Multi-Strain Host-Vector Dengue Modeling: Dynamics and Control

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Since dengue is characterized by a multitude of specific mechanisms that drive

the course of the disease (possibility of reinfection, antibody-dependent enhancement

(ADE) [30, 28], and so on), the mathematical models often have many compartments and

become high-dimensional. Dengue models without ADE but with or without temporary

cross-immunity are proposed and studied in [22, 23, 24], with ADE in multiple strain host-

only models [26, 12, 2, 1, 34], as well as host-vector models [25, 27, 44, 54, 42, 41]. By

using different dimension reduction arguments to construct mathematically tractable mod-

els it is possible to focus on different aspects of the disease dynamics.

We shall discuss the complexity reduction by the means of time scale separation and

singular perturbation analysis. These model reduction methods allow for the rigorous set-

up of host-only models which represent the dynamics of a vector-borne disease, but with-

out explicit inclusion of the vector population. We are interested in the role of vector

modelling in models with multiple dengue virus serotypes and give an overview of the

literature. Some models consider a single virus serotype/strain and model host-vector in-

teractions [22]. Similar models are widely used in the modeling of other vector-borne

diseases such as malaria. Many host-only models include implicitly the vector in their

parameters [26, 12, 2, 43, 1, 34], whereas real world control measures (entomological

surveillance, insecticide or larvicide spraying, fumigation, repellents for personal protec-

tion, long-lasting insecticidal nets) are usually aimed at altering the vector’s demography,

or host seeking behavior.

Those host-only models are not directly suited for studies of effects such as pest con-

trol or personal protection via repellents, which influence the mosquito dynamics, so such

models require the explicit inclusion of vector dynamics. We provide an overview of host-

vector models and approaches for complexity reduction based on time-scale separation.

Finally, we touch upon simple dengue models incorporating control measures for dengue

given by vaccination campaigns or control measures targeted at the vector (personal pro-

tection, use of repellents, and so on) that can be used to study efficacy of the measures

undertaken to reduce the disease burden.

6.2

DESCRIPTION OF THE MODELS

Mechanisms included in epidemic models are transmission, i.e. contact either between

susceptible and infected or, in the case of vector-borne diseases, between humans and vec-

tors (mosquitos), infection of susceptible hosts/vectors, recovery, development of tempo-

rary or lifelong immunity, development of cross-immunity, possibility of reinfection by a

virus of a different serotype (strain). The basic models are the classical SI, SIS and SIR

models where a (typically constant) population is subdivided in two or three compartments

of individuals: susceptible, infected and recovered.

Demographic trends in the host and vector populations are usually neglected; hence,

birth and death of the two populations is such that the total number of individuals in the

populations remains constant over time. However, a seasonally varying vector population