Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations

Economic optimization of Wolbachia-infected Aedes aegypti release to prevent dengue

BACKGROUND

Dengue virus, primarily transmitted by the Aedes aegypti mosquito, is a major public health concern affecting ≈3.83 billion people worldwide. Recent releases of Wolbachia-transinfected Ae. aegypti in several cities worldwide have shown that it can reduce dengue transmission. However, these releases are costly, and, to date, no framework has been proposed for determining economically optimal release strategies that account for both costs associated with disease risk and releases.

RESULTS

We present a flexible stochastic dynamic programming framework for determining optimal release schedules for Wolbachia-transinfected mosquitoes that balances the cost of dengue infection with the costs of rearing and releasing transinfected mosquitoes. Using an ordinary differential equation model of Wolbachia and dengue in a hypothetical city loosely describing areas at risk of new dengue epidemics, we determined that an all-or-nothing release strategy that quickly brings Wolbachia to fixation is often the optimal solution. Based on this, we examined the optimal facility size, finding that it was inelastic with respect to the mosquito population size, with a 100% increase in population size resulting in a 50-67% increase in optimal facility size. Furthermore, we found that these results are robust to mosquito life-history parameters and are mostly determined by the mosquito population size and the fitness costs associated with Wolbachia.

CONCLUSIONS

These results reinforce that Wolbachia-transinfected mosquitoes can reduce the cost of dengue epidemics. Furthermore, they emphasize the importance of determining the size of the target population and fitness costs associated with Wolbachia before releases occur. © 2024 The Authors. Pest Management Science published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes

This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model's parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures.

Wolbachia invasion dynamics of a random mosquito population model with imperfect maternal transmission and incomplete CI

In this work, we formulate a random Wolbachia invasion model incorporating the effects of imperfect maternal transmission and incomplete cytoplasmic incompatibility (CI). Under constant environments, we obtain the following results: Firstly, the complete invasion equilibrium of Wolbachia does not exist, and thus the population replacement is not achievable in the case of imperfect maternal transmission; Secondly, imperfect maternal transmission or incomplete CI may obliterate bistability and backward bifurcation, which leads to the failure of Wolbachia invasion, no matter how many infected mosquitoes would be released; Thirdly, the threshold number of the infected mosquitoes to be released would increase with the decrease of the maternal transmission rate or the intensity of CI effect. In random environments, we investigate in detail the Wolbachia invasion dynamics of the random mosquito population model and establish the initial release threshold of infected mosquitoes for successful invasion of Wolbachia into the wild mosquito population. In particular, the existence and stability of invariant probability measures for the establishment and extinction of Wolbachia are determined.

Mathematical modelling of the interactive dynamics of wild and Microsporidia MB-infected mosquitoes

A recent discovery highlighted that mosquitoes infected with Microsporidia MB are unable to transmit the Plasmodium to humans. Microsporidia MB is a symbiont transmitted vertically and horizontally in the mosquito population, and these transmission routes are known to favor the persistence of the parasite in the mosquito population. Despite the dual transmission, data from field experiments reveal a low prevalence of MB-infected mosquitoes in nature. This study proposes a compartmental model to understand the prevalence of MB-infected mosquitoes. The dynamic of the model is obtained through the computation of the basic reproduction number and the analysis of the stability of the MB-free and coexistence equilibria. The model shows that, in spite of the high vertical transmission efficiency of Microsporidia MB, there can still be a low prevalence of MB-infected mosquitoes. Numerical analysis of the model shows that male-to-female horizontal transmission contributes more than female-to-male horizontal transmission to the spread of MB-infected mosquitoes. Moreover, the female-to-male horizontal transmission contributes to the spread of the symbiont only if there are multiple mating occurrences for male mosquitoes. Furthermore, when fixing the efficiencies of vertical transmission, the parameters having the greater influence on the ratio of MB-positive to wild mosquitoes are identified. In addition, by assuming a similar impact of the temperature on wild and MB-infected mosquitoes, our model shows the seasonal fluctuation of MB-infected mosquitoes. This study serves as a reference for further studies, on the release strategies of MB-infected mosquitoes, to avoid overestimating the MB-infection spread.

Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries

Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.

A Systematic Review of Mathematical Models of Dengue Transmission and Vector Control: 2010-2020

Vector control methods are considered effective in averting dengue transmission. However, several factors may modify their impact. Of these controls, chemical methods, in the long run, may increase mosquitoes' resistance to chemicides, thereby decreasing control efficacy. The biological methods, which may be self-sustaining and very effective, could be hampered by seasonality or heatwaves (resulting in, e.g., loss of Wolbachia infection). The environmental methods that could be more effective than the chemical methods are under-investigated. In this study, a systematic review is conducted to explore the present understanding of the effectiveness of vector control approaches via dengue transmission models.

Monotonicity properties arising in a simple model of Wolbachia invasion for wild mosquito populations

In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the Wolbachia symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called principle of competitive exclusion. Using tools borrowed from monotone dynamical system theory, in the proposed model, we prove the existence of an invariant threshold manifold that allows us to provide practical recommendations for performing single and periodic releases of Wolbachia-carrying mosquitoes, seeking the eventual elimination of wild insects that are capable of transmitting infections to humans. We illustrate these findings with numerical simulations using parameter values corresponding to the wMelPop strain of Wolbachia that is considered the best virus blocker but induces fitness loss in its carriers. In these tests, we considered multiple scenarios contrasting a periodic release strategy against a strategy with a single inundative release, comparing their effectiveness. Our study is presented as an expository and mathematically accessible tool to study the use of Wolbachia-based biocontrol versus more complex models.

Modelling the ecological dynamics of mosquito populations with multiple co-circulating Wolbachia strains

Wolbachia intracellular bacteria successfully reduce the transmissibility of arthropod-borne viruses (arboviruses) when introduced into virus-carrying vectors such as mosquitoes. Despite the progress made by introducing Wolbachia bacteria into the Aedes aegypti wild-type population to control arboviral infections, reports suggest that heat-induced loss-of-Wolbachia-infection as a result of climate change may reverse these gains. Novel, supplemental Wolbachia strains that are more resilient to increased temperatures may circumvent these concerns, and could potentially act synergistically with existing variants. In this article, we model the ecological dynamics among three distinct mosquito (sub)populations: a wild-type population free of any Wolbachia infection; an invading population infected with a particular Wolbachia strain; and a second invading population infected with a distinct Wolbachia strain from that of the first invader. We explore how the range of possible characteristics of each Wolbachia strain impacts mosquito prevalence. Further, we analyse the differential system governing the mosquito populations and the Wolbachia infection dynamics by computing the full set of basic and invasive reproduction numbers and use these to establish stability of identified equilibria. Our results show that releasing mosquitoes with two different strains of Wolbachia did not increase their prevalence, compared with a single-strain Wolbachia-infected mosquito introduction and only delayed Wolbachia dominance.

Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

Although the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$\end{document}(i.e.R0<1). This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$\end{document}(i.e.R0<1), and if greater than one \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$\end{document}(i.e.R0>1) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{R}}_{0}$$\end{document}R0. The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{R}}_{0}$$\end{document}R0 and measles prevalence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left({\mathrm{I}}^{*}\right)$$\end{document}I∗ with respect to the estimated and fitted model parameters. We found that the transmission rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\upbeta )$$\end{document}(β) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

Analysis of COVID-19 using a modified SLIR model with nonlinear incidence

Infectious diseases kill millions of people each year, and they are the major public health problem in the world. This paper presents a modified Susceptible-Latent-Infected-Removed (SLIR) compartmental model of disease transmission with nonlinear incidence. We have obtained a threshold value of basic reproduction number ( R 0 ) and shown that only a disease-free equilibrium exists whenR 0 < 1 and endemic equilibrium whenR 0 > 1 . With the help of the Lyapunov-LaSalle Invariance Principle, we have shown that disease-free equilibrium and endemic equilibrium are both globally asymptotically stable. The study has also provided the model calibration to estimate parameters with month wise coronavirus (COVID-19) data, i.e. reported cases by worldometer from March 2020 to May 2021 and provides prediction until December 2021 in China. The Partial Rank Correlation Coefficient (PRCC) method was used to investigate how the model parameters' variation impact the model outcomes. We observed that the most important parameter is transmission rate which had the most significant impact on COVID-19 cases. We also discuss the epidemiology of COVID-19 cases and several control policies and make recommendations for controlling this disease in China.

Optimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains

In this paper, we propose a dengue transmission model of SIR(S)-SI type that accounts for two sex-structured mosquito populations: the wild mosquitoes (males and females that are Wolbachia-free), and those deliberately infected with either wMel or wMelPop strain of Wolbachia. This epidemiological model has four possible outcomes: with or without Wolbachia and with or without dengue. To reach the desired outcome, with Wolbachia and without dengue, we employ the dynamic optimization approach and then design optimal programs for releasing Wolbachia-carrying male and female mosquitoes. Our discussion is focused on advantages and drawbacks of two Wolbachia strains, wMelPop and wMel, that are recommended for dengue prevention and control. On the one hand, the wMel strain guarantees a faster population replacement, ensures durable Wolbachia persistence in the wild mosquito population, and requiters fewer releases. On the other hand, the wMelPop strain displays better results for averting dengue infections in the human population.

A Review: Aedes-Borne Arboviral Infections, Controls and Wolbachia-Based Strategies

Arthropod-borne viruses (Arboviruses) continue to generate significant health and economic burdens for people living in endemic regions. Of these viruses, some of the most important (e.g., dengue, Zika, chikungunya, and yellow fever virus), are transmitted mainly by Aedes mosquitoes. Over the years, viral infection control has targeted vector population reduction and inhibition of arboviral replication and transmission. This control includes the vector control methods which are classified into chemical, environmental, and biological methods. Some of these control methods may be largely experimental (both field and laboratory investigations) or widely practised. Perceptively, one of the biological methods of vector control, in particular, Wolbachia-based control, shows a promising control strategy for eradicating Aedes-borne arboviruses. This can either be through the artificial introduction of Wolbachia, a naturally present bacterium that impedes viral growth in mosquitoes into heterologous Aedes aegypti mosquito vectors (vectors that are not natural hosts of Wolbachia) thereby limiting arboviral transmission or via Aedes albopictus mosquitoes, which naturally harbour Wolbachia infection. These strategies are potentially undermined by the tendency of mosquitoes to lose Wolbachia infection in unfavourable weather conditions (e.g., high temperature) and the inhibitory competitive dynamics among co-circulating Wolbachia strains. The main objective of this review was to critically appraise published articles on vector control strategies and specifically highlight the use of Wolbachia-based control to suppress vector population growth or disrupt viral transmission. We retrieved studies on the control strategies for arboviral transmissions via arthropod vectors and discussed the use of Wolbachia control strategies for eradicating arboviral diseases to identify literature gaps that will be instrumental in developing models to estimate the impact of these control strategies and, in essence, the use of different Wolbachia strains and features.

Biological and Chemical Control of Mosquito Population by Optimal Control Approach

This paper focuses on the design and analysis of short-term control intervention measures seeking to suppress local populations of Aedes aegypti mosquitoes, the major transmitters of dengue and other vector-borne infections. Besides traditional measures involving the spraying of larvicides and/or insecticides, we include biological control based on the deliberate introduction of predacious species feeding on the aquatic stages of mosquitoes. From the methodological standpoint, our study relies on application of the optimal control modeling framework in combination with the cost-effectiveness analysis. This approach not only enables the design of optimal strategies for external control intervention but also allows for assessment of their performance in terms of the cost-benefit relationship. By examining numerous scenarios derived from combinations of chemical and biological control measures, we try to find out whether the presence of predacious species at the mosquito breeding sites may (partially) replace the common practices of larvicide/insecticide spraying and thus reduce their negative impact on non-target organisms. As a result, we identify two strategies exhibiting the best metrics of cost-effectiveness and provide some useful insights for their possible implementation in practical settings.

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.

Releasing Wolbachia-infected Aedes aegypti to prevent the spread of dengue virus: A mathematical study

Wolbachia is a bacterium that is present in 60% of insects but it is not generally found in Aedes aegypti, the primary vector responsible for the transmission of dengue virus, Zika virus, and other human diseases caused by RNA viruses. Wolbachia has been shown to stop the growth of a variety of RNA viruses in Drosophila and in mosquitoes. Wolbachia-infected Ae. aegypti have both reproductive advantages and disadvantages over wild types. If Wolbachia-infected females are fertilized by either normal or infected males, the offspring are healthy and Wolbachia-positive. On the other hand, if Wolbachia-negative females are fertilized by Wolbachia-positive males, the offspring do not hatch. This phenomenon is called cytoplasmic incompatibility. Thus, Wolbachia-positive females have a reproductive advantage, and the Wolbachia is expanded in the population. On the other hand, Wolbachia-infected mosquitoes lay fewer eggs and generally have a shorter lifespan. In recent years, scientists have successfully released these Wolbachia-adapted mosquitoes into the wild in several countries and have achieved a high level of replacement with Wolbachia-positive mosquitoes. Here, we propose a minimal mathematical model to investigate the feasibility of such a release method. The model has five steady-states two of which are locally asymptotically stable. One of these stable steady-states has no Wolbachia-infected mosquitoes while for the other steady-state, all mosquitoes are infected with Wolbachia. We apply optimal control theory to find a release method that will drive the mosquito population close to the steady-state with only Wolbachia-infected mosquitoes in a two-year time period. Because some of the model parameters cannot be accurately measured or predicted, we also perform uncertainty and sensitivity analysis to quantify how variations in our model parameters affect our results.

Mathematical analysis of a Wolbachia invasive model with imperfect maternal transmission and loss of Wolbachia infection

Arboviral infections, especially dengue, continue to cause significant health burden in their endemic regions. One of the strategies to tackle these infections is to replace the main vector agent, Ae. aegypti, with the ones incapable of transmitting the virus. Wolbachia, an intracellular bacterium, has shown promise in achieving this goal. However, key factors such as imperfect maternal transmission, loss of Wolbachia infection, reduced reproductive capacity and shortened life-span affect the dynamics of Wolbachia in different forms in the Ae. aegypti population. In this study, we developed a Wolbachia transmission dynamic model adjusting for imperfect maternal transmission and loss of Wolbachia infection. The invasive reproductive number that determines the likelihood of replacement of the Wolbachia-uninfected (WU) population is derived and with it, we established the local and global stability of the equilibrium points. This analysis clearly shows that cytoplasmic incompatibility (CI) does not guarantee establishment of the Wolbachia-infected (WI) mosquitoes as imperfect maternal transmission and loss of Wolbachia infection could outweigh the gains from CI. Optimal release programs depending on the level of imperfect maternal transmission and loss of Wolbachia infection are shown. Hence, it is left to decision makers to either aim for replacement or co-existence of both populations.

Implementation of control strategies for sterile insect techniques

In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing sufficient conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with the releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, under which the release size is adjusted in accordance with the wild population size estimate. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects.

The Threshold Infection Level for [Formula: see text] Invasion in a Two-Sex Mosquito Population Model

In this paper, we formulate a new [Formula: see text] infection model in a two-sex mosquito population with stage structure. Some key factors of [Formula: see text] infection, including cytoplasmic incompatibility (CI), male killing (MK) effect, maternal transmission, fecundity cost due to fitness effect and different mortality rates for infected individuals, are captured. Dynamical analysis has been carried out, and the basic reproduction number [Formula: see text] for [Formula: see text] infection has been calculated. Our analysis shows that [Formula: see text] can establish in a mosquito population if [Formula: see text] is greater than unity. If [Formula: see text] is less than unity, [Formula: see text] establishment still can be achieved if backward bifurcation occurs. Under this circumstance, the initial values lying in the basin of attraction of the stable [Formula: see text]-established equilibrium are essential to guarantee [Formula: see text] establishment. In particular, the method to find the basin of attraction and evaluate the threshold initial values is given. Besides, according to a comparison of different releasing strategies, it is shown that, from the perspective of economy and disease control, keeping the number of infected female mosquitoes to a necessary minimum by relying on higher number of male mosquitoes released is a desirable strategy. Moreover, global and local sensitivity analysis and numerical simulation have been performed to explore the impact of model parameters to the success of population establishment. Our results suggest that low levels of MK effect and fitness costs as well as high levels of CI and maternal inheritance are in favor of [Formula: see text] establishment. Moreover, not considering MK effect and incomplete CI effect may result in the underestimation of the number of infected mosquitoes needed to be released.