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Mechanisms and scenarios of pattern formation in predator-prey systems have been a focus of many studies recently as they are thought to mimic the processes of ecological patterning in real-world ecosystems. Considerable work has been done with regards to both Turing and non-Turing patterns where the latter often appears to be chaotic. In particular, spatiotemporal chaos remains a controversial issue as it can have important implications for population dynamics. Most of the results, however, were obtained in terms of 'traditional' predator-prey models where the per capita predation rate depends on the prey density only. A relatively new family of ratio-dependent predator-prey models remains less studied and still poorly understood, especially when space is taken into account explicitly, in spite of their apparent ecological relevance. In this paper, we consider spatiotemporal pattern formation in a ratio-dependent predator-prey system. We show that the system can develop patterns both inside and outside of the Turing parameter domain. Contrary to widespread opinion, we show that the interaction between two different type of instability, such as the TuringHopf bifurcation, does not necessarily lead to the onset of chaos; on the contrary, the emerging patterns remain stationary and almost regular. Spatiotemporal chaos can only be observed for parameters well inside the Turing-Hopf domain. We then investigate the relative importance of these two instability types on the onset of chaos and show that, in a ratio-dependent predatorprey system, the Hopf bifurcation is indeed essential for the onset of chaos whilst the Turing instability is not.

Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in such a way that they cannot infect other people. Disease progression in this model is determined by the basic reproduction number R 0 (the number of newly infected individuals during the incubation period), which is different compared to that for the standard SIR model. If R 0 > 1, then the number of latently infected individuals exponentially grows. However, if R 0 < 1 (e.g. due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the available data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growthdecays dynamics, and patchy dynamics (growth-decay-growth). Analysis of the data in China and Korea shows that the peak of infection (maximum of daily cases) is reached about 10 days after the restricting measures are introduced. During this period of time, the growth rate of the total number of infected was gradually decreasing. However, the growth rate remains exponential in Italy. Arguably, it suggests that the introduced quarantine is not sufficient and stricter measures are needed.

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Resistance to early blight in the tomato was assessed by examining various parameters of the progress of the disease. Artificial inoculation and the scoring technique were standardized. Test plants were inoculated with 125 cfu/ ml of a 12-day-old culture of a pathogenic isolate of Alternaria solani. Screening under artificial conditions was more informative than that under natural epidemic conditions. Tomato cultivars CLN-2071-C, CLN-2070-A, BSS-174, and DTH-7 with resistance expressed as slow blighting against four pathogenic isolates of A. solani, were selected for cultivation in disease-prone areas. Disease intensity increased with the age of plants under the same inoculum load. The area under the disease progress curve (AUDPC) was positively correlated with the percentage disease index and negatively with resistance. Calculation of the apparent infection rate (r) was more informative for natural epidemics than for artificial conditions. The sequential apparent infection rate between observation periods was better correlated with disease progress than was the total apparent infection rate between the first and last observations. A double sigmoidal disease progress curve during the same cropping season was characteristic of some varieties when fungal infection took place during the vegetative phase of crop growth.

The biological and molecular properties of Tomato leaf curl Gujarat virus from Varanasi, India (ToLCGV-[Var]) were characterized. ToLCGV-[Var] could be transmitted by grafting and through whitefly transmission in a persistent manner. The full-length genome of DNA-A and DNA-B of ToLCGV-[Var] was cloned in pUC18. Sequence analysis revealed that DNA-A (AY190290) is 2,757 bp and DNA-B (AY190291) is 2,688 bp in length. ToLCGV-[Var] could infect and cause symptoms in tomato, pepper, Nicotiana benthamiana, and N. tabacum when partial tandem dimeric constructs of DNA-A and DNA-B were co-inoculated by particle bombardment. DNA-A alone also is infectious, but symptoms were milder and took longer to develop. ToLCGV-Var virus can be transmitted through sap inoculation from infected tomato plants to the above-mentioned hosts causing the same symptoms. Open reading frames (ORFs) in both DNA-A and DNA-B are organized similarly to those in other begomoviruses. DNA-A and DNA-B share a common region of 155 bp with only 60% sequence identity. DNA-B of ToLCGV-[Var] shares overall 80% identity with DNA-B of Tomato leaf curl New Delhi virus-Severe (ToLCNDV-Svr) and 75% with ToLCNDV-[Lucknow] (ToLCNDV-[Luc]). Comparison of DNA-A sequence with different begomoviruses indicates that ToLCGV-[Var] shares 84% identity with Tomato leaf curl Karnataka virus (ToLCKV) and 66% with ToLCNDV-Svr. ToLCGV-[Var] shares a maximum of 98% identity with another isolate of the same region (ToLCGV-[Mir]; AF449999) and 97% identity with one isolate from Gujarat (ToLCGV-[Vad]; AF413671). All three viruses belong to the same species that is distinct from all the other geminivirus species described so far in the genus Begomovirus of the family Geminiviridae. The name Tomato leaf curl Gujarat virus is proposed because the first sequence was taken from an isolate of Gujarat, India.