Modelling population dynamics based on experimental trials with genetically modified (RIDL) mosquitoes

Mathematical modelling and release thresholds of transgenic sterile mosquitoes

We formulate simple differential equation models to study the impact of releases of transgenic sterile mosquitoes carrying a dominant lethal on mosquito control based on the modified sterile insects technique. The early acting bisex, late acting bisex, early acting female-killing, and late acting female-killing lethality strategies are all considered. We determine release thresholds of the transgenic sterile mosquitoes, respectively, for these models by investigating the existence of positive equilibria and their stability. We compare the model dynamics, in particular, the thresholds of the models numerically. The late acting lethality strategies are generally more effective than their corresponding early acting lethality strategies, but the comparison between the late acting bisex and early acting female-killing lethality strategies depends on different parameter settings.

The optimal strategy of incompatible insect technique (IIT) using Wolbachia and the application to malaria control

For decades, techniques to control vector population with low environmental impact have been widely explored in both field and theoretical studies. The incompatible insect technique (IIT) using Wolbachia, based on cytoplasmic incompatibility, is a technique that Wolbachia-infected male mosquitoes are incapable of producing viable offspring after mating with wild-type female mosquitoes. While the IIT method experimentally ensured its effectiveness in several field works, the failure of female mosquito population control by replacement owing to the accidental contamination of Wolbachia-infected female mosquitoes has been a concern and an obstacle in implementing the IIT method in nature. In this study, we develop a population-based IIT mathematical model using cytoplasmic incompatibility and evaluate the effectiveness of the IIT method in scenarios where contamination is present or absent. In addition, by extending the model to assess the disease infection status of the human population with malaria, we evaluate the optimal release strategy and cost for successful disease control. Our study proves that IIT could be a promising method to control mosquito-borne diseases without perfect suppression of vector mosquito population regardless of contamination.

Robust control strategy by the Sterile Insect Technique for reducing epidemiological risk in presence of vector migration

The Sterile Insect Technique (SIT) is a promising technique to control mosquitoes, vectors of diseases, like dengue, chikungunya or Zika. However, its application in the field is not easy, and its success hinges upon several constraints, one of them being that the treated area must be sufficiently isolated to limit migration or re-invasion by mosquitoes from the outside. In this manuscript we study the impact of males and (fertile) females migration on SIT. We show that a critical release rate for sterile males exists for every migration level, in the context of continuous or periodic releases. In particular, when (fertile) females migration is sufficiently low, then SIT can be conducted successfully using either open-loop control or closed-loop control (or a combination of both methods) when regular measurements of the wild population are completed. Numerical simulations to illustrate our theoretical results are presented and discussed. Finally, we derive a threshold value for the females migration rate, when viruses are circulating, under which it is possible to lower the epidemiological risk in the treated area, according to the size of the human population.

Modeling the impact of genetically modified male mosquitoes in the spatial population dynamics of Aedes aegypti

The mosquito Aedes aegypti is the primary vector of diseases such as dengue, Zika, chikungunya, and yellow fever. Improving control techniques requires a better understanding of the mosquito’s life cycle, including spatial population dynamics in endemic regions. One of the most promising techniques consists of introducing genetically modified male mosquitoes. Several models proposed to describe this technique present mathematical issues or rely on numerous parameters, making their application challenging to real-world situations. We propose a model describing the spatial population dynamics of the Aedes aegypti in the presence of genetically modified males. This model presents some mathematical improvements compared to the literature allowing deeper mathematical analysis. Moreover, this model relies on few parameters, which we show how to obtain or estimate from the literature. Through numerical simulations, we investigate the impacts of environmental heterogeneity, the periodicity of genetically modified male releases, and released genetically modified males quantity on the population dynamics of Aedes aegypti. The main results point to that the successful application of this vector control technique relies on releasing more than a critical amount of modified males with a frequency exceeding a specific critical value.

Modeling the effects of Aedes aegypti's larval environment on adult body mass at emergence

Mosquitoes vector harmful pathogens that infect millions of people every year, and developing approaches to effectively control mosquitoes is a topic of great interest. However, the success of many control measures is highly dependent upon ecological, physiological, and life history traits of mosquito species. The behavior of mosquitoes and their potential to vector pathogens can also be impacted by these traits. One trait of interest is mosquito body mass, which depends upon many factors associated with the environment in which juvenile mosquitoes develop. Our experiments examined the impact of larval density on the body mass of Aedes aegypti mosquitoes, which are important vectors of dengue, Zika, yellow fever, and other pathogens. To investigate the interactions between the larval environment and mosquito body mass, we built a discrete time mathematical model that incorporates body mass, larval density, and food availability and fit the model to our experimental data. We considered three categories of model complexity informed by data, and selected the best model within each category using Akaike’s Information Criterion. We found that the larval environment is an important determinant of the body mass of mosquitoes upon emergence. Furthermore, we found that larval density has greater impact on body mass of adults at emergence than on development time, and that inclusion of density dependence in the survival of female aquatic stages in models is important. We discuss the implications of our results for the control of Aedes mosquitoes and on their potential to spread disease.

In this work we examined how the environment in which juvenile mosquitoes develop affects their adult body size as measured by adult body mass. Adult size has potential impacts on mosquito behavior and the ability of mosquitoes to transmit disease. We used a combination of experimental work and mathematical modeling to determine important factors affecting adult mosquito body size. In our model, we incorporated potentially interacting aspects of the mosquito life cycle and traits that affect mosquito growth as juveniles. These aspects include body mass, density of the population, and level of available resource. We compared different models to determine the one that best describes the data. As mass at emergence is linked to the success of adult mosquitoes to produce offspring and to their ability transmit pathogens, we discuss how important influences on development and survival of young mosquitoes affect mosquito control and disease spread.

Stochastic model for COVID-19 in slums: interaction between biology and public policies

We present a mathematical model for the simulation of the development of an outbreak of coronavirus disease 2019 (COVID-19) in a slum area under different interventions. Instead of representing interventions as modulations of the parameters of a free-running epidemic, we introduce a model structure that accounts for the actions but does not assume the results. The disease is modelled in terms of the progression of viraemia reported in scientific studies. The emergence of symptoms in the model reflects the statistics of a nation-wide highly detailed database consisting of more than 62 000 cases (about a half of them confirmed by reverse transcription-polymerase chain reaction tests) with recorded symptoms in Argentina. The stochastic model displays several of the characteristics of COVID-19 such as a high variability in the evolution of the outbreaks, including long periods in which they run undetected, spontaneous extinction followed by a late outbreak and unimodal as well as bimodal progressions of daily counts of cases (second waves without ad-hoc hypothesis). We show how the relation between undetected cases (including the ‘asymptomatic’ cases) and detected cases changes as a function of the public policies, the efficiency of the implementation and the timing with respect to the development of the outbreak. We show also that the relation between detected cases and total cases strongly depends on the implemented policies and that detected cases cannot be regarded as a measure of the outbreak, being the dependency between total cases and detected cases in general not monotonic as a function of the efficiency in the intervention method. According to the model, it is possible to control an outbreak with interventions based on the detection of symptoms only in the case when the presence of just one symptom prompts isolation and the detection efficiency reaches about 80% of the cases. Requesting two symptoms to trigger intervention can be enough to fail in the goals.