In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving a priori estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences.

The global outbreak of coronavirus disease 2019 (COVID-19) is greatly threatening the public health in the world. We reconstructed global transmissions and potential demographic expansions of severe acute respiratory syndrome coronavirus 2 based on genomic information. We found that intercontinental transmissions were rare in January and early February but drastically increased since late February. After world-wide implements of travel restrictions, the transmission frequencies decreased to a low level in April. We identified a total of 88 potential demographic expansions over the world based on the star-radiative networks and 75 of them were found in Europe and North America. The expansion numbers peaked in March and quickly dropped since April. These findings are highly concordant with epidemic reports and modelling results and highlight the significance of quarantine validity on the global spread of COVID-19. Our analyses indicate that the travel restrictions and social distancing measures are effective in containing the spread of COVID-19.

Sugarcane brown rust, caused by Puccinia melanocephala, is one of the main diseases of sugarcane in China. The identification and discovery of new resistance genes have important theoretical and practical significance for preventing outbreaks of brown rust and ensuring the sustainable production of sugarcane. To screen for polymorphic simple-sequence repeat (SSR) molecular markers for localization of brown rust resistance genes, we used two populations that are suitable for genetic linkage map construction and mapping of new resistance genes to construct resistant and susceptible genetic pools. We then screened 449 pairs of primers to identify polymorphic SSR markers in the parental lines and the resistant/susceptible genetic pools. The results showed that 25 pairs of primers directed amplification of polymorphic DNA fragments between the parents of the cross combination ‘Yuetang 03-393’ × ‘ROC 24’, and 16 pairs of primers amplified polymorphic fragments between the parents of the cross combination ‘Liucheng 03-1137’ × ‘Dezhe 93-88’. Four pairs of primers (SMC236CG, SCESSR0928, SCESSR0636 and SCESSR2551) amplified polymorphic DNA fragments between the parental lines and the resistant/susceptible genetic pools in ‘Yuetang 03-393’ × ‘ROC 24’. The results of this study will establish a solid foundation for the mapping of new brown rust resistance genes, genetic linkage map construction and the development of closely-associated molecular markers in sugarcane.

We assessed inheritance of resistance to sugarcane brown rust (Puccinia melanocephala) in selfing F1 populations of wild sugarcane germplasm Erianthus rockii ‘Yundian 95-19’ and E. rockii ‘Yundian 95-20’. We tested parent and selfing F1 individuals for the brown rust resistance gene, Bru1, that has been shown to confer resistance to brown rust in sugarcane. The Bru1 gene was not detected in E. rockii ‘Yundian 95-19’, E. rockii ‘Yundian 95-20’ or their selfing F1 individuals, and we found there was segregation of resistance in the two selfing F1 populations (segregation ratio: 3:1). The results confirmed resistance in E. rockii ‘Yundian 95-19’ and E. rockii ‘Yundian 95-20’ to sugarcane brown rust is controlled by a novel, single dominant gene.

The Linkuo terrace, situated to the west of the Taipei Basin in NW Taiwan, has thick red soils that have been little studied. This paper aims to interpret the development of these soils through chemical and micromorphological investigations, and relate the soils to their palaeo-environments. The soil samples were air dried, crushed and passed through a 2 mm sieve, and then subjected to conventional soil chemical and physical analyses, together with clay mineralogical and morphological characterization. Pedons I and II were clay with low base saturation (BS), cation-exchange capacity (CEC), and exchangeable cations. The pH of pedons I and II ranged from 3.80 to 5.26. The low magnetic susceptibility of these soils indicates that no magnetite (Fe3O4) or maghemite (γ-Fe2O3) are present. X-ray diffraction patterns of the magnetic clay fraction showed lepidocrocite, goethite and hematite, the amounts of which may relate to water fluctuation in the soil environments. Illite, kaolinite and quartz are major clay minerals in the red soil clay fractions. The micromorphology of all horizons showed a great accumulation of Fe-oxides. The upper horizon showed darkened isotropic Fe-oxide materials, and lower horizon showed a black to reddish dense plasma with soil matrix. The groundmass of the oxic horizon is generally characterized by a homogeneous distribution of the different coarse and fine constituents. The thick (4 m depth) and homogeneous red soils of the Linkuo terrace were developed from fine sediments after the gradual subsidence of the Taipei Basin. Alarge amount of gravel was flushed from the Xindian River before the Taipei Basin subsided. The Linkuo red soils can be classified as mesic, Typic Kandiudox. From the chemical compositions of clay fractions and the red soil features, these red soils can be considered as lateritic red earths or red earths that do not reach the criteria for laterite.

In this paper, we study the regularity of a weak solution for a coupled system derived from a microwave-heating model. The main feature of this model is that electric conductivity in the electromagnetic field is assumed to be temperature dependent. It is shown that the weak solution of the coupled system possesses some regularity under certain conditions. In particular, it is shown that the temperature is Hölder continuous, even if electric conductivity has a jump discontinuity with respect to the temperature change. The main idea in the proof is based on an estimate for a linear degenerate system in Campanato space. As an application, the regularity result for the coupled system is used to derive the necessary condition for an optimal control problem arising in microwave heating processes.

In some chemical reaction–diffusion processes, the reaction takes place only at some local sites, due to the presence of a catalyst. In this paper we study the well-posedness of a model problem of this type. Sufficient conditions are found to ensure global existence and finite time blowup. The blowup rate and the blowup set are also investigated in the case of special nonlinearity.

This paper deals with Maxwell's equations in a quasi-stationary electromagnetic field subject to the effects of temperature. This model is encountered in the penetration of a magnetic field in substances where the electrical conductivity depends on the temperature. Similar phenomena also occur in some industrial problems such as the thermistor. Taking the effect of Joule heating into the consideration, we obtain a strongly coupled nonlinear system. Global solvability is established for this system.

In order to investigate the molecular mechanism of rehydration after serious drought in broomcorn millet (Panicum miliaceum L.), a forward subtracted cDNA library was constructed between normal watered leaves and rehydrated leaves after serious drought conditions, using the suppressive subtraction hybridization (SSH) technique. A total of 60 positive clones were picked out at random from the subtracted library and sequenced, and redundancy sequences were removed after sequence alignment. Based on the results of sequence homologous comparison and function querying, 32 expressed sequence tags (EST) were highly homologous with known ESTs. Most of those sequences were related to either abiotic or biotic stress in plants. Of those sequences, 11 ESTs were homologous with ESTs in rat (Rattus norvegicus) liver after partial hepatectomy. The Blast result of proteins revealed that 28 ESTs were similar to known proteins. The functions of these proteins mainly involve signal transduction, transcription and protein processing. This experiment demonstrated that a range of specific genes was induced and expressed in broomcorn millet during the rehydration stage after serious drought.

This paper deals with the Stefan-type problem with a zone of coexistence of both phases. We formulate the problem in the enthalpy form and show that the interfaces between the liquid and the mushy, the mushy and the solid phase are smooth. Our approach is to study the structures of the level sets of the solution via Sard's Lemma and the implicit function theorem.