Modelling the Use of Vaccine and Wolbachia on Dengue Transmission Dynamics

A Fractional-Order Density-Dependent Mathematical Model to Find the Better Strain of Wolbachia

The primary objective of the current study was to create a mathematical model utilizing fractional-order calculus for the purpose of analyzing the symmetrical characteristics of Wolbachia dissemination among Aedesaegypti mosquitoes. We investigated various strains of Wolbachia to determine the most sustainable one through predicting their dynamics. Wolbachia is an effective tool for controlling mosquito-borne diseases, and several strains have been tested in laboratories and released into outbreak locations. This study aimed to determine the symmetrical features of the most efficient strain from a mathematical perspective. This was accomplished by integrating a density-dependent death rate and the rate of cytoplasmic incompatibility (CI) into the model to examine the spread of Wolbachia and non-Wolbachia mosquitoes. The fractional-order mathematical model developed here is physically meaningful and was assessed for equilibrium points in the presence and absence of disease. Eight equilibrium points were determined, and their local and global stability were determined using the Routh–Hurwitz criterion and linear matrix inequality theory. The basic reproduction number was calculated using the next-generation matrix method. The research also involved conducting numerical simulations to evaluate the behavior of the basic reproduction number for different equilibrium points and identify the optimal CI value for reducing disease spread.

Estimating the Time Reproduction Number in Kupang City Indonesia, 2016–2020, and Assessing the Effects of Vaccination and Different Wolbachia Strains on Dengue Transmission Dynamics

The use of a vaccine and Wolbachia bacterium have been proposed as new strategies against dengue. However, the performance of Wolbachia in reducing dengue incidence may depend on the Wolbachia strains. Therefore, in this paper, the performance of two Wolbachia strains which are WMel and WAu, in combination with the vaccine, has been assessed by using an age-dependent mathematical model. An effective reproduction number has been calculated using the Extended Kalman Filter (EKF) algorithm. The results revealed that the time reproduction number varies overtime with the highest one being around 2.75. Moreover, it has also found that use of the vaccine and Wolbachia possibly leads to dengue elimination. Furthermore, vaccination on one group only reduces dengue incidence in that group but dengue infection in the other group is still high. Furthermore, the performance of the WAu strain is better than the WMel strain in reducing dengue incidence. However, both strains can still be used for dengue elimination strategies depending on the level of loss of Wolbachia infections in both strains.

Reducing dengue fever cases at the lowest budget: a constrained optimization approach applied to Thailand

Background

With the challenges that dengue fever (DF) presents to healthcare systems and societies, public health officials must determine where best to allocate scarce resources and restricted budgets. Constrained optimization (CO) helps to address some of the acknowledged limitations of conventional health economic analyses and has typically been used to identify the optimal allocation of resources across interventions subject to a variety of constraints.

Methods

A dynamic transmission model was developed to predict the number of dengue cases in Thailand at steady state. A CO was then applied to identify the optimal combination of interventions (release of Wolbachia-infected mosquitoes and paediatric vaccination) within the constraints of a fixed budget, set no higher than cost estimates of the current vector control programme, to minimize the number of dengue cases and disability-adjusted life years (DALYs) lost. Epidemiological, cost, and effectiveness data were informed by national data and the research literature. The time horizon was 10 years. Scenario analyses examined different disease management and intervention costs, budget constraints, vaccine efficacy, and optimization time horizon.

Results

Under base-case budget constraints, the optimal coverage of the two interventions to minimize dengue incidence was predicted to be nearly equal (Wolbachia 50%; paediatric vaccination 49%) with corresponding coverages under lower bound (Wolbachia 54%; paediatric vaccination 10%) and upper bound (Wolbachia 67%; paediatric vaccination 100%) budget ceilings. Scenario analyses indicated that the most impactful situations related to the costs of Wolbachia and paediatric vaccination with decreases/ increases in costs of interventions demonstrating a direct correlation with coverage (increases/ decreases) of the respective control strategies under examination.

Conclusions

Determining the best investment strategy for dengue control requires the identification of the optimal mix of interventions to implement in order to maximize public health outcomes, often under fixed budget constraints. A CO model was developed with the objective of minimizing dengue cases (and DALYs lost) over a 10-year time horizon, within the constraints of the estimated budgets for vector control in the absence of vaccination and Wolbachia. The model provides a tool for developing estimates of optimal coverage of combined dengue control strategies that minimize dengue burden at the lowest budget.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-021-10747-3.

Optimal vaccination strategy for dengue transmission in Kupang city, Indonesia

Dengue is a public health problem with around 390 million cases annually and is caused by four distinct serotypes. Infection by one of the serotypes provides lifelong immunity to that serotype but have a higher chance of attracting the more dangerous forms of dengue in subsequent infections. Therefore, a perfect strategy against dengue is required. Dengue vaccine with 42-80% efficacy level has been licensed for the use in reducing disease transmission. However, this may increase the likelihood of obtaining the dangerous forms of dengue. In this paper, we have developed single and two-serotype dengue mathematical models to investigate the effects of vaccination on dengue transmission dynamics. The model is validated against dengue data from Kupang city, Indonesia. We investigate the effects of vaccination on seronegative and seropositive individuals and perform a global sensitivity analysis to determine the most influential parameters of the model. A sensitivity analysis suggests that the vaccination rate, the transmission probability and the biting rate have greater effects on the reduction of the proportion of dengue cases. Interestingly, with vaccine implementation, the mosquito-related parameters do not have significant impact on the reduction in the proportion of dengue cases. If the vaccination is implemented on seronegative individuals only, it may increase the likelihood of obtaining the severe dengue. To reduce the proportion of severe dengue cases, it is better to vaccinate seropositive individuals. In the context of Kupang City where the majority of individuals have been infected by at least one dengue serotype, the implementation of vaccination strategy is possible. However, understanding the serotype-specific differences is required to optimise the delivery of the intervention.

Modeling the potential of wAu-Wolbachia strain invasion in mosquitoes to control Aedes-borne arboviral infections

Arboviral infections such as dengue, Zika and chikungunya are fast spreading diseases that pose significant health problems globally. In order to control these infections, an intracellular bacterium called Wolbachia has been introduced into wild-type mosquito populations in the hopes of replacing the vector transmitting agent, Aedes aegypti with one that is incapable of transmission. In this study, we developed a Wolbachia transmission model for the novel wAu strain which possesses several favourable traits (e.g., enhanced viral blockage and maintenance at higher temperature) but not cyctoplasmic incompatibility (CI)-when a Wolbachia-infected male mosquito mates with an uninfected female mosquito, producing no viable offspring. This model describes the competitive dynamics between wAu-Wolbachia-infected and uninfected mosquitoes and the role of imperfect maternal transmission. By analysing the system via computing the basic reproduction number(s) and stability properties, the potential of the wAu strain as a viable strategy to control arboviral infections is established. The results of this work show that enhanced maintenance of Wolbachia infection at higher temperatures can overcome the lack of CI induction to support wAu-Wolbachia infected mosquito invasion. This study will support future arboviral control programs, that rely on the introduction of new Wolbachia variants.