India is one of the severely affected countries by the Covid-19 pandemic at present. Within the stochastic framework of the SEQIR model, we studied publicly available data of the Covid-19 patients in India and analysed possible impacts of quarantine and social distancing as controlling strategies for the pandemic. Our stochastic simulation results clearly show that proper quarantine and social distancing should be maintained right from the start of the pandemic and continued until its end for effective control. This calls for a more disciplined social lifestyle in the future. However, only social distancing and quarantine of the exposed population are found not sufficient enough to end the pandemic in India. Therefore, implementation of other stringent policies like complete lockdown as well as increased testing of susceptible populations is necessary. The demographic stochasticity, which is quite visible in the system dynamics, has a critical role in regulating and controlling the pandemic.

In this paper, we revisit the Nested Stochastic Simulation Algorithm (NSSA) for stochastic chemical reacting networks by first proving its strong convergence. We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes, for which strong error estimates can also be obtained. Numerical experiments are presented to demonstrate the validity of our analysis.

We use the recently proposed Nested Stochastic Simulation Algorithm (Nested SSA) to simulate the cell cycle model for budding yeast. The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.

We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations. To benchmark performance, we compare simulation results with steady-state and time-dependent analytical solutions for several scenarios, including steady-state and time-dependent gene expression, and the effects on population heterogeneity of cell growth, division, and DNA replication. This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression. We also use the algorithm to model gene expression dynamics within “bet-hedging” cell populations during their adaption to environmental stress. These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics, relevant physiological details and phenotypic variability.