hokkien golden triangle could transmit among the population. Therefore, there is a need of further optimization for developing HPV vaccines and better detection methods in the region.

A computational model for the cancer field effect

Introduction

The Cancer Field Effect describes an area of pre-cancerous cells that results from continued exposure to carcinogens. Cells in the cancer field can easily develop into cancer. Removal of the main tumor mass might leave the cancer field behind, increasing risk of recurrence.

Methods

The model we propose for the cancer field effect is a hybrid cellular automaton (CA), which includes a multi-layer perceptron (MLP) to compute the effects of the carcinogens on the gene expression of the genes related to cancer development. We use carcinogen interactions that are typically associated with smoking and alcohol consumption and their effect on cancer fields of the tongue.

Results

Using simulations we support the understanding that tobacco smoking is a potent carcinogen, which can be reinforced by alcohol consumption. The effect of alcohol alone is significantly less than the effect of tobacco. We further observe that pairing tumor excision with field removal delays recurrence compared to tumor excision alone. We track cell lineages and find that, in most cases, a polyclonal field develops, where the number of distinct cell lineages decreases over time as some lineages become dominant over others. Finally, we find tumor masses rarely form via monoclonal origin.

Projections of human papillomavirus vaccination and its impact on cervical cancer using the Caputo fractional derivative

We propose a fractional order model for human papillomavirus (HPV) dynamics, including the effects of vaccination and public health education on developing cervical cancer. First, we discuss the general structure of Caputo fractional derivatives and integrals. Next, we define the fractional HPV model using Caputo derivatives. The model equilibrium quantities, with their stability, are discussed based on the magnitude of the reproduction number. We compute and simulate numerical solutions of the presented fractional model using the Adams-Bashforth-Moulton scheme. Meanwhile, real data sourced from reports from the World Health Organization is used to establish the parameters and compute the basic reproduction number. We present figures of state variables for different fractional orders and the classical integer order. The impacts of vaccination and public health education are discussed through numerical simulations. From the results, we observe that an increase in both vaccination rates and public health education increases the quality of life, and thus, reduces disease burden and suffering in communities. The results also confirm that modeling HPV transmission dynamics using fractional derivatives includes history effects in the model, making the model further insightful and appropriate for studying HPV dynamics.

Proton-induced DNA damage promotes integration of foreign plasmid DNA into human genome

High-risk human papillomaviruses (HPVs) cause virtually all cervical cancer cases and are also associated with other types of anogenital and oropharyngeal cancers. Normally, HPV exists as a circular episomal DNA in the infected cell. However, in some instances, it integrates into the human genome in such a way as to enable increased expression of viral oncogenes, thereby leading to carcinogenesis. Since viral integration requires breaks in both viral and human genomes, DNA damage likely plays a key role in this critical process. One potentially significant source of DNA damage is exposure to elevated doses of ionizing radiation. Natural background radiation is ubiquitous; however, some populations, including radiological workers, radiotherapy patients, and astronauts, are exposed to significantly higher radiation doses, as well as to different types of radiation such as particle radiation. We hypothesize that ionizing radiation-induced DNA damage facilitates the integration of HPV into the human genome, increasing the risk of developing HPV-related cancers in the exposed population. To test this, we first determined the kinetics of DNA damage in keratinocytes exposed to ionizing radiation (protons) by assessing γ-H2AX foci formation using immunofluorescence (direct damage), and also measured ROS and 8-oxoG levels via DCFDA and Avidin-FITC (indirect damage).As anticipated, direct DNA damage was observed promptly, within 30 min, whereas indirect DNA damage was delayed due to the time required for ROS to accumulate and cause oxidative damage. Although radiation was lethal at high doses, we were able to establish an experimental system where radiation exposure (protons and X-rays) induced DNA damage dose-dependently without causing major cytotoxic effects as assessed by several cytotoxicity assays. Most importantly, we explored the impact of radiation exposure on integration frequency using a clonogenic assay and demonstrated that as predicted, proton-induced DNA damage promotes the integration of HPV-like foreign DNA in oral keratinocytes. Overall, the insights gained from this work enable us to better understand the contribution of radiation exposure and DNA damage to HPV-mediated carcinogenesis and direct us toward strategies aimed at preventing malignancies in HPV-infected individuals.

The impact of vaccination on human papillomavirus infection with disassortative geographical mixing: a two-patch modeling study

Human papillomavirus (HPV) infection can spread between regions. What is the impact of disassortative geographical mixing on the dynamics of HPV transmission? Vaccination is effective in preventing HPV infection. How to allocate HPV vaccines between genders within each region and between regions to reduce the total infection? Here we develop a two-patch two-sex model to address these questions. The control reproduction number [Formula: see text] under vaccination is obtained and shown to provide a critical threshold for disease elimination. Both analytical and numerical results reveal that disassortative geographical mixing does not affect [Formula: see text] and only has a minor impact on the disease prevalence in the total population given the vaccine uptake proportional to the population size for each gender in the two patches. When the vaccine uptake is not proportional to the population size, sexual mixing between the two patches can reduce [Formula: see text] and mitigate the consequence of disproportionate vaccine coverage. Using parameters calibrated from the data of a case study, we find that if the two patches have the same or similar sex ratios, allocating vaccines proportionally according to the new recruits in two patches and giving priority to the gender with a smaller recruit rate within each patch will bring the maximum benefit in reducing the total prevalence. We also show that a time-variable vaccination strategy between the two patches can further reduce the disease prevalence. This study provides some quantitative information that may help to develop vaccine distribution strategies in multiple regions with disassortative mixing.

A two-sex model of human papillomavirus infection: Vaccination strategies and a case study

Vaccination is effective in preventing human papillomavirus (HPV) infection. It still remains debatable whether males should be included in a vaccination program and unclear how to allocate the vaccine in genders to achieve the maximum benefits. In this paper, we use a two-sex model to assess HPV vaccination strategies and use the data from Guangxi Province in China as a case study. Both mathematical analysis and numerical simulations show that the basic reproduction number, an important indicator of the transmission potential of the infection, achieves its minimum when the priority of vaccination is given to the gender with a smaller recruit rate. Given a fixed amount of vaccine, splitting the vaccine evenly usually leads to a larger basic reproduction number and a higher prevalence of infection. Vaccination becomes less effective in reducing the infection once the vaccine amount exceeds the smaller recruit rate of the two genders. In the case study, we estimate the basic reproduction number is 1.0333 for HPV 16/18 in people aged 15-55. The minimal bivalent HPV vaccine needed for the disease prevalence to be below 0.05% is 24050 per year, which should be given to females. However, with this vaccination strategy it would require a very long time and a large amount of vaccine to achieve the goal. In contrast with allocating the same vaccine amount every year, we find that a variable vaccination strategy with more vaccine given in the beginning followed by less vaccine in later years can save time and total vaccine amount. The variable vaccination strategy illustrated in this study can help to better distribute the vaccine to reduce the HPV prevalence. Although this work is for HPV infection and the case study is for a province in China, the model, analysis and conclusions may be applicable to other sexually transmitted diseases in other regions or countries.

DETERMINING PROBABILITY OF CANCER CELL TRANSFOMATION AT HUMAN PAPILLOMAVIRUS INFECTION

Aim. The purpose of the work was to assess the probability of cancerous transformation of cells for viruses of high and low oncogenic risk. Aim. The purpose of the work was to assess the probability of cancerous transformation of cells for viruses of high and low oncogenic risk. Results. Using normalized squared error (NSE) for viruses of high (20 strains) and low (153 strains) oncogenic risk, rank statistic of 2-exponential type was build. For productive papillomavirus infection, NSE function was determined as the growing accurate 2-exponent of a cell layer basal to the epithelial surface. Logarithm of NSE numerical values is proportional to the cell entropy that is connected with the availability of virus DNA. To calculate entropy, generalized Hartley formula was used with the informational cell of dimension d: H = NdLOG(NSE), where N is the generalized cell coordinate. Conclusions. Using a statistical ensemble of E6 proteins separately for viruses of high and low oncogenic risk made it possible to assess the probability of cancerous transformation of cells, which was proportional to the ratio of the area of entropy of cancer transformation to the area of the productive entropy region papillomavirus infection.

Fractal geometry applied to the analysis of cervix biopsy

BACKGROUND

the measurement of the spaces of occupation of irregular objects in the context of fractal geometry has had some applications at a cellular morphometric level, where characterizations of normality and disease have been established. The objective of the present study is to apply a fractal methodology to characterize images from cervical colposcopy.

MATERIALS AND METHODS

a mathematical and geometrical characterization of 67 cell samples was performed by measuring cellular fractal characteristics through the Box-Counting method, being nine normal, eight low-intraepithelial lesions, 16 high-intraepithelial lesions, eight carcinomas in situ, 20 squamous cell carcinomas and six endocervical carcinomas.

RESULTS

the values of fractal dimension of the nuclear and cytoplasmic borders with respect to the totality varied between 0.719 to 1128 and 0.81 to 1024 while the occupation spaces in the 2 pixels grid were between 293 to 1606 and 64 to 693 respectively and in the 4 pixels grid oscillated between 153 to 894 and 36 to 361, respectively. Exocervical cells values had sensitivities between 78.3% to 100% in order to differentiate them from different types of cervical lesions.

CONCLUSIONS

according to the results obtained, the mathematical values found are suggestive of being able to differentiate between normality and some colposcopy-guided cervical biopsy lesions.

The basic reproductive number and particle-to-plaque ratio: comparison of these two parameters of viral infectivity

The COVID-19 pandemic has brought more widespread attention to the basic reproductive number (R_o), an epidemiologic measurement. A lesser-known measure of virologic infectivity is the particle-to-plaque ratio (P:PFU). We suggest that comparison between the two parameters may assist in better understanding viral transmission dynamics.

Computational modeling of human papillomavirus with impulsive vaccination

In this study, a new SIVS epidemic model for human papillomavirus (HPV) is proposed. The global dynamics of the proposed model are analyzed under pulse vaccination for the susceptible unvaccinated females and males. The threshold value for the disease-free periodic solution is obtained using the comparison theory for ordinary differential equations. It is demonstrated that the disease-free periodic solution is globally stable if the reproduction number is less than unity under some defined parameters. Moreover, we found the critical value of the pulse vaccination for susceptible females needed to control the HPV. The uniform persistence of the disease for some parameter values is also analyzed. The numerical simulations conducted agreed with the theoretical findings. It is found out using numerical simulation that the pulse vaccination has a good impact on reducing the disease.

Stability analysis and optimal control of HPV infection model with early-stage cervical cancer

Cervical cancer cells may develop from any cell infected by human papillomavirus (HPV). The aim of this paper is to study whether an optimal control of HPV infection can reduce those resulting cancer cells. To this end, the problem will be modelled by five differential equations that describe the interactions between healthy cells, infected cells, free virus, precancerous cells and cancer cells. A saturated infection rate and two treatments are incorporated into the model. The first therapy stands for the efficacy of drug treatment in blocking new infections, whereas the second serves as the drug effectiveness in inhibiting viral production. First, The problem well-posedness is fulfilled in terms of existence, positivity and boundedness of solution. Next, the existence for the two optimal control pair is established, Pontryagin's maximum principle is used to characterize these two optimal controls. Moreover, the optimality system is derived and solved numerically using the forward and backward difference approximation scheme. Finally, numerical simulations are established in order to show the role of optimal therapy in controlling cancer cells proliferation. It was revealed that the antiviral drug therapies do not act only on the viral infection spread but also on reducing the amount of precancerous and cancerous cells. Consequently, the antiviral therapies can be considered amongst the most promising measures to reduce cervical cancer cells invasion.

Stochastic modeling of human papillomavirusearly promoter gene regulation

High risk forms of human papillomaviruses (HPVs) promote cancerous lesions and are implicated in almost all cervical cancer. Of particular relevance to cancer progression is regulation of the early promoter that controls gene expression in the initial phases of infection and can eventually lead to pre-cancer progression. Our goal was to develop a stochastic model to investigate the control mechanisms that regulate gene expression from the HPV early promoter. Our model integrates modules that account for transcriptional, post-transcriptional, translational and post-translational regulation of E1 and E2 early genes to form a functioning gene regulatory network. Each module consists of a set of biochemical steps whose stochastic evolution is governed by a chemical Master Equation and can be simulated using the Gillespie algorithm. To investigate the role of noise in gene expression, we compared our stochastic simulations with solutions to ordinary differential equations for the mean behavior of the system that are valid under the conditions of large molecular abundances and quasi-equilibrium for fast reactions. The model produced results consistent with known HPV biology. Our simulation results suggest that stochasticity plays a pivotal role in determining the dynamics of HPV gene expression. In particular, the combination of positive and negative feedback regulation generates stochastic bursts of gene expression. Analysis of the model reveals that regulation at the promoter affects burst amplitude and frequency, whereas splicing is more specialized to regulate burst frequency. Our results also suggest that splicing enhancers are a significant source of stochasticity in pre-mRNA abundance and that the number of viruses infecting the host cell represents a third important source of stochasticity in gene expression.

Mathematical Modeling of E6-p53 interactions in Cervical Cancer

Background:

Cervical cancer is the third most common cancer in women throughout the world. The human papillomavirus (HPV) E6 viral protein plays an essential role in proteasomal degradation of the cancer suppressant protein p53. As a result, p53 negative regulation and apoptosis relevant activities are abrogated, facilitating development of cervical cancer.

Methods:

A mathematical model of E6-p53 interactions was developed using mathematical laws. In-silico simulations were carried out on CellDesigner and as a test case the small molecule drug RITA was considered for its ability to rescue the functions of tumor suppressor p53 by inhibiting E6 mediated proteasomal degradation.

Results:

Using a computational model we scrutinized how p53 responds to RITA, and chemical reactions of this small molecule drug were incorporated to perceive the full effects. The evolved strategy allowed the p53 response and rescue of its tumor suppressor function to be delineated, RITA being found to block p53 interactions with E6 associated proteins.

Conclusion:

We could develop a model of E6-p53 interactions with incorporation of actions of the small molecule drug RITA. Suppression of E6 associated proteins by RITA induces accumulation of tumor suppressant p53. Using CellDesigner to encode the model ensured that it can be easily modified and extended as more data become available. This strategy should play an effective role in the development of therapies against cancer.

A male-female mathematical model of human papillomavirus (HPV) in African American population

We introduce mathematical human papillomavirus (HPV) epidemic models (with and without vaccination) for African American females (AAF) and African American males (AAM) with ''fitted'' logistic demographics and use these models to study the HPV disease dynamics. The US Census Bureau data of AAF and AAM of 16 years and older from 2000 to 2014 is used to ''fit'' the logistic demographic models. We compute the basic reproduction number, R0, and use it to show that R0 is less than 1 in the African American (AA) population with or without implementation of HPV vaccination program. Furthermore, we obtain that adopting a HPV vaccination policy in the AAF and AAM populations lower R0 and the number of HPV infections. Sensitivity analysis is used to illustrate the impact of each model parameter on the basic reproduction number.

The Dynamics of HPV Infection and Cervical Cancer Cells

The development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus. The cell populations are separated into four compartments: susceptible cells, infected cells, precancerous cells and cancer cells. The model system of differential equations also has a free virus compartment in the system, which infect normal cells. We analyze the local stability of the equilibrium points of the model and investigate the parameters, which play an important role in the progression toward invasive cancer. By simulation, we investigate the boundary between initial conditions of solutions, which tend to stable equilibrium point, representing controlled infection, and those which tend to unbounded growth of the cancer cell population. Parameters affected by drug treatment are varied, and their effect on the risk of cancer progression is explored.