Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

Bis-4,4′-biphenyl Ring Embedded Octaphyrin with Three Distinct Conformational Structures

Three distinct conformational structures of carbaoctaphyrins were prepared by incorporating bis-4,4'-biphenyl units in the macrocyclic core. The free-base form adopts a figure-eight conformation, whereas the protonation triggers a conformational change with a pyrrole ring inversion and acquires an open-framework structure. The insertion of bis-Rh^I metal ion in the macrocyclic core affords a singly twisted conformational structure. Furthermore, the local aromaticity in the bis-4,4'-biphenyl ring dominates the overall macrocyclic aromaticity in all three forms, and thus adopts nonaromatic characteristics. These results are supported by spectral as well as theoretical studies, and they are unambiguously confirmed by X-ray crystal analyses.     

Can a Six‐Letter Alphabet Increase the Likelihood of Photochemical Assault to the Genetic Code?

In 2014, two unnatural nucleosides, d5SICS and dNaM, were shown to selectively base pair and replicate with high fidelity in a modified strain of E. coli, thus effectively expanding its genetic alphabet from four to six letters. More recently, a significant reduction in cell proliferation was reported in cells cultured with d5SICS, and putatively with dNaM, upon exposure to brief periods of near‐visible radiation. The photosensitizing properties of the lowest‐energy excited triplet state of both d5SICS and dNaM were implicated in their cytotoxicity. Importantly, however, the excited‐state mechanisms by which near‐visible excitation populates the triplet states of d5SICS and dNaM are currently unknown. In this study, steady‐state and time‐resolved spectroscopies are combined with quantum‐chemical calculations in order to reveal the excited‐state relaxation mechanisms leading to efficient population of the triplet states in these unnatural nucleosides in solution. It is shown that excitation of d5SICS or dNaM with near‐visible light leads overwhelmingly to ultrafast population of their triplet states on the femtosecond time scale. The results presented in this work lend strong support to the proposal that photoexcitation of these unnatural nucleosides can accelerate oxidatively generated damage to DNA and other biomolecules within the cellular environment.     

带有潜伏期的狂犬病模型及控制策略研究

研究建立了狗与人两个群体的SEIR狂犬病模型,把狂犬病潜伏期阶段的传染性加入到模型中,利用遗传算法对1996年到2015年的数据进行拟合,估出了中国狂犬病的基本再生数R0≈1.66,证明了狂犬病无病平衡点的全局稳定性以及模型的一致持续性.根据数值模拟结果,发现处于潜伏期的犬类对人类狂犬病造成威胁.因此控制狂犬病的一个关键措施就是要做好犬的管理,减少与犬只的接触,这对抑制狂犬病的爆发有着重要的作用,也为我国狂犬病的控制提供了可靠的理论依据.     

Mathematical analysis of the dynamics of COVID-19 in Africa under the influence of asymptomatic cases and re-infection

Coronavirus pandemic (COVID-19) hit the world in December 2019, and only less than 5% of the 15 million cases were recorded in Africa. A major call for concern was the significant rise from 2% in May 2020 to 4.67% by the end of July 15, 2020. This drastic increase calls for quick intervention in the transmission and control strategy of COVID-19 in Africa. A mathematical model to theoretically investigate the consequence of ignoring asymptomatic cases on COVID-19 spread in Africa is proposed in this study. A qualitative analysis of the model is carried out with and without re-infection, and the reproduction number is obtained under re-infection. The results indicate that increasing case detection to detect asymptomatically infected individuals will be very effective in containing and reducing the burden of COVID-19 in Africa. In addition, the fact that it has not been confirmed whether a recovered individual can be re-infected or not, then enforcing a living condition where recovered individuals are not allowed to mix with the susceptible or exposed individuals will help in containing the spread of COVID-19.     

Mechanochemically Triggered Topology Changes in Expanded Porphyrins

A hitherto unexplored class of molecules for molecular force probe applications are expanded porphyrins. This work proves that mechanical force is an effective stimulus to trigger the interconversion between Hückel and Möbius topologies in [28]hexaphyrin, making these expanded porphyrins suitable to act as conformational mechanophores operating at mild (sub-1 nN ) force conditions. A straightforward approach based on distance matrices is proposed for the selection of pulling scenarios that promote either the planar Hückel topology or the three lowest lying Möbius topologies. This approach is supported by quantum mechanochemical calculations. Force distribution analyses reveal that [28]hexaphyrin selectively allocates the external mechanical energy to molecular regions that trigger Hückel–Möbius interconversions, explaining why certain pulling scenarios favor the Hückel two-sided topology and others favor Möbius single-sided topologies. The meso-substitution pattern on [28]hexaphyrin determines whether the energy difference between the different topologies can be overcome by mechanical activation.