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

Abstract

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.

Keywords: Antibody dependent-enhancement; Dengue fever; Mathematical models; Multi-strain; Vector-host; Within-host.

Fig. 1

Schematic flow diagram for the selection process with inclusion and exclusion criteria. PubMed, Web of Knowledge, Mendeley and ScienceOpen databases were used to search for scientific papers dealing with mathematical models applied to dengue fever epidemiology.

Fig. 2

(a) Yearly distribution of single-strain models, multi-strain and within-host models. In (b) and in (c) pie-charts for single-strain models and multi-strain/within-host models distribution respectively. In total, 56 (out of 225) papers are considered. That is because 5 papers were excluded only after the full-text papers were assessed in detail.

Fig. 3

(a) Pie-chart for the distribution of the selected papers included in this review: multi-strain host-to-host models in pink, multi-strain vector-host models in green and within-host models in yellow. In (b) yearly distribution of the papers included in this review.

Fig. 4

State-flow diagram of a simple epidemiological SIR-type model. The disease-related stages are Susceptible S, Infected I and Recovered R. For a host population of N individuals, the transitions from one to another disease-related state are parameterized by infection rate β, recovery rate γ, and waning immunity rate α.

Fig. 5

Schematic flow diagram for vector compartments. With vector population size M = U + V_i + V_j, susceptible vector population (U) and infected vector population carrying i,j dengue strain (V_i, V_j), with i,j = 1,2,3,4 and i ≠ j. For host population size N, the infection rate is parametrized by β, and ϕ is a scaling factor used to differentiate the infectivity ϕβ of secondary infections with respect to the baseline infectivity β of primary infection.

Fig. 6

State-flow diagram of a minimal within-host SIV model. With susceptible target cells S, infected cells I and viral particles V, the transitions from one to another state are parametrized by a, the infection rate of susceptible target cells, κμ_i, the viral replication with disease induced mortality rate μ_i of infected cells, and b the removal rate of viral particles during the infection process of a susceptible target cell.