Moxun Tang

Modeling Wolbachia Spread in Mosquitoes Through Delay Differential Equations

Dengue fever is the most common mosquito-borne viral disease. A promising control strategy targets the mosquito vector Aedes aegypti by releasing the mosquitoes infected by the endosymbiotic bacterium Wolbachia to invade and replace the wild population. With infection, Wolbachia reduces the mosquitos dengue transmission potential and brings infected females a reproductive advantage through cytoplasmic incompatibility. As Wolbachia often induces fitness costs, it is important to analyze how the reproductive advantage offsets the fitness costs for the success of population replacement. In this work, we develop a model of delay differential equations to study Wolbachia infection dynamics. We prove that, when the infection does not alter the mean life span, Wolbachia can spread into the whole population as long as the infection frequency stays strictly above a threshold value for a period no less than the prereproductive time

Wolbachia spread dynamics in stochastic environments

\tau

Modulation of gene transcription noise by competing transcription factors

. For the other cases, we find that such a threshold value cannot be well def...

The mean and noise of protein numbers in stochastic gene expression

Dengue fever is a mosquito-borne viral disease with 100 million people infected annually. A novel strategy for dengue control uses the bacterium Wolbachia to invade dengue vector Aedes mosquitoes. As the impact of environmental heterogeneity on Wolbachia spread dynamics in natural areas has been rarely quantified, we develop a model of differential equations for which the environmental conditions switch randomly between two regimes. We find some striking phenomena that random regime transitions could drive Wolbachia to extinction from certain initial states confirmed Wolbachia fixation in homogeneous environments, and mosquito releasing facilitates Wolbachia invasion more effectively when the regimes transit frequently. By superimposing the phase spaces of the ODE systems defined in each regime, we identify the threshold curves below which Wolbachia invades the whole population, which extends the theory of threshold infection frequency to stochastic environments.

Temporal profile of gene transcription noise modulated by cross-talking signal transduction pathways.

Sequence specific transcription factors (TFs) are critical to ensuring that genes are transcribed in the right cell at the right time. Often, the gene promoter is flanked by multiple binding sites, some of which can be bound by different types of TFs in the cell. To investigate how the transcription noise is modulated by the competition of these TFs at their shared binding sites, we model gene transcription as a renewal process where the time spent in each transcription cycle is assumed to be independently and identically distributed. With the help of the elementary renewal theorem and the central limit theorem, we prove that the stationary noise strength

Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission

{\Phi}

Distribution Modes and Their Corresponding Parameter Regions in Stochastic Gene Transcription

of transcription frequency equals the noise η2 of the time spent in a single transcription cycle. Subsequent analysis shows that competitive TF binding could produce an unbounded spectrum of