Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics

Naveen K. Vaidya; Xianping Li; Feng-Bin Wang

doi:10.3934/dcdsb.2018099

Article Contents

2019, Volume 24, Issue 1: 321-349. Doi: 10.3934/dcdsb.2018099

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Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics

1.
Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA
2.
Department of Mathematics and Statistics, University of Missouri -Kansas City, Kansas City, MO 64110, USA
3.
Department of Natural Science in the Center for General Education, Chang Gung University, Guishan, Taoyuan 333, Taiwan
4.
Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung, Keelung 204, Taiwan

Received: January 2017

Revised: December 2017

Early access: March 2018

Published: January 2019

Abstract Full Text(HTML) Figure(8) / Table(1) Related Papers Cited by

Abstract

In recent years, the growing spatial spread of dengue, a mosquito-borne disease, has been a major international public health concern. In this paper, we propose a mathematical model to describe an impact of spatially heterogeneous temperature on the dynamics of dengue epidemics. We first consider homogeneous temperature profiles across space and study sensitivity of the basic reproduction number to the environmental temperature. We then introduce spatially heterogeneous temperature into the model and establish some important properties of dengue dynamics. In particular, we formulate two indices, mosquito reproduction number and infection invasion threshold, which completely determine the global threshold dynamics of the model. We also perform numerical simulations to explore the impact of spatially heterogeneous temperature on the disease dynamics. Our analytical and numerical results reveal that spatial heterogeneity of temperature can have significant impact on expansion of dengue epidemics. Our results, including threshold indices, may provide useful information for effective deployment of spatially targeted interventions.

Keywords:

Mathematics Subject Classification: 35K57, 37N25, 92D30.

Citation:

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Figure 2.1. Functional curves $\delta (T)$, oviposition rate, $\mu_a(T)$, aquatic phase mortality rate, $\theta (T)$, mosquito emergence rate from acuatic phase, and $\mu_m(T)$, mosquito mortality rate, fitted to the experimental data [44]

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Figure 2.2. Functional curve $\beta_m (T)$, the transmission probability from human to mosquito, fitted to the data generated from the previous estimates [17]

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Figure 3.1. The basic reproduction number, $\bar{\mathcal{R}}_0$, vs. environmental temperature, $T$, for different values of carrying capacity, $C$.

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Figure 4.1. Spatio-temporal distribution of prevalence (left) and new infection (right) during an epidemic. Here, $T_m = 22.5$℃ and $\Delta T = 25$℃, and $D_M = D_H = 0.0001$.

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Figure 4.2. Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right). Here, $T_m = 22.5$℃ and $\Delta T = 25$℃, and $D_M = D_H = 0.0001$.

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Figure 4.3. Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right) for the end point temperature difference $\Delta T = 15$℃ (upper panel) and $\Delta T = 35$℃ (lower panel). Here $T_m = 22.5$℃ and $D_M = D_H = 0.0001$.

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Figure 4.4. Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right) for the mean temperature $T_m = 15$℃ (upper panel) and $T_m = 30$℃ (lower panel). Here $\Delta T = 25$℃ and $D_M = D_H = 0.0001$.

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Figure 4.5. Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right) for $D_M/D_H = 0.1$ (upper panel) and $D_M/D_H = 10$ (lower panel). Here $T_m = 22.5$℃ and $\Delta T = 25$℃.

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Table 2.1. Model parameters

Parameter	Description	Value	Reference
$k$	fraction of female larvae from eggs	0.5 (0-1)	[18,27]
$b$	per capita biting rate	0.1	[4,27]
$\mu_h$	Natural death rate of humans	4.22$\times 10^{-5}$ d$^{-1}$	Calculated, [16]
$1/\gamma_h$	Intrinsic period	10 days	[4,16,18,27]
$\alpha_h$	Human recovery rate	0.1 d$^{-1}$	[18,27]
$D_M, D_H$	Diffusion coefficients	-	varied
$\delta_m$	In $\delta(x)$	9.531	Data fitting
$\delta_h$	In $\delta(x)$	22.55	Data fitting
$N_{\delta}$	In $\delta(x)$	7.084	Data fitting
$a_{0\mu_a}$	In $\mu_a(x)$	2.914	Data fitting
$a_{1\mu_a}$	In $\mu_a(x)$	-0.4986	Data fitting
$a_{2\mu_a}$	In $\mu_a(x)$	0.03099	Data fitting
$a_{3\mu_a}$	In $\mu_a(x)$	-0.0008236	Data fitting
$a_{4\mu_a}$	In $\mu_a(x)$	7.975$\times 10^{-6}$	Data fitting
$a_{0\theta}$	In $\theta(x)$	8.044$\times 10^{-5}$	Data fitting
$a_{1\theta}$	In $\theta(x)$	11.386	Data fitting
$a_{2\theta}$	In $\theta(x)$	40.1461	Data fitting
$a_{0\mu_m}$	In $\mu_m(x)$	0.1901	Data fitting
$a_{1\mu_m}$	In $\mu_m(x)$	-0.0134	Data fitting
$a_{2\mu_m}$	In $\mu_m(x)$	2.739$\times 10^{-4}$	Data fitting
$a_{0\gamma_m}$	In $\gamma_m(x)$	5$\times 10^{4/3}$	Data fitting
$a_{1\gamma_m}$	In $\gamma_m(x)$	0.0768	Data fitting
$\beta_{mh}$	In $\beta_m(x)$	18.9871	Data fitting
$N_{\beta_m}$	In $\beta_m(x)$	7	Data fitting
$a_{0\beta_h}$	In $\beta_h(x)$	1.044$\times 10^{-3}$	Data fitting
$a_{1\beta_h}$	In $\beta_h(x)$	12.286	Data fitting
$a_{2\beta_h}$	In $\beta_h(x)$	32.461	Data fitting

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