Recently, Lenski et al [1,2,3] have carried out several experiments on bacterial evolution. Their findings support the theory of punctuated equilibrium in biological evolution. They have further quantified the relative contributions of adaptation, chance and history to bacterial evolution. In this paper, we show that a modified M -trait Bak-Sneppen model can explain many of the experimental results in a qualitative manner.

We study the effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems. For this purpose, the GiererMeinhardt model of pattern formation is considered. The cases we study are: (i)randomness in the underlying lattice structure, (ii)the case in which there is a probablity p that at a lattice site both reaction and diffusion occur, otherwise there is only diffusion and lastly, the effect of (iii)anisotropic and(iv)random diffusion coefficients on the formation of Turing patterns. The general conclusion is that the Turing mechanism of pattern formation is fairly robust in the presence of randomness and anisotropy.

COVID-19 pandemic has been raging all around the world for almost a year now, as of November 1, 2020. In this paper, we try to analyze the variation of the COVID-19 pandemic in different countries in the light of some modifications to the susceptible-infected-recovered (SIR) model. The SIR model was modified by taking time-dependent rate parameters. From this modified SIR model, the basic reproduction number, effective reproduction number, herd immunity, and herd immunity threshold are redefined. The re-outbreak of the COVID-19 is a real threat to various countries. We have used the above-mentioned quantities to find the reasons behind the re-outbreak of this disease. Also, the effectiveness of herd immunity to prevent an epidemic has been analyzed with respect to this model. We have also tried to show that there are certain universal aspects in the spread and containment of the disease in various countries for a short period of time. Finally, we have also analyzed the current pandemic situation in India and have attempted to discuss the possibilities in order to predict its future behavior using our model.

Currently, the world has been facing the brunt of a pandemic due to a disease called COVID-19 for the last 2 years. To study the spread of such infectious diseases it is important to not only understand their temporal evolution but also the spatial evolution. In this work, the spread of this disease has been studied with a cellular automata (CA) model to find the temporal and the spatial behavior of it. Here, we have proposed a neighborhood criteria which will help us to measure the social confinement at the time of the disease spread. The two main parameters of our model are (i) disease transmission probability ( q ) which helps us to measure the infectivity of a disease and (ii) exponent ( n ) which helps us to measure the degree of the social confinement. Here, we have studied various spatial growths of the disease by simulating this CA model. Finally we have tried to fit our model with the COVID-19 data of India for various waves and have attempted to match our model predictions with regards to each wave to see how the different parameters vary with respect to infectivity and restrictions in social interaction.

COVID-19 pandemic is one of the major disasters that humanity has ever faced. In this paper, we try to model the effect of vaccination in controlling the pandemic, particularly in context to the third wave which is predicted to hit globally. Here, we have modified the susceptible–exposed–infected–recovered–dead model by introducing a vaccination term. One of our main assumptions is that the infection rate ([Formula: see text]) is oscillatory. This oscillatory nature has been discussed earlier in literature with reference to the seasonality of epidemics. However, in our case, we invoke this nature of the infection rate ([Formula: see text]) to model the cyclical behavior of the COVID-19 pandemic within a short period. This study focuses on a minimalistic approach where we have logically deduced that the infection rate ([Formula: see text]) and the vaccination rate ([Formula: see text]) are the most important parameters while the other parameters can be assumed to be constants throughout the simulation. Finally, we have studied the rich interplay between the infection rate ([Formula: see text]) and the vaccination rate ([Formula: see text]) on the infectious cases of COVID-19 and made some robust conclusions regarding the global behavior of this pandemic in near future.