Experimental and mathematical insights on the interactions between poliovirus and a defective interfering genome

During replication, RNA viruses accumulate genome alterations, such as mutations and deletions. The interactions between individual variants can determine the fitness of the virus population and, thus, the outcome of infection. To investigate the effects of defective interfering genomes (DI) on wild-type (WT) poliovirus replication, we developed an ordinary differential equation model, which enables exploring the parameter space of the WT and DI competition. We also experimentally examined virus and DI replication kinetics during co-infection, and used these data to infer model parameters. Our model identifies, and our experimental measurements confirm, that the efficiencies of DI genome replication and encapsidation are two most critical parameters determining the outcome of WT replication. However, an equilibrium can be established which enables WT to replicate, albeit to reduced levels.

C. elegans colony formation as a condensation phenomenon

Phase separation at the molecular scale affects many biological processes. The theoretical requirements for phase separation are fairly minimal, and there is growing evidence that analogous phenomena occur at other scales in biology. Here we examine colony formation in the nematode C. elegans as a possible example of phase separation by a population of organisms. The population density of worms determines whether a colony will form in a thresholded fashion, and a simple two-compartment ordinary differential equation model correctly predicts the threshold. Furthermore, small, round colonies sometimes fuse to form larger, round colonies, and a phenomenon akin to Ostwald ripening – a coarsening process seen in many systems that undergo phase separation – also occurs. These findings support the emerging view that the principles of microscopic phase separation can also apply to collective behaviors of living organisms.

Experimental and mathematical insights on the interactions between poliovirus and a defective interfering genome

1AbstractDuring replication, RNA viruses accumulate genome alterations, such as mutations and deletions. The interactions between individual variants can determine the fitness of the virus population and, thus, the outcome of infection. To investigate the effects of defective interfering genomes (DI) on wild-type (WT) poliovirus replication, we developed an ordinary differential equation model. We experimentally determined virus and DI replication during co-infection, and use these data to infer model parameters. Our model predicts, and our experimental measurements confirm, that DI replication and encapsidation are the most important determinants for the outcome of the competition. WT replication inversely correlates with DI replication. Our model predicts that genome replication and effective DI genome encapsidation are critical to effectively inhibit WT production, but an equilibrium can be established which enables WT to replicate, albeit to reduce levels.

Transient dynamics of the renal disease epidemic among HIV-infected individuals

The prevalence of end stage renal disease (ESRD) is rising among HIV-infected populations in several regions worldwide. We used an ordinary differential equation model of the dynamics of the AIDS and HIV+ ESRD populations to investigate the effect of antiretroviral therapy (ART) on the transient dynamics of the epidemic. We considered ART that blocks the entry to each population, by preventing individuals from joining the AIDS population and by reducing the development from AIDS to HIV+ ESRD, as well as the combined effects together. Numerical simulation of our model revealed that when levels of ART are below 100%, the prevalence of HIV+ ESRD drops, but then increases again due to the recovery in the AIDS population. The effect can be seen with ART acting to block entry into either population. We then examined the dip in HIV+ ESRD seen with ART analytically by calculating the minimum HIV+ ESRD level and the time to achieve this minimum. We also evaluated the length of time to reach the minimum and its dependence on ART parameters, both singly and in combination. We conclude that our model predicts that the drop in HIV+ ESRD prevalence seen after increased ART will be followed by an increase, unless ART is sufficiently high enough to eradicate HIV/AIDS.

Optimal Strategies for Control of COVID-19: A Mathematical Perspective

A deterministic ordinary differential equation model for SARS-CoV-2 is developed and analysed, taking into account the role of exposed, mildly symptomatic, and severely symptomatic persons in the spread of the disease. It is shown that in the absence of infective immigrants, the model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number is below unity. In the absence of immigration of infective persons, the disease can be eradicated whenever ℛ 0 < 1 . Specifically, if the controls u i , i = 1,2,3,4 , are implemented to 100% efficiency, the disease dies away easily. It is shown that border closure (or at least screening) is indispensable in the fight against the spread of SARS-CoV-2. Simulation of optimal control of the model suggests that the most cost-effective strategy to combat SARS-CoV-2 is to reduce contact through use of nose masks and physical distancing.

Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.