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# Epidemiological frameworks. (a) Schematic illustration of the epidemiological framework for two serotypes of dengue circulating in a host population. (b) Schematic illustration of the epidemiological framework for the mosquito vector dynamics. All state variables are defined in table 1.

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Dengue is a debilitating and devastating viral infection spread by mosquito vectors, and over half the world’s population currently live at risk of dengue (and other flavivirus) infections. Here, we use an integrated epidemiological and vector ecology framework to predict optimal approaches for tackling dengue. Our aim is to investigate how vector...

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Background
Dengue is a severe environmental public health challenge in tropical and subtropical regions. In Singapore, decreasing seroprevalence and herd immunity due to successful vector control has paradoxically led to increased transmission potential of the dengue virus. We have previously demonstrated that incompatible insect technique coupled...

Aedes aegypti is the primary vector of arthropod-borne viruses including dengue, chikungunya and Zika. Vector population control methods are reviving to impede disease transmission. An efficient sex separation for male-only releases is crucial for area-wide mosquito population suppression strategies. Here, we report on the construction of two genet...

## Citations

... In this work, they used transmission of the disease and treatment of the infective as control and suggested that if both controls are applied simultaneously, then disease control will be easy [27]. In [28], Rawson et al. showed that combination of sterile insect techniques for the mosquito population and vaccination for the human population is beneficial to reduce the disease in population. Tang et al. considered vaccination with insecticide administration and isolation with insecticide administration as two control policies for control of the dengue disease [29]. ...

This study presents a mathematical model for dengue transmission which quantifies two very important aspects: one, the impact of information-based behavioural response, and the other, the segregation of infected human population into two subclasses, ‘detected’ and ‘undetected’. For the proposed model, the sensitivity analysis is conducted to identify the key model parameters which not only influence the basic reproduction number, but also regulate the transmission of dengue. Further, in order to find the optimal pathways for suitable control interventions that reduce the dengue prevalence and economic burden, an optimal control problem is proposed by considering information-induced behavioural change, quarantine, screening, use of repulsive measures and culling of mosquitoes as control interventions. A weighted sum of various costs incurred in applied controls and the cost due to dengue disease (productivity loss) is incorporated in the proposed cost functional. The analysis of control system using Pontryagin’s maximum principle leads the existence of the optimal control profiles. Further, an exhaustive comparative study for seven different control strategies is conducted numerically. Our findings emphasize that every individual control strategy has their own impact on reducing the cumulative count of infection as well as cost. The combined impact of all control interventions is highly effective and economically viable in controlling the prevalence of dengue. We also investigated the effect of the basic reproduction number on the designed control strategies and observed that the comprehensive use of controls keeps a strong tab on the infective even if the severity of epidemic is high.

... Such methods have been successful in informing public health strategies regarding the avian influenza pandemic (36), the Chikungunya epidemic (37), and influenza (38). Optimal control has also been used in terms of minimising the cost of vaccine programmes, for human papillomavirus (HPV) (39) and influenza (40), and sometimes in tandem with other disease prevention methods e.g., mosquito control for dengue (41). Optimal control methods are elegant, ultimately the most appropriate mathematically, and provide a level of verification unachieveable by scanning numerically for a solution. ...

Countries around the world have observed reduced infections from the SARS-CoV-2 virus, that causes COVID-19 illness, primarily due to non-pharmaceutical interventions (NPIs) such as lockdowns and social distancing measures designed to limit physical proximity between people. However, economies and societal interactions require restarting, and so lockdowns cannot continue indefinitely. Therefore, much hope is placed in using newly developed vaccines as a route back to normality, but this raises key questions about how they are shared. There are also emerging questions regarding travel. For instance, international business and trade necessitates at least some in-person exchanges, alongside restarting travel also for tourist purposes. By utilising a Susceptible-Infected-Recovered-Vaccinated (SIRV) mathematical model, we simulate the populations of two nations in parallel, where the first nation produces a vaccine and decides the extent to which it is shared with the second. Overlaying our mathematical structure is the virus-related effects of travel between the two nations. We find that even with extensive travel, nation one minimises its total number of deaths by simply retaining vaccines, aiming for full inoculation as fast as possible, suggesting that the risks posed by travel can be mitigated by rapidly vaccinating its own population. If instead we consider the total deaths i.e., sum of deaths of both nations, then such a policy of not sharing by nation one until full vaccination is highly sub-optimal. A policy of low initial sharing causes many more deaths in nation two than lives saved in nation one, raising important ethical issues. This imbalance in the health impact of vaccination provision must be considered as some countries begin to approach the point of extensive vaccination, while others lack the resources to do so.

... First, it is common for there to be uncertainty around model parameters and structure [97,98]. In this case, solving optimal control problems over several model structures and sets of model parameters provides insight into the sensitivity of the control strategy [99][100][101][102]. Secondly, when performing multi-objective optimization, a trade-off is made between objectives. ...

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021 .

... Mathematical models have been commonly formulated to understand disease transmission dynamics [12,[15][16][17][18] and the effects of public health interventions [4,9,12,18,19]. The use of mathematical models to assess the effects of Wolbachia and vaccine on dengue transmission dynamics has been conducted [4,9,[11][12][13]. ...

... Mathematical models have been commonly formulated to understand disease transmission dynamics [12,[15][16][17][18] and the effects of public health interventions [4,9,12,18,19]. The use of mathematical models to assess the effects of Wolbachia and vaccine on dengue transmission dynamics has been conducted [4,9,[11][12][13]. It showed that Wolbachia can reduce the number of dengue cases by up tp 80% [9] and is strongly effective in areas with low to moderate transmission setting [20]. ...

... These research assumed the constant implementation of vaccination and vector control. Rawson et al. [18] used the optimal control approach to study the effects of the combination of medicine/vaccination and vector controls in dengue transmission dynamics. They found that the combination of vaccination and the release of genetically modified self-limiting mosquitoes is the most beneficial strategy for reducing the number of dengue cases. ...

Dengue poses social and economic burden in the world. Around 390 million cases have been identified with 96 millions showing clinical symptoms. Vector control methods have been widely used as strategies against dengue. The newly proposed methods, which are currently under investigation, are by the use of vaccine and Wolbachia bacterium. Research to assess their impact on dengue transmission dynamics needs to be conducted before they are publicly implemented. In this paper, the performance of integrated strategies for dengue control using vector controls, vaccine and Wolbachia bacterium has been explored by the use of a mathematical model. The reproduction number, the key quantity to measure the endemic level, has been calculated based on dengue incidence data of Kupang City, Indonesia. An optimal control approach has been applied to investigate the performance of these strategies overtime. We also perform a global sensitivity analysis using the combination of Latin Hypercube Sampling and Partial Rank Correlation Coefficient to determine the influential parameters on the reproduction number and an increase number of dengue cases. The results showed that the dengue reproduction number in Kupang city, Indonesia varies between 1.27 to 2.02, which reflects the reality that dengue is still endemic in Kupang city, Indonesia. The results of sensitivity analysis suggest that the vector control holds an important role in determining the reproduction number. Reduction in the reproduction number would be obtained when the rate of vector control is high. Numerical solutions of the model showed that the combination of vaccine and vector control is sufficient to minimize the dengue incidence. Furthermore, to reach an optimal result, the vector control on adult mosquitoes should be implemented for the entire time period. Our results suggest that although vaccine may be available near future, the implementation of vector control is still required. However, further research needs to be undertaken to assess the impact of the integrated strategies on secondary infections.

... We use the quadratic terms in the control variables to represent the nonlinear cost in the implementation of the control. It is generally believed that there is no linear relationship between effects of intervention and the cost of intervention [23,11] and hence the quadratic costs have been commonly used [11,13,23,24,25,26]. This approach is rather conventional in the optimal control problems of the epidemiological modelling and this simplifies the mathematical analysis [23,26]. ...

... We use the quadratic terms in the control variables to represent the nonlinear cost in the implementation of the control. It is generally believed that there is no linear relationship between effects of intervention and the cost of intervention [23,11] and hence the quadratic costs have been commonly used [11,13,23,24,25,26]. This approach is rather conventional in the optimal control problems of the epidemiological modelling and this simplifies the mathematical analysis [23,26]. ...

... It is generally believed that there is no linear relationship between effects of intervention and the cost of intervention [23,11] and hence the quadratic costs have been commonly used [11,13,23,24,25,26]. This approach is rather conventional in the optimal control problems of the epidemiological modelling and this simplifies the mathematical analysis [23,26]. The use of linear term in the cost function leads to bang-bang control [23,27,28]. ...

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.