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In this research paper, we consider a Leslie–Gower Reaction–Diffusion (RD) model with a predator-driven Allee term in the prey population. We derive conditions for the existence of nontrivial solutions, uniform boundedness, local stability at co-existing equilibrium points, and Hopf bifurcation criteria from the temporal system. We identify sufficient conditions for Turing instability with no-flux boundary condition for the spatial system. Our investigation delves into the analysis of diffusion-induced Turing instability, incorporating stability conditions for the constant steady-state in the spatial model. We also investigate the conditions for the existence and nonexistence of nonconstant steady states in the diffusion-induced model. During numerical simulations, we observe that the predator-driven Allee term is essential for the model to generate Turing structures. Our findings reveal intriguing properties within the RD system, demonstrating its ability to produce patterns within the Turing domain. The simulation confirms that cold–hot spots and stripes-like patterns (a mixture of spots and strips) arises for different strengths of the predation parameter and Allee parameter. In contrast, we observe that for the above threshold value of the Allee parameter, the above-mentioned patterns may disappear from the system. Interestingly, we also observe that the stationary system produces patterns for both large and small amplitudes of perturbation in the vicinity of the Turing boundary. Our research may contribute valuable insights into the Allee effect and enhance our understanding of predator–prey interactions in naturalistic environments. [ABSTRACT FROM AUTHOR]

Background: Gall Bladder carcinoma (GBC) being an aggressive disease with a very poor 5year survival rate needs an early diagnosis. Though in recent times surgical resection with neoadjuvant therapy the survival rate has improved but still it is very difficult to treat patients presenting with large tumour. we conducted this study as very limited data is available regarding the molecular changes of gall bladder carcinoma which are very much essential to find out an early therapeutic approach. We tried to reveal the degree of ERBB2/Her2-Neu amplification in GBC and looked for as if any correlation existed between adenocarcinoma of gall bladder and ERBB2/Her2-neu receptor amplification. Methods: A hospital based observational, analytical study conducted in a tertiary hospital in Kolkata. A non-probability purposive sampling was done and included 31 patients conforming to our guideline from Jan. 2018 to May 2019. Patients were admitted followed by a thorough history taking, clinical examination and radiological imaging. After taking 5ml of blood as sample they were posted for elective operation. Intra-operatively four containers of gall bladder tissue (two of tumour tissue and two of normal tissue) were collected for tumour analysis. Thirty-one such tissue of Adenocarcinoma Gall Bladder collected for studying the ERBB2/Her2Neu amplification. Tissue genetic analysis was done by ERBB2 amplification study, DNA isolation and quantification, ERBB2/Her2-neu amplification. Result: Mean age of patients was 59.84±10.26 yrs. 87% were in 40-70 yrs. age group with 74% being female. 97% had gall bladder stone.. In staging and resection of the disease we found the origin of lesion from the body of gall bladder (47%) >Neck (34%)> fundus (19%) with patients being detected at fairly advanced stage i.e. 52% in stage III and 42% in stage II. The Grade of differentiation was 42% poorly, 35% moderately and 23% well differentiated cancer. Fifty two percent (n=16) of the samples showed above 2-fold amplification in the tumor tissue when compared with corresponding normal tissue. The p-values for Ct values distribution of RNASEP and ERBB2 for both tumor and normal group were <0.05. 2-tailed Peerson correlation for the binary variables revealed no significant correlation between HER2/ERBB2 amplification with any other variables. Negative correlation (p= 0.001, r= - 0.558) between diabetes and gall stone disease existed in our patient group while positive correlation (p=0.002; r = 0.559) was observed between lymph node status and tumor histopathological grade. No significant difference was seen for survival analysis between HER-2/ERBB2 amplified and not amplified group. (p=0.48). Conclusion: Despite efforts gall bladder carcinoma remains a major challenge. Till now surgical excision remains the definitive treatment. Our study revealed a significant association between ERBB2/Her2-neu amplification and gall bladder carcinoma. So this gene can be targeted using monoclonal antibody which can help in early management of GBC. [ABSTRACT FROM AUTHOR]