Assessing the Impact of Prophylactic Vaccines on HPV Prevalence

AZEVEDO, F.; ESTEVA, L.; FERREIRA, C.P.

doi:10.5540/tema.2019.020.02.0305

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Articles • TEMA (São Carlos) 20 (2) • May-Aug 2019 • https://doi.org/10.5540/tema.2019.020.02.0305 copy

Assessing the Impact of Prophylactic Vaccines on HPV Prevalence

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

A mathematical model considering female and male individuals is proposed to evaluate vaccination strategies applied to control of HPV transmission in human population. The basic reproductive number of the disease, R ₀ is given by the geometric mean of the basic reproductive number of female and male populations. The model has a globally asymptotically stable disease-free equilibrium whenever $R_{0} < 1$ . Furthermore, it has an unique endemic state when R ₀ exceeds unity which is globally asymptotically stable. Numerical simulations were done to compare several different vaccination schedules. The results showed that the vaccination strategies that do not include vaccination of men can only control the disease if more than 90% of women are vaccinated. The sensitivity analysis indicated that the relevant parameters to control HPV transmission, in order of importance, are vaccine efficacy times the fraction of population that is vaccinated, disease recovery-rate, and disease transmission rate. Therefore, health politics that promoting the increase of vaccine coverage, and screening for the disease in both population can improve disease control.

Keywords:
sensitivity analysis; basic reproductive number; ordinary differential equation

Variable	Description	Initial condition (time $t = 0$ )
S _f	proportion of susceptible females at time t	$S_{f} = 0.73$
V _f	proportion of vaccinated females at time t	$V_{f} = 0.0$
I _f	proportion of infected females at time t	$I_{f} = 0.27$
Z _f	proportion of recover females at time t	$Z_{f} = 0$
S _m	proportion of susceptible males at time t	$S_{m} = 0.64$
V _m	proportion of vaccinated males at time t	$V_{m} = 0.0$
I _m	proportion of infected males at time t	$I_{m} = 0.36$
Z _m	proportion of recover males at time t	$Z_{m} = 0$

Parameter	Description	Value	Interval	Unit
μ	natural mortality rate	$3.65 \times 10^{- 5}$	-	days^-1
c_f β_f	transmission rate from male to female per person, per month	0.29	0.22 - 0.37	months^-1
c_m β_m	transmission rate from female to male per person, per month	0.21	0.16 - 0.29	month^-1
$σ_{f 1} \times σ_{f 2}$	proportion of vaccinated females with 2-dose	0.40	0 - 1.0	-
$σ_{m 1} \times σ_{m 2}$	proportion of vaccinated males with 2-dose	0.28	0 - 1.0	-
γ_f , γ_m	recovered rates for female and male	1.0	0.5 - 2.0	years^-1
$ε_{1} \times ε_{2}$	vaccine efficacy	0.9	0.45 - 1.0	-
η_f , η_m	age of sexual initiation for female and male	16.2	14 - 20	years
η	interval between the first and second vaccine dose	6.0	6 - 12	months

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[1] *Corresponding author: Claudia Ferreira - E-mail: claudia.pio@unesp.br