Modified deterministic models for dengue disease transmission and optimal control in Malaysia regions

Abstract

Dengue is an acute viral illness caused by RNA virus of the family Flaviviridae and spread by Aedes mosquitoes. It has imposed significant social, economic and medical burdens which have led to loss of lives in dengue-endemic areas. In order to understand its mode of transmission, dynamics and assess optimal strategies for controlling the disease spread, several researchers have proposed different compartmental deterministic models (single-patch, multi-strain and multipatch models). However, these models have the shortcomings of either not covering all dengue transmission phases or feature the aquatic stage mosquito. Thus, the existing model is not suitable as model frameworks in assessing different control intervention strategies to effectively control the disease transmission in a homogeneous environment, with coexistence of multiple Dengue Virus (DENV) serotypes in a community, and in a patchy environment. Therefore, the deterministic models that can explain the mechanisms involved in these aspects of dengue transmission and optimal control are needed. This research proposes and analysed single-patch deterministic model featuring all the necessary transmission phases of dengue fever in human, and both the aquatic and adult mosquitoes. This is to facilitate the understanding of the real nature of the dengue spread in a homogeneous environment and reliably use optimal personal protection (uP), larvicide (uL) and adulticide (uA) for its effective control by formulating different optimal control frameworks. By modifying the proposed single-patch model, a two-strain model which groups the four DENV serotypes into two (DENV-1 and DENV-j, j = 2; 3; 4) is developed to analyse the transmission dynamics and optimal strategy for the dengue control using Dengvaxia vaccine (uV) combined with the efforts of controls uP and uA. A two-patch model is formulated using the single-patch model to analyse the effect of human travels on the spatial spread and optimal control of dengue using uP, uL and uA controls in two connected patches. Qualitative analysis of the basic properties of the three models is performed. Meanwhile, the associated optimal control problems are analysed using Pontryagin’s Maximum Principle. Data from the 2012 dengue outbreaks in Johor and Kuala Lumpur, Malaysia is used in these models. The simulated results of the single-patch model indicate that dengue outbreak can be controlled using a combination strategy of optimal controls uP, uL and uA in Johor and Kuala Lumpur. The results obtained from numerical simulations of the two-strain model reveal that the use of combined efforts of optimal controls uV, uP and uA adequately decreases both the primary and secondary human infections in the population. Numerical results of two-patch model show that the spatial spread of dengue in Johor and Kuala Lumpur can be minimised by implementing optimal controls uP, uL and uA simultaneously during an outbreak in the states.