Deterministic modelling for transmission of Human Papillomavirus 6/11: impact of vaccination

Abstract

This paper is devoted to assess the impact of quadrivalent human papillomavirus (HPV) vaccine on the prevalence of non-oncogenic HPV 6/11 types in French males and females. For this purpose, a non-linear dynamic model of heterosexual transmission for HPV 6/11 types infection is developed, which accounts for immunity due to vaccination, in particular. The vaccinated reproduction number Rv is derived using the approach described by Diekmann et al. (2010) called the next generation operator approach. The model proposed is analysed, with regard to existence and uniqueness of the solution, steady-state stability. Precisely, the stability of the model is investigated depending on the sign of Rv-1. Prevalence data are used to fit a numerical HPV model, so as to assess infection rates. Our approach suggests that 10 years after introducing vaccination, the prevalence of HPV 6/11 types in females will be halved and that in males will be reduced by one-quarter, assuming a sustained vaccine coverage of 30% among females. Using the formula, we derived for the vaccinated reproduction number, we show that the non-oncogenic HPV 6/11 types would be eradicated if vaccine coverage in females is kept above 12%.

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

“…Demographic equations. In [14], Ribassin-Majed et al used a HPV model with constant recruitment rate in the demographic equation to study HPV disease dynamics in male and female populations of France. In the absence of the HPV disease, the demographic equation of their model is the following ordinary differential equation:…”

“…(9) In Figure 1, we compare the "fitted" solution (8) of Model (1), and our "fitted" solution (5) of Model (2), to the US Census Bureau data in Table 1. Figure 1 shows that Model (2), the "fitted" logistic model, captures better the 2000 − 2014 US Census Bureau data of the AAF population of 16 years and older than Model (1), the constant recruitment demographic equation used in the France study [14] and in the study of Lee and Tameru [13]. Similarly, Figure 2 shows that, as in the female population, the "fitted" solution (9) of Model (1) over estimates the AAM US Census Bureau data while our "fitted" solution (5) of Model (2) captures it.…”

“…To study the HPV dynamics in male and female African American populations of 16 years and older, we assume that the total AAF population (respectively, total AAM population) of 16 years and older is governed by Model (2) with i = f (respectively, Model (2) with i = m). As in [14], we divide the population into four compartments: S f = susceptible AAF population, S m = susceptible AAM population, I f = HPV infected AAF population, I m = HPV infected AAM population. It is known that females and males recover from HPV at about the same rate [11].…”

“…Disease-free equilibria, stability and basic reproduction number (R 0 ). Unlike in [14], it is possible for Model (10) to exhibit up to four disease-free equilibrium points (DFEs), where R d f > 1 and R dm > 1.…”

“…For example, Alsaleh and Gummel [1] in a recent paper, used a deterministic model to assess the impact of vaccination on both high-risk and lowrisk HPV infection types. Ribassin-Majed and Clemencon [14] used a deterministic mathematical model to assess the impact of vaccination on non-cancer causing HPV (6/11) in French males and females. Lee and Tameru [13] used a deterministic model to assess the impact of HPV on cervical cancer in African American females (AAF).…”