Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number $R_0$ is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced.
Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit dengue virus. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to establish an endemic infection in a wild mosquito population. We developed and analyzed an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachia-infected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Our transmission model for the adult and aquatic-stage mosquitoes ta…
We develop and analyze an ordinary differential equation model to assess the potential effectiveness of infecting mosquitoes with the Wolbachia bacteria to control the ongoing mosquito-borne epidemics, such as dengue fever, chikungunya, and Zika. Wolbachia is a natural parasitic microbe that stops the proliferation of the harmful viruses inside the mosquito and reduces disease transmission. It is difficult to sustain an infection of the maternal transmitted Wolbachia in a wild mosquito population because of the reduced fitness of the Wolbachia-infected mosquitoes and cytoplasmic incompatibilit…
Wolbachia infection in Anopheles albimanus mosquitoes can render mosquitoes less capable of spreading malaria. We develop and analyze an ordinary differential equation model to evaluate the effectiveness of Wolbachia-based vector control strategies among wild Anopheles mosquitoes in Haiti. The model tracks the mosquito life stages, including egg, larva, and adult (male and female). It also accounts for critical biological effects, such as the maternal transmission of Wolbachia through infected females and cytoplasmic incompatibility, which effectively sterilizes uninfected females when they ma…
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. Since Wolbachia-based bioco…
The introduction of Wolbachia-carrying mosquitoes into the population has recently been proposed as an alternative strategy against dengue. Although laboratory experiments have shown that the Wolbachia bacterium can reduce the levels of dengue virus in mosquitoes, it is also important to assess the performance of Wolbachia in reducing the incidence of dengue in human populations.In this thesis, deterministic mathematical models of human and mosquito populations in which either one or two dengue serotypes circulate are developed. We adapt these models to enable the investigation of dengue disea…
In this paper, a novel West Nile Virus model looking upon the infected birds as monitoring threshold, for the mosquitoes and birds with impulsive state feedback control is considered. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive state feedback control via comprehensively qualitative analysis. By using the Poincaré map, we obtain that the system with impulsive state feedback control has a positive periodic solution of order-1 or order-2 which is asymptotical stability due to the analogue of Poincaré criterion, theory of differential inequa…
We present a model for the growth of West Nile virus in mosquito and bird populations based on observations of the initial epidemic in the U.S. Increase of bird mortality as a result of infection, which is a feature of the epidemic, is found to yield an effect which is observable in principle, viz., periodic variations in the extent of infection. The vast difference between mosquito and bird lifespans, another peculiarity of the system, is shown to lead to interesting consequences regarding delay in the onset of the steady-state infection. An outline of a framework is provided to treat mosquit…
This is the first paper in the sequel studying the Wolbachia-infection in bisexual populations. This paper considers the behavior of the population as a discrete dynamical system. The recurrence relation is obtained as a function of the initial infected male/female frequencies and the cytoplasmic incompatibility of the population. The experimental data from Wolbachia-infected terrestrial isopod populations and the model proposed in Wolbachia-infected mosquitoes from literature is compared with the discrete dynamical system achieved.
Modelling the control of West Nile virus using mosquito reduction methods, vaccination of equids, and human behavioral adaptation to the usage of personal protective equipment
In 2018, West Nile Virus (WNV) was detected for the first time in Germany. Since the first detection, 36 human cases and 175 cases in horses and birds are detected. The transmission cycle of West Nile Virus includes birds and mosquitoes and -- as dead-end hosts -- people and horses. Spatial dissemination of the disease is caused by the movements of birds and mosquitoes. While the activity and movement of mosquitoes are depending mainly on temperature, in the birds there is a complex movement pattern caused by local birds and long range dispersal birds. To this end, we have developed a metapopu…
West Nile virus outbreak in Italy modelled with the quantum Game of Life
Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）；INFN Napoli（意大利国家核物理研究所那不勒斯分部）；Università degli Studi di Palermo（巴勒莫大学）；Lobachevsky University of Nizhny Novgorod（下诺夫哥罗德罗巴切夫斯基大学）
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 …
Forecasting West Nile Virus with Graph Neural Networks: Harnessing Spatial Dependence in Irregularly Sampled Geospatial Data
Department of Statistics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校统计系）；Department of Statistics, Texas A&M University（德克萨斯A&M大学统计系）；Department of Pathobiology, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校病理生物学系）
According to the World Health Organization the global incidence rate of dengue infections have risen drastically in recent years. It is estimated that globally the number of new infections is in the range of $100$ to $400$ million per annum. At the same time a number of recent studies reported the existence of Wolbachia strains, which inhibit dengue virus replication in mosquito species that are primary vectors for dengue transmission. In this study we focus on the impact of Wolbachia on dengue transmission dynamics in an age-structured human population. We introduce a mathematical model, whic…
West Nile virus (WNV) is a vector-borne pathogen of global relevance and is currently the most widely distributed flavivirus of encephalitis worldwide. This virus infects birds, humans, horses, and other mammals, and its transmission cycle occurs in urban and rural areas. Climate conditions have direct and indirect impacts on vector abundance and virus dynamics within the mosquito. The significance of environmental variables as drivers in WNV epidemiology is increasing under the current climate change scenario. In this study, we used a machine learning algorithm to model WNV distributions in S…
We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we es…
