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The authors approach the problem of solving differential equations using neural networks (NN) including cellular NN. A brief overview of differential equations including considerations regarding numerical methods is given in the first chapter. In the following chapter, a brief history of NN is presented. The next chapters are dedicated to specific aspects regarding the subject of the book. Thus, chapter 3 gives preliminaries on NN starting from definitions and continuing with biological and artificial NN, mathematical models, types of activation function, architectures, various kinds of learning in NN, the multilayer perceptron and, last but not least, NN as universal approximators. The last and largest chapter deals with NN methods for solving differential equations, i.e., the method of multilayer perceptron, the method of radial basis function NN, the method of multiquadric radial basis functions, the method of cellular NN, the method of finite elements NN and wavelet NN. The last part of the chapter contains several workout examples. The book ends with conclusions, an appendix with Matlab codes, a list of 112 references papers and an index. The book is intended to enable the reader to get an image on the variety of NN and the NN methods can be used in solving differential equations. It is a valuable reference material both from the presentation point of view and the provided references.Reviewer: Liviu Goraş (Iaşi)

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Infection born by Coronavirus SARS-CoV-2 has swept the world within a time of a few months. It has created a devastating effect on humanity with social and economic depressions. Europe and America were the hardest hit continents. India has also lost several lives, making the country fourth most deadly worldwide. However, the infection and death rate per million and the case fatality ratio in India were substantially lower than many of the developed nations. Several factors have been proposed including the genetics. One of the important facts is that a large chunk of Indian population is asymptomatic to the SARS-CoV-2 infection. Thus, the real infection in India is much higher than the reported number of cases. Therefore, the majority of people are already immune in the country. To understand the dynamics of real infection as well as level of immunity against SARS-CoV-2, we have performed antibody testing (serosurveillance) in the urban region of fourteen Indian districts encompassing six states. In our survey, the seroprevalence frequency varied between 0.01-0.48, suggesting high variability of viral transmission among states. We also found out that the cases reported by the Government were several fold lower than the real infection. This discrepancy is majorly driven by a higher number of asymptomatic cases. Overall, we suggest that with the high level of immunity developed against SARS-CoV-2 in the majority of the districts, it is less likely to have a second wave in India.