Department of Mathematics and Computer Science, Alabama State University, 915 S. Jackson St., Montgomery, AL 36101, USA.
Background: Mathematical models can be useful tools in exploring disease trends and health consequences of interventions in a population over time. Most cancers, in particular cervical cancer, have long incubation periods. The time from acquisition of HPV infection to development of invasive cancer can be up to two decades or more. Mathematical models can be used to translate short-term findings from prevention and mitigations trials into predictions of long-term health outcomes. The main objective of this paper is to develop a mathematical model of HPV for African American women (AAW) in the United States and give quantitative insight into current U.S. prevention and mitigations against cervical cancer.
Methods: A compartmental mathematical model of the cycle of HPV that includes the choices individuals make once they become infected; treatment versus no treatment, was developed. Using this mathematical model we evaluated the impact of human papillomavirus (HPV) on a given population and determined what could decrease the rate at which AAW become infected. All state equations in the model were approximated using the Runge-Kutta 4th order numerical approximation method using MatLab software.
Results: In this paper we found that the basic reproductive number ROU is directly proportional to the rate of infectivity of HPV and the contact rate in which a human infects another human with HPV. The ROU was indirectly proportional to the recovery rate plus the mortality by natural causes and the disease. The second ROT is also directly proportional to the rate of infectivity of HPV and contact rate in which humans infect another human with HPV and indirectly proportional to the recovery rate plus the mortality from HPV related cause and natural causes. Based on the data of AAW for the parameters; we found that ROU and ROT were 0.519798 and 0.070249 respectively. As both of these basic reproductive numbers are less than one, infection cannot therefore get started in a fully susceptible population, however, if mitigation is to be implemented effectively it should focus on the HPV untreated population as ROT is greater than 0.5.
Conclusion: Mathematical models, from individual and population perspectives, will help decision makers to evaluate different prevention and mitigation measures of HPV and deploy synergistically to improve cancer outcomes. Integrating the best-available epidemiologic data, computer-based mathematical models used in a decision-analytic framework can identify those factors most likely to influence outcomes and can help in formulating decisions that need to be made amidst considerable lack of data and uncertainty. Specifically, the model provides a tool that can accommodate new information, and can be modified as needed, to iteratively assess the expected benefits, costs, and cost-effectiveness of different policies in the United States. This model can help show the direct relationship between HPV and cervical cancer. If any of the rates change it will greatly impact the graphs. These graphs can be used to discover new methods of treatment that will decrease the rate of infectivity of HPV and Cervical cancer with time.
Keywords: Human Papillomavirus (HPV), reproductive number.