Analysis of the optimal vaccination age for dengue in Brazil with a tetravalent dengue vaccine

Optimal vaccine allocation for the control of sexually transmitted infections

The burden of sexually transmitted infections (STIs) poses a challenge due to its large negative impact on sexual and reproductive health worldwide. Besides simple prevention measures and available treatment efforts, prophylactic vaccination is a powerful tool for controlling some viral STIs and their associated diseases. Here, we investigate how prophylactic vaccines are best distributed to prevent and control STIs. We consider sex-specific differences in susceptibility to infection, as well as disease severity outcomes. Different vaccination strategies are compared assuming distinct budget constraints that mimic a scarce vaccine stockpile. Vaccination strategies are obtained as solutions to an optimal control problem subject to a two-sex Kermack-McKendrick-type model, where the control variables are the daily vaccination rates for females and males. One important aspect of our approach relies on conceptualizing a limited but specific vaccine stockpile via an isoperimetric constraint. We solve the optimal control problem via Pontryagin's Maximum Principle and obtain a numerical approximation for the solution using a modified version of the forward-backward sweep method that handles the isoperimetric budget constraint in our formulation. The results suggest that for a limited vaccine supply ([Formula: see text]-[Formula: see text] vaccination coverage), one-sex vaccination, prioritizing females, appears to be more beneficial than the inclusion of both sexes into the vaccination program. Whereas, if the vaccine supply is relatively large (enough to reach at least [Formula: see text] coverage), vaccinating both sexes, with a slightly higher rate for females, is optimal and provides an effective and faster approach to reducing the prevalence of the infection.

Mathematical models for dengue fever epidemiology: A 10-year systematic review

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.

Cross immunity protection and antibody-dependent enhancement in a distributed delay dynamic model

Dengue fever is endemic in tropical and subtropical countries, and certain important features of the spread of dengue fever continue to pose challenges for mathematical modelling. Here we propose a system of integro-differential equations (IDE) to study the disease transmission dynamics that involve multi-serotypes and cross immunity. Our main objective is to incorporate and analyze the effect of a general time delay term describing acquired cross immunity protection and the effect of antibody-dependent enhancement (ADE), both characteristics of Dengue fever. We perform qualitative analysis of the model and obtain results to show the stability of the epidemiologically important steady solutions that are completely determined by the basic reproduction number and the invasion reproduction number. We establish the global dynamics by constructing a suitable Lyapunov functional. We also conduct some numerical experiments to illustrate bifurcation structures, indicating the occurrence of periodic oscillations for a specific range of values of a key parameter representing ADE.

Benefit-Risk Assessment of Vaccines. Part I: A Systematic Review to Identify and Describe Studies About Quantitative Benefit-Risk Models Applied to Vaccines

Introduction

Understanding the balance between the benefits and risks of vaccination is essential to ensure informed and adequate public health decision making. Quantitative benefit–risk models (qBRm) represent useful tools to help decision makers with supporting benefit–risk assessment throughout the lifecycle of a medical product. However, few initiatives have been launched to harmonise qBRm approaches, specifically for vaccines.

Objectives

The aim of this paper was to identify publications about qBRm applied to vaccines through a systematic literature review, and to describe their characteristics.

Methods

Medline, Scopus and Institute for Scientific Information Web of Knowledge databases were searched to identify articles in English, published from database inceptions up to December 2019. The search strategy included the combination of three key concepts: ‘benefit–risk’, ‘modelling’ and ‘vaccines’. Data extracted included the modelling context and the methodological approaches used.

Results

Of 3172 publications screened, 48 original publications were included. Most of the selected studies were published over the past decade and focused on rotavirus (15), dengue (10) and influenza (6) vaccines. The majority (30) of studies reported analyses related to high-income countries. The methodology of the studies differed, particularly in modelling techniques, benefit–risk measures, and sensitivity analyses. The present work also pointed out a high level of variability in the quality of reporting across studies, with particular regard to input parameters and methodological approaches.

Conclusions

This review provides an extensive list of qBRm applied to vaccines. Discrepancies across studies were identified during our review. While the number of published qBRm studies is increasing, no reporting guidance for qBRm applied to vaccines is currently available. This may affect decision makers’ confidence in the results and their benefit–risk assessment(s); therefore, the development of such reporting guidance is highly needed.

Electronic supplementary material

The online version of this article (10.1007/s40264-020-00984-7) contains supplementary material, which is available to authorized users.

The optimal age of vaccination against dengue in Brazil based on serotype-specific forces of infection derived from serological data

In this paper, we study a single serotype transmission model of dengue to determine the optimal vaccination age for Dengvaxia. The transmission dynamics are modelled with an age-dependent force of infection. The force of infection for each serotype is derived from the serological profile of dengue in Brazil without serotype distinction and from serotype-specific reported cases. The risk due to an infection is measured by the probability of requiring hospitalization based on Brazilian Ministry of Health data. The optimal vaccination age is determined for any number and combination of the four distinct dengue virus serotypes DENv1-4. The lifetime expected risk is adapted to include antibody dependent enhancement (ADE) and permanent cross-immunity after two heterologous infections. The risk is assumed to be serostatus-dependent. The optimal vaccination age is computed for constant, serostatus-specific vaccine efficacies. Additionally, the vaccination age is restricted to conform to the licence of Dengvaxia in Brazil and the achievable and minimal lifetime expected risks are compared. The optimal vaccination age obtained for the risk of hospitalization varies significantly with the assumptions relating to ADE and cross-immunity. Risk-free primary infections lead to higher optimal vaccination ages, as do asymptomatic third and fourth infections. Sometimes vaccination is not recommended at all, e.g. for any endemic area with a single serotype if primary infections are risk-free. Restricting the vaccination age to Dengvaxia licensed ages mostly leads to only a slightly higher lifetime expected risk and the vaccine should be administered as close as possible to the optimal vaccination age.

Estimation of the expected number of cases of microcephaly in Brazil as a result of Zika

In this paper we have adapted a delayed dengue model to Zika. By assuming that the epidemic starts by a single infected individual entering a disease-free population at some initial time t₀ we have used the least squares parameter estimation technique in R to estimate the initial time t₀ using observed Zika data from Brazil as well as the transmission probabilities of Zika in Brazil between humans and mosquitoes and vice-versa. Different values of Aedes aegypti (A. aegypti) biting rate are used throughout the paper. We have estimated the value of the basic reproduction number for Zika in Brazil and calculated the expected number of cases of microcephaly in newborns as a result of women infected with Zika during pregnancy. We started off with a non-age-structured model then introduced age-structure into the model. However in reality seasonality, in particular temperature and rainfall, have a great impact on the population size of A. aegypti. Hence we repeat both the non-age-structured and age-structured analyses introducing seasonality into the A. aegypti birth function to model the effect of these environmental factors.

Modelling the Effect of a Novel Autodissemination Trap on the Spread of Dengue in Shah Alam and Malaysia

In this paper, we will start off by introducing the classical Ross-Macdonald model for vector-borne diseases which we use to describe the transmission of dengue between humans and Aedes mosquitoes in Shah Alam, which is a city and the state capital of Selangor, Malaysia. We will focus on analysing the effect of using the Mosquito Home System (MHS), which is an example of an autodissemination trap, in reducing the number of dengue cases by changing the Ross-Macdonald model. By using the national dengue data from Malaysia, we are able to estimate λ, which represents the initial growth rate of the dengue epidemic, and this allows us to estimate the number of mosquitoes in Malaysia. A mathematical expression is also constructed which allows us to estimate the potential number of breeding sites of Aedes mosquitoes. By using the data available from the MHS trial carried out in Section 15 of Shah Alam, we included the potential effect of the MHS into the dengue model and thus modelled the impact MHS has on the spread of dengue within the trial area. We then extended our results to analyse the effect of the MHSs on reducing the number of dengue cases in the whole of Malaysia. A new model was constructed with a basic reproduction number, R _0,Mala ^MHS, which allows us to identify the required MHSs coverage needed to achieve extinction in Malaysia. Numerical simulations and tables of results were also produced to illustrate our results.

Heterogeneities in dengue spatial-temporal transmission in Brazilian cities and its influence on the optimal age of vaccination

Background

The development of a safe and effective vaccine is considered crucial for dengue transmission control since vetor control has been failed; some potential candidates are currently in test, and in this context theoretical studies are necessary to evaluate vaccination strategies such as the age groups that should be vaccinated, the percentage of the population at risk, and the target geographic regions to make dengue control feasible and optimal.

Methods

A partial differential model is used to mimics dengue transmission in human population in order to estimate the optimal vaccination age, using data collected from dengue reported cases in ten cities of Brazil from 2001 to 2014. For this purpose, the basic reproduction number of the disease was minimized assuming a single-dose vaccination strategy, equal vaccine efficacy for all circulating serotypes, and no vaccine failure. Numerical methods were used to assess the optimal vaccination age and its confidence age range.

Results

The results reveal complex spatial-temporal patterns associated to the disease transmission, highlighting the heterogeneity in defining the target population for dengue vaccination. However, the values obtained for the optimal age of vaccination, as targeting individuals under 13 years old, are compatible with the ones reported in similar studies in Brazil. The results also show that the optimal age for vaccination in general does not match with the age of the highest number of cases.

Conclusions

The variation of the optimal age for vaccination across the country reflects heterogeneities in dengue spatial-temporal transmission in Brazilian cities, and can be used to define the target population and cities to optimize vaccination strategies in a context of high cost and low quantity of available vaccine.

Optimal control strategies for dengue transmission in pakistan

This paper presents a deterministic model for dengue virus transmission. The model is parameterized using data from the 2017 dengue outbreak in Pakistan. We estimated the basic reproduction number (R₀) without any interventions for the 2017 dengue outbreak in Peshawar district of Pakistan as R₀≈2.64, the distribution of the reproduction number lies in the range R₀∈[1.21,5.24] (with a mean R₀≈2.64). Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using two time-dependent control variables determined from sensitivity analysis. These control variables are insecticide use and vaccination. The results show that the two controls avert the same number of infections in the district regardless of the weights on the costs this is due to the reciprocal relationship between the cost of insecticide use and vaccination. A strong reciprocal relationship exists between the use of insecticide and vaccination; as the cost of insecticide increases the use of vaccination increases. The use of insecticide on the other hand slightly increases when vaccination level decreases due to increase in cost.