Analysis of deterministic models for dengue disease transmission dynamics with vaccination perspective in Johor, Malaysia

Abstract

Dengue is a mosquito-borne disease which has continued to be a public health issue in Malaysia. This paper investigates the impact of singular use of vaccination and its combined effort with treatment and adulticide controls on the population dynamics of dengue in Johor, Malaysia. In a first step, a compartmental model capturing vaccination compartment with mass random vaccination distribution process is appropriately formulated. The model with or without imperfect vaccination exhibits backward bifurcation phenomenon. Using the available data and facts from the 2012 dengue outbreak in Johor, basic reproduction number for the outbreak is estimated. Sensitivity analysis is performed to investigate how the model parameters influence dengue disease transmission and spread in a population. In a second step, a new deterministic model incorporating vaccination as a control parameter of distinct constant rates with the efforts of treatment and adulticide controls is developed. Numerical simulations are carried out to evaluate the impact of the three control measures by implementing several control strategies. It is observed that the transmission of dengue can be curtailed using any of the control strategies analysed in this work. Efficiency analysis further reveals that a strategy that combines vaccination, treatment and adulticide controls is most efficient for dengue prevention and control in Johor, Malaysia.

Keywords: Bifurcation; Dengue disease transmission; Efficiency analysis; Stability analysis; Vaccination.

Fig. 1

Scheme of the SVEIR + ASEI dengue model (5)

Fig. 2

Bifurcation diagrams for the vaccination model (5)

Fig. 3

Scheme of the SEIR + ASEI dengue model (35)

Fig. 4

Bifurcation diagrams for the vaccination-free model (35)

Fig. 5

Fitting of the dengue model (35) with the cumulative number of weekly reported dengue cases in Johor from January to December 2012

Fig. 6

PRCC values for the parameters of model (5) and model (35) using ${\mathcal{R}}_c$ and ${\mathcal{R}}_0$ as response functions respectively

Fig. 7

Contour plots of $\mathcal{R}$

Fig. 8

Dynamics of dengue model (5) with and without vaccination control ($u_V$) implementation

Fig. 9

Dynamics of dengue model (5) with and without treatment control ($u_T$) implementation

Fig. 10

Dynamics of dengue model (5) with and without adulticide control ($u_A$) implementation

Fig. 11

Dynamics of dengue model (5) with and without combined use of vaccination ($u_V$) and treatment ($u_T$) controls

Fig. 12

Dynamics of dengue model (5) with and without combined application of vaccination ($u_V$) and adulticide ($u_A$) controls only

Fig. 13

Dynamics of dengue model (5) with and without the combination of treatment ($u_T$) and adulticide ($u_A$) controls implementation only

Fig. 14

Dynamics of dengue model (5) with and without the combination of vaccination ($u_V$), treatment ($u_T$) and adulticide ($u_A$) controls implementation only