A model for mosquito-borne epidemic outbreaks with information-dependent protective behaviour

TL;DR

This study develops a vector-host epidemic framework where humans adopt protective behaviour in response to information on epidemic prevalence. By combining a two-group human population with a non-human host pool and employing Geometric Singular Perturbation Theory, the authors derive a reduced homogeneous-host model and analyze how information-driven behaviour shapes transient dynamics. They formulate an information-index-driven modification of the reproduction number and establish conditions for disease extinction, potential oscillations, or sustained waves, highlighting how memory length and reaction speed influence outbreak trajectories. Numerical simulations corroborate the analytical results, showing that information-driven protection can either aid containment or, under certain conditions, prolong or destabilize outbreaks, with implications for public health strategies in mosquito-borne diseases. The work provides a mathematically rigorous treatment of behavioural feedback in vector-borne epidemics and outlines avenues for incorporating demography and broader behavioural dynamics in future studies.

Abstract

We study a model for a mosquito-borne epidemic outbreak in which humans can adopt protective behaviour against vector bites depending on information on the past and present prevalence. Assuming that mosquitoes can also feed on other non-competent hosts (i.e. hosts that cannot infect others), we first review some results from the literature by showing that protective behaviour may either decrease or increase the value of the reproduction number of the epidemic depending on multiple elements. Then, assuming that changes in opinion occur much faster than the spread of the disease, we exploit an approach based on the Geometric Singular Perturbation Theory to reduce the two-group model to a model for a homogeneous host population. Then, we use the resulting model to investigate the effect of information-induced behavioural changes on the transient dynamics of the epidemic, discussing the case when protective measures induced an outbreak with a low attack rate. We illustrate how behavioural changes might either help in containing an epidemic outbreak or make the epidemic last longer, even triggering recurrent damped epidemic waves. We conclude with numerical simulations to illustrate our analytical results.

Figures (17)

• Figure 1: The split of the human population in protected and non-protected individuals.
• Figure 2: Flow chart for system \ref{['VBH']}. Straight lines: compartmental movements within each population; dashed lines: infections between populations (mosquitoes infecting humans and viceversa).
• Figure 3: The behaviour of the function $F(p,q)$ in \ref{['threshold']}. Note that this is independent of all the parameters of the model but $p$ and $q$.
• Figure 4: $R_c$ as a function of $q$ for different values of $p$ and $l$, with $\rho=2$ and epidemiological parameters as in \ref{['TableValues']}.
• Figure 5: A simulation for model \ref{['VBH']} with $l= 0.25$, $\rho=2$, epidemiological parameters as in \ref{['TableValues']}, $q = 0.2$ and $p=0.6$, which give $R_0\approx 2.12$ and $R_c\approx 2.24$. Top row: fraction of protected individuals (solid blue), fraction of non-protected individuals (solid red), total fraction of individuals (solid yellow) and the corresponding simulation for the total fraction for the model without protection ($q=1$, dashed green) in the infected class (left) and the removed class (right). Bottom row: fractions of individuals taken over each subgroup. Left: $I_P/p$ (solid blue), $I_{NP}/(1-p)$ (solid red) and the corresponding simulation for the model without protective behaviour ($q=1$) $I_H=I_P/p=I_{NP}/(1-p)$ (dashed green). Right: $R_P/p$ (solid blue), $R_{NP}/(1-p)$ (solid red) and the corresponding simulation for the model without protective behaviour ($q=1$) $R_H=R_P/p=R_{NP}/(1-p)$ (dashed green). The initial conditions are $I_M(0)=10^{-4}$, $S_M(0)=1-I(0)$, $S_P(0)=p$, $S_{NP}(0)=1-p$, $I_P(0)=I_{NP}(0)=R_P(0)=R_{NP}(0)=0$.

Theorems & Definitions (33)

• Remark 2.1
• Remark 2.2
• Remark 2.3
• Remark 2.4
• Proposition 2.5
• proof
• Proposition 2.6
• proof
• Corollary 2.7
• proof