Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-III and Holling Type-IV Functional Responses

In recent years, time-optimal control studies on additional food provided prey-predator systems have gained significant attention from researchers in the field of mathematical biology. In this study, we initially consider an additional food provided prey-predator model exhibiting Holling type-III functional response and the intra-specific competition among predators. We prove the existence and uniqueness of global positive solutions for the proposed model. We do the time optimal control studies with respect quality and quantity of additional food as control variables by transforming the independent variable in the control system. Making use of the Pontraygin maximum principle, we characterize the optimal quality of additional food and optimal quantity of additional food. We show that the findings of these time-optimal control studies on additional food provided prey-predator systems involving Holling type III functional response have the potential to be applied to a variety of problems in pest management. In the later half of this study, we consider an additional food provided prey-predator model exhibiting Holling type-IV functional response and study the above aspects for this system

Stochastic Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-IV Functional Response

We consider an additional food provided prey-predator model exhibiting Holling type IV functional response with combined continuous white noise and discontinuous L\'evy noise. We prove the existence and uniqueness of global positive solutions for the considered model. By considering the quality and quantity of additional food as control parameters, we formulate a time-optimal control problem. We obtain the condition for the existence of an optimal control. Furthermore, making use of the arrow condition of the sufficient stochastic maximum principle, we characterize the optimal quality of additional food and optimal quantity of additional food. Numerical results are given to illustrate the theoretical findings with applications in biological conservation and pest management

Stochastic Optimal and Time-Optimal Control Studies for Additional Food provided prey-predator Systems involving Holling Type-III Functional Response

This paper consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modeled as additional food provided prey-predator system with Holling Type-III functional response for predator and intra-specific competition among predators. We firstly discuss the optimal control problem as a Lagrangian problem with a linear quadratic control. Secondly we consider an optimal control problem in the time-optimal control setting. Stochastic maximum principle is used for establishing the existence of optimal controls for both these problems. Numerical simulations are performed based on stochastic forward-backward sweep methods for realizing the theoretical findings. The results obtained in these optimal control problems are discussed in the context of biological conservation and pest management

Stevens-Johnson syndrome induced by phenytoin: a case report

Stevens-Johnson syndrome (SJS) and Toxic epidermal necrolysis (TEN) are rare (one to two per 10,00,00 population per year) but life threatening adverse drug reactions. Antiepileptic drugs-induced Stevens-Johnson syndrome (SJS) is a life-threatening severe cutaneous adverse reaction, amongst anti-epileptics; carbamazepine and phenytoin are the major culprits. We report here a case of SJS due to phenytoin (CTC vs 2 Grade 3)

A Study of Within-Host Dynamics of Dengue Infection incorporating both Humoral and Cellular Response with a Time Delay for Production of Antibodies

Abstract a. Background: Dengue is an acute illness caused by a virus. The complex behaviour of the virus in human body can be captured using mathematical models. These models helps us to enhance our understanding on the dynamics of the virus. b. Objectives: We propose to study the dynamics of within-host epidemic model of dengue infection which incorporates both innate immune response and adaptive immune response (Cellular and Humoral). The proposed model also incorporates the time delay for production of antibodies from B cells. We propose to understand the dynamics of the this model using the dynamical systems approach by performing the stability and sensitivity analysis. c. Methods used: The basic reproduction number (R0) has been computed using the next generation matrix method. The standard stability analysis and sensitivity analysis were performed on the proposed model. d. Results: The critical level of the antibody recruitment rate(q) was found to be responsible for the existence and stability of various steady states. The stability of endemic state was found to be dependent on time delay(τ). The sensitivity analysis identified the production rate of antibodies (q) to be highly sensitive parameter. e. Conclusions: The existence and stability conditions for the equilibrium points have been obtained. The threshold value of time delay (τ0) has been computed which is critical for change in stability of the endemic state. Sensitivity analysis was performed to identify the crucial and sensitive parameters of the model

Identification of QTLs and candidate genes for high grain Fe and Zn concentration in sorghum [Sorghum bicolor (L.)Moench]

Sorghum is a major food crop in the semi-arid tropics of Africa and Asia. Enhancing the grain iron (Fe) and zinc (Zn) concentration in sorghum using genetic approaches would help alleviate micronutrient malnutrition in millions of poor people consuming sorghum as a staple food. To localize genomic regions associated with grain Fe and Zn, a sorghum F6 recombinant inbred line (RIL) population (342 lines derived from cross 296B PVK 801) was phenotyped in six environments, and genotyped with simple sequence repeat (SSR), DArT (Diversity Array Technology) and DArTSeq (Diversity Array Technology) markers. Highly significant genotype environment interactions were observed for both micronutrients. Grain Fe showed greater variation than Zn. A sorghum genetic map was constructed with 2088 markers (1148 DArTs, 927 DArTSeqs and 13 SSRs) covering 1355.52 cM with an average marker interval of 0.6 cM. Eleven QTLs (individual) and 3 QTLs (across) environments for Fe and Zn were identified. We identified putative candidate genes from the QTL interval of qfe7.1, qzn7.1, and qzn7.2 (across environments) located on SBI-07 involved in Fe and Zn metabolism. These were CYP71B34, and ZFP 8 (ZINC FINGER PROTEIN 8). After validation, the linked markers identified in this study can help in developing high grain Fe and Zn sorghum cultivars in sorghum improvement programs globally

Comparative SNP and Haplotype Analysis Reveals a Higher Genetic Diversity and Rapider LD Decay in Tropical than Temperate Germplasm in Maize

Understanding of genetic diversity and linkage disequilibrium (LD) decay in diverse maize germplasm is fundamentally important for maize improvement. A total of 287 tropical and 160 temperate inbred lines were genotyped with 1943 single nucleotide polymorphism (SNP) markers of high quality and compared for genetic diversity and LD decay using the SNPs and their haplotypes developed from genic and intergenic regions. Intronic SNPs revealed a substantial higher variation than exonic SNPs. The big window size haplotypes (3-SNP slide-window covering 2160 kb on average) revealed much higher genetic diversity than the 10 kb-window and gene-window haplotypes. The polymorphic information content values revealed by the haplotypes (0.436–0.566) were generally much higher than individual SNPs (0.247–0.259). Cluster analysis classified the 447 maize lines into two major groups, corresponding to temperate and tropical types. The level of genetic diversity and subpopulation structure were associated with the germplasm origin and post-domestication selection. Compared to temperate lines, the tropical lines had a much higher level of genetic diversity with no significant subpopulation structure identified. Significant variation in LD decay distance (2–100 kb) was found across the genome, chromosomal regions and germplasm groups. The average of LD decay distance (10–100 kb) in the temperate germplasm was two to ten times larger than that in the tropical germplasm (5–10 kb). In conclusion, tropical maize not only host high genetic diversity that can be exploited for future plant breeding, but also show rapid LD decay that provides more opportunity for selection

Development and use of genic molecular markers (GMMs) for construction of a transcript map of chickpea (Cicer arietinum L.)

A transcript map has been constructed by the development and integration of genic molecular markers (GMMs) including single nucleotide polymorphism (SNP), genic microsatellite or simple sequence repeat (SSR) and intron spanning region (ISR)-based markers, on an inter-specific mapping population of chickpea, the third food legume crop of the world and the first food legume crop of India. For SNP discovery through allele re-sequencing, primer pairs were designed for 688 genes/expressed sequence tags (ESTs) of chickpea and 657 genes/ESTs of closely related species of chickpea. High-quality sequence data obtained for 220 candidate genic regions on 2–20 genotypes representing 9 Cicer species provided 1,893 SNPs with an average frequency of 1/35.83 bp and 0.34 PIC (polymorphism information content) value. On an average 2.9 haplotypes were present in 220 candidate genic regions with an average haplotype diversity of 0.6326. SNP2CAPS analysis of 220 sequence alignments, as mentioned above, provided a total of 192 CAPS candidates. Experimental analysis of these 192 CAPS candidates together with 87 CAPS candidates identified earlier through in silico mining of ESTs provided scorable amplification in 173 (62.01%) cases of which predicted assays were validated in 143 (82.66%) cases (CGMM). Alignments of chickpea unigenes with Medicago truncatula genome were used to develop 121 intron spanning region (CISR) markers of which 87 yielded scorable products. In addition, optimization of 77 EST-derived SSR (ICCeM) markers provided 51 scorable markers. Screening of easily assayable 281 markers including 143 CGMMs, 87 CISRs and 51 ICCeMs on 5 parental genotypes of three mapping populations identified 104 polymorphic markers including 90 markers on the inter-specific mapping population. Sixty-two of these GMMs together with 218 earlier published markers (including 64 GMM loci) and 20 other unpublished markers could be integrated into this genetic map. A genetic map developed here, therefore, has a total of 300 loci including 126 GMM loci and spans 766.56 cM, with an average inter-marker distance of 2.55 cM. In summary, this is the first report on the development of large-scale genic markers including development of easily assayable markers and a transcript map of chickpea. These resources should be useful not only for genome analysis and genetics and breeding applications of chickpea, but also for comparative legume genomics