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Antarctica's ice shelves modulate the grounded ice flow, and weakening of ice shelves due to climate forcing will decrease their ‘buttressing’ effect, causing a response in the grounded ice. While the processes governing ice-shelf weakening are complex, uncertainties in the response of the grounded ice sheet are also difficult to assess. The Antarctic BUttressing Model Intercomparison Project (ABUMIP) compares ice-sheet model responses to decrease in buttressing by investigating the ‘end-member’ scenario of total and sustained loss of ice shelves. Although unrealistic, this scenario enables gauging the sensitivity of an ensemble of 15 ice-sheet models to a total loss of buttressing, hence exhibiting the full potential of marine ice-sheet instability. All models predict that this scenario leads to multi-metre (1–12 m) sea-level rise over 500 years from present day. West Antarctic ice sheet collapse alone leads to a 1.91–5.08 m sea-level rise due to the marine ice-sheet instability. Mass loss rates are a strong function of the sliding/friction law, with plastic laws cause a further destabilization of the Aurora and Wilkes Subglacial Basins, East Antarctica. Improvements to marine ice-sheet models have greatly reduced variability between modelled ice-sheet responses to extreme ice-shelf loss, e.g. compared to the SeaRISE assessments.
Klebsiella pneumoniae is a common pathogen associated with nosocomial infections and is characterised serologically by capsular polysaccharide (K) and lipopolysaccharide O antigens. We surveyed a total of 348 non-duplicate K. pneumoniae clinical isolates collected over a 1-year period in a tertiary care hospital, and determined their O and K serotypes by sequencing of the wbb Y and wzi gene loci, respectively. Isolates were also screened for antimicrobial resistance and hypervirulent phenotypes; 94 (27.0%) were identified as carbapenem-resistant (CRKP) and 110 (31.6%) as hypervirulent (hvKP). isolates fell into 58 K, and six O types, with 92.0% and 94.2% typeability, respectively. The predominant K types were K14K64 (16.38%), K1 (14.66%), K2 (8.05%) and K57 (5.46%), while O1 (46%), O2a (27.9%) and O3 (11.8%) were the most common. CRKP and hvKP strains had different serotype distributions with O2a:K14K64 (41.0%) being the most frequent among CRKP, and O1:K1 (26.4%) and O1:K2 (17.3%) among hvKP strains. Serotyping by gene sequencing proved to be a useful tool to inform the clinical epidemiology of K. pneumoniae infections and provides valuable data relevant to vaccine design.
Coated copper sulphate (CCS) could be used as a Cu supplement in cows. To investigate the influences of copper sulphate (CS) and CCS on milk performance, nutrient digestion and rumen fermentation, fifty Holstein dairy cows were arranged in a randomised block design to five groups: control, CS addition (7·5 mg Cu/kg DM from CS) or CCS addition (5, 7·5 and 10 mg Cu/kg DM from CCS, respectively). When comparing Cu source at equal inclusion rates (7·5 mg/kg DM), cows receiving CCS addition had higher yields of fat-corrected milk, milk fat and protein; digestibility of DM, organic matter (OM) and neutral-detergent fibre (NDF); ruminal total volatile fatty acid (VFA) concentration; activities of carboxymethyl cellulase, cellobiase, pectinase and α-amylase; populations of Ruminococcus albus, Ruminococcus flavefaciens and Fibrobacter succinogenes; and liver Cu content than cows receiving CS addition. Increasing CCS addition, DM intake was unchanged, yields of milk, milk fat and protein; feed efficiency; digestibility of DM, OM, NDF and acid-detergent fibre; ruminal total VFA concentration; acetate:propionate ratio; activity of cellulolytic enzyme; populations of total bacteria, protozoa and dominant cellulolytic bacteria; and concentrations of Cu in serum and liver increased linearly, but ruminal propionate percentage, ammonia-N concentration, α-amylase activity and populations of Prevotella ruminicola and Ruminobacter amylophilus decreased linearly. The results indicated that supplement of CS could be substituted with CCS and addition of CCS improved milk performance and nutrient digestion in dairy cows.
Previous work led to the proposal that the precision feeding of a high-concentrate diet may represent a potential method with which to enhance feed efficiency (FE) when rearing dairy heifers. However, the physiological and metabolic mechanisms underlying this approach remain unclear. This study used metabolomics analysis to investigate the changes in plasma metabolites of heifers precision-fed diets containing a wide range of forage to concentrate ratios. Twenty-four half-sib Holstein heifers, with a similar body condition, were randomly assigned into four groups and precision fed with diets containing different proportions of concentrate (20%, 40%, 60% and 80% based on DM). After 28 days of feeding, blood samples were collected 6 h after morning feeding and gas chromatography time-of-ﬂight/MS was used to analyze the plasma samples. Parameters of oxidative status were also determined in the plasma. The FE (after being corrected for gut fill) increased linearly (P < 0.01) with increasing level of dietary concentrate. Significant changes were identified for 38 different metabolites in the plasma of heifers fed different dietary forage to concentrate ratios. The main pathways showing alterations were clustered into those relating to carbohydrate and amino acid metabolism; all of which have been previously associated with FE changes in ruminants. Heifers fed with a high-concentrate diet had higher (P < 0.01) plasma total antioxidant capacity and superoxide dismutase but lower (P ≤ 0.02) hydroxyl radical and hydrogen peroxide than heifers fed with a low-concentrate diet, which might indicate a lower plasma oxidative status in the heifers fed a high-concentrate diet. Thus, heifers fed with a high-concentrate diet had higher FE and antioxidant capacity but a lower plasma oxidative status as well as changed carbohydrate and amino acid metabolism. Our findings provide a better understanding of how forage to concentrate ratios affect FE and metabolism in the precision-fed growing heifers.
Se can enhance lactation performance by improving nutrient utilization and antioxidant status. However, sodium selenite (SS) can be reduced to non-absorbable elemental Se in the rumen, thereby reducing the intestinal availability of Se. The study investigated the impacts of SS and coated SS (CSS) supplementation on lactation performance, nutrient digestibility, ruminal fermentation and microbiota in dairy cows. Sixty multiparous Holstein dairy cows were blocked by parity, daily milk yield and days in milk and randomly assigned to five treatments: control, SS addition (0.3 mg Se/kg DM as SS addition) or CSS addition (0.1, 0.2 and 0.3 mg Se/kg DM as CSS addition for low CSS (LCSS), medium CSS (MCSS) and high CSS (HCSS), respectively). Experiment period was 110 days with 20 days of adaptation and 90 days of sample collection. Dry matter intake was higher for MCSS and HCSS compared with control. Yields of milk, milk fat and milk protein and feed efficiency were higher for MCSS and HCSS than for control, SS and LCSS. Digestibility of DM and organic matter was highest for CSS addition, followed by SS addition and then control. Digestibility of CP was higher for MCSS and HCSS than for control, SS and LCSS. Higher digestibility of ether extract, NDF and ADF was observed for SS or CSS addition. Ruminal pH decreased with dietary Se addition. Acetate to propionate ratio and ammonia N were lower, and total volatile fatty acids (VFAs) concentration was greater for SS, MCSS and HCSS than control. Ruminal H ion concentration was highest for MCSS and HCSS and lowest for control. Activities of cellobiase, carboxymethyl-cellulase, xylanase and protease and copies of total bacteria, fungi, Ruminococcus flavefaciens, Fibrobacter succinogenes and Ruminococcus amylophilus increased with SS or CSS addition. Activity of α-amylase, copies of protozoa, Ruminococcus albus and Butyrivibrio fibrisolvens and serum glucose, total protein, albumin and glutathione peroxidase were higher for SS, MCSS and HCSS than for control and LCSS. Dietary SS or CSS supplementation elevated blood Se concentration and total antioxidant capacity activity. The data implied that milk yield was elevated due to the increase in total tract nutrient digestibility, total VFA concentration and microorganism population with 0.2 or 0.3 mg Se/kg DM from CSS supplementation in dairy cows. Compared with SS, HCSS addition was more efficient in promoting lactation performance of dairy cows.
Accretionary orogens contain key evidence for the conversion of oceanic to continental crust. The late tectonic history and closure time of the Palaeo-Asian Ocean are recorded in the Mazongshan subduction–accretion complex in the southern Beishan margin of the Central Asian Orogenic Belt. We present new data on the structure, petrology, geochemistry and zircon U–Pb isotope ages of the Mazongshan subduction–accretion complex, which is a tectonic mélange with a block-in-matrix structure. The blocks are of serpentinized peridotite, basalt, gabbro, basaltic andesite, chert and seamount sediments within a matrix that is mainly composed of fore-arc-trench turbidites. U–Pb zircon ages of two gabbros are 454.6 ± 2.5 Ma and 434.1 ± 3.6 Ma, an andesite has a U–Pb zircon age of 451.3 ± 3.5 Ma and a tuffaceous slate has the youngest U–Pb zircon age of 353.6 ± 5.1 Ma. These new isotopic ages, combined with published data on ophiolitic mélanges from central Beishan, indicate that the subduction–accretion of Beishan in the southernmost Central Asian Orogenic Belt lasted until Late Ordovician – Early Carboniferous time. Structure and age data demonstrate that the younging direction of accretion was southwards and that the subduction zone dipped continuously to the north. Accordingly, these results record the conversion of oceanic to continental crust in the southern Beishan accretionary collage.
Depression and anxiety disorders are prevalent mental disorders in China. But some those patients do not seek help from psychiatrists firstly but see internists first.
Objectives and aims
This study aimed to investigate the prevalence of depressive - anxiety disorders in gastroenterology outpatients and assess the detection rate provided by physicians in China.
A multicenter, hospital-based cross-sectional study was carried on in the 15 large general hospitals of five cities cross China. A total of 1995 gastroenterological outpatients were screened by Hospital Anxiety and Depression Scale (HADS). Subjects whose HADS scores ≥ 8 were interviewed by psychiatrists, using Mini International Neuropsychiatric Interview (M.I.N.I) to make further diagnoses. Physicians’ diagnoses and treatment were recorded.
The adjusted prevalence of depressive disorder and anxiety disorders was 14.39% and 9.42% respectively.
The prevalence of depressive-anxiety disorder is high in gastroenterology outpatients in China, which suggests the related training of detecting these mental disorders is needed to gastroenterologists.
Schizophrenia is one of the most severe and chronic forms of mental illness. Quantum resonance spectrometer (QRS) test may be useful as a biological marker for the clinical diagnosis of psychiatric disorders of Schizophrenia.
To evaluate reliability and psychiatric clinical value of QRS via thought disorder detection.
We studied 1014 schizophrenic patients, 155 patients with bipolar disorders patient, and 100 normal controls. Thought disorder symptoms of same subjects obtained from QRS test and psychiatrists' diagnoses were compared. Also Thought disorder symptoms of renumbered 65 schizophrenia patient and 100 normal controls were discriminated using QRS test.
Kappa values of thought disorders detection and diagnosed were more than 65% in 6/9 symptoms of schizophrenia, and more than 74% in all 3 symptoms of bipolar disorder. Same consistency could also be seen in Pearson R value, and ROC AUC. In the discriminated analysis, sensitivity, specificity, positive predictive value and negative predictive of delusion, looseness of thought and paralogism thinking detected utilizing QRS are more than 70% same compared with psychiatrists diagnoses.
QRS in thought disorder detection seem to have a predictable value for outcome in schizophrenia and bipolar disorder, would become an objective identification and diagnosis instrument, and might promote psychiatric clinical diagnosis.
Brain-derived neurotrophic factor (BDNF) has an important role in learning, motivation and regulation of mood. A body of research indicates that dysregulation of BDNF is found in post-traumatic stress disorder (PTSD). The aim of this study was to investigate the association of baseline plasma BDNF and follow-up PTSD symptoms in Chinese motor vehicle accident survivors.
Motor vehicle accident (MVA) survivors were recruited from one Emergency Room of Shanghai. BDNF plasma levels were measured in 24 hours after motor vehicle accident. The Clinician-Administered PTSD Scale (CAPS) was used to evaluated PTSD symptoms one month after accident. Totally, 60 MVA survivors participated in this study and 49 of them completed follow-up evaluation.
In the one month follow-up interview, 14 of the MVA survivors met the PTSD diagnosis. The PTSD MVA survivors shown lower baseline BDNF plasma level when compare with non-PTSD participants (p < 0.05).
People who show lower plasma BDNF after traumatic event may be more susceptible to PTSD, and plasma BDNF could be a predictor of PTSD.
Current available antidepressants exhibit low remission rate with a long response lag time. Growing evidence has demonstrated acute sub-anesthetic dose of ketamine exerts rapid, robust, and lasting antidepressant effects. However, a long term use of ketamine tends to elicit its adverse reactions. The present study aimed to investigate the antidepressant-like effects of intermittent and consecutive administrations of ketamine on chronic unpredictable mild stress (CUMS) rats, and to determine whether ketamine can redeem the time lag for treatment response of classic antidepressants. The behavioral responses were assessed by the sucrose preference test, forced swimming test, and open field test. In the first stage of experiments, all the four treatment regimens of ketamine (10 mg/kg ip, once daily for 3 or 7 consecutive days, or once every 7 or 3 days, in a total 21 days) showed robust antidepressant-like effects, with no significant influence on locomotor activity and stereotype behavior in the CUMS rats. The intermittent administration regimens produced longer antidepressant-like effects than the consecutive administration regimens and the administration every 7 days presented similar antidepressant-like effects with less administration times compared with the administration every 3 days. In the second stage of experiments, the combination of ketamine (10 mg/kg ip, once every 7 days) and citalopram (20 mg/kg po, once daily) for 21 days caused more rapid and sustained antidepressant-like effects than citalopram administered alone. In summary, repeated sub-anesthestic doses of ketamine can redeem the time lag for the antidepressant-like effects of citalopram, suggesting the combination of ketamine and classic antidepressants is a promising regimen for depression with quick onset time and stable and lasting effects.
The aim of this study was to develop and externally validate a simple-to-use nomogram for predicting the survival of hospitalised human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) patients (hospitalised person living with HIV/AIDS (PLWHAs)). Hospitalised PLWHAs (n = 3724) between January 2012 and December 2014 were enrolled in the training cohort. HIV-infected inpatients (n = 1987) admitted in 2015 were included as the external-validation cohort. The least absolute shrinkage and selection operator method was used to perform data dimension reduction and select the optimal predictors. The nomogram incorporated 11 independent predictors, including occupation, antiretroviral therapy, pneumonia, tuberculosis, Talaromyces marneffei, hypertension, septicemia, anaemia, respiratory failure, hypoproteinemia and electrolyte disturbances. The Likelihood χ2 statistic of the model was 516.30 (P = 0.000). Integrated Brier Score was 0.076 and Brier scores of the nomogram at the 10-day and 20-day time points were 0.046 and 0.071, respectively. The area under the curves for receiver operating characteristic were 0.819 and 0.828, and precision-recall curves were 0.242 and 0.378 at two time points. Calibration plots and decision curve analysis in the two sets showed good performance and a high net benefit of nomogram. In conclusion, the nomogram developed in the current study has relatively high calibration and is clinically useful. It provides a convenient and useful tool for timely clinical decision-making and the risk management of hospitalised PLWHAs.
Combining different swine populations in genomic prediction can be an important tool, leading to an increased accuracy of genomic prediction using single nucleotide polymorphism (SNP) chip data compared with within-population genomic. However, the expected higher accuracy of multi-population genomic prediction has not been realized. This may be due to an inconsistent linkage disequilibrium (LD) between SNPs and quantitative trait loci (QTL) across populations, and the weak genetic relationships across populations. In this study, we determined the impact of different genomic relationship matrices, SNP density and pre-selected variants on prediction accuracy using a combined Yorkshire pig population. Our objective was to provide useful strategies for improving the accuracy of genomic prediction within a combined population. Results showed that the accuracy of genomic best linear unbiased prediction (GBLUP) using imputed whole-genome sequencing (WGS) data in the combined population was always higher than that within populations. Furthermore, the use of imputed WGS data always resulted in a higher accuracy of GBLUP than the use of 80K chip data for the combined population. Additionally, the accuracy of GBLUP with a non-linear genomic relationship matrix was markedly increased (0.87% to 15.17% for 80K chip data, and 0.43% to 4.01% for imputed WGS data) compared with that obtained with a linear genomic relationship matrix, except for the prediction of XD population in the combined population using imputed WGS data. More importantly, the application of pre-selected variants based on fixation index (Fst) scores improved the accuracy of multi-population genomic prediction, especially for 80K chip data. For BLUP|GA (BLUP approach given the genetic architecture), the use of a linear method with an appropriate weight to build a weight-relatedness matrix led to a higher prediction accuracy compared with the use of only pre-selected SNPs for genomic evaluations, especially for the total number of piglets born. However, for the non-linear method, BLUP|GA showed only a small increase or even a decrease in prediction accuracy compared with the use of only pre-selected SNPs. Overall, the best genomic evaluation strategy for reproduction-related traits for a combined population was found to be GBLUP performed with a non-linear genomic relationship matrix using variants pre-selected from the 80K chip data based on Fst scores.
Recently, a triple-network model suggested the abnormal interactions between the executive-control network (ECN), default-mode network (DMN) and salience network (SN) are important characteristics of addiction, in which the SN plays a critical role in allocating attentional resources toward the ECN and DMN. Although increasing studies have reported dysfunctions in these brain networks in Internet gaming disorder (IGD), interactions between these networks, particularly in the context of the triple-network model, have not been investigated in IGD. Thus, we aimed to assess alterations in the inter-network interactions of these large-scale networks in IGD, and to associate the alterations with IGD-related behaviors.
DMN, ECN and SN were identified using group-level independent component analysis (gICA) in 39 individuals with IGD and 34 age and gender matched healthy controls (HCs). Then alterations in the SN-ECN and SN-DMN connectivity, as well as in the modulation of ECN versus DMN by SN, using a resource allocation index (RAI) developed and validated previously in nicotine addiction, were assessed. Further, associations between these altered network coupling and clinical assessments were also examined.
Compared with HCs, IGD had significantly increased SN-DMN connectivity and decreased RAI in right hemisphere (rRAI), and the rRAI in IGD was negatively associated with their scores of craving.
These findings suggest that the deficient modulation of ECN versus DMN by SN might provide a mechanistic framework to better understand the neural basis of IGD and might provide novel evidence for the triple-network model in IGD.
Childhoods in urban or rural environments may differentially affect risk for neuropsychiatric disorders. Here, we leveraged on dramatic urbanization and rural-urban migration since the 1980s in China to explore the hypothesis that rural or urban childhoods may differentially influence memory processing and neural responses to neutral and aversive stimuli.
Explore the underlying mechanisms of childhood environment effect on brain function and neuropsychiatric risk.
We examined 420 adult subjects with similar current socioeconomic status and living in Beijing, China, but with differing rural (n = 227) or urban (n = 193) childhoods. In an episodic memory paradigm scanned in a 3 T GE MRI, subjects viewed blocks of neutral or aversive pictures in the encoding and retrieval sessions.
Episodic memory accuracy for neutral stimuli was less than for aversive stimuli (P < 0.001). However, subjects with rural childhoods apparently performed less accurately for memory of aversive but not neutral stimuli (P < 0.01). In subjects with rural childhoods, there was relatively increased engagement of bilateral striatum at encoding, increased engagement of bilateral hippocampus at retrieval of neutral and aversive stimuli, and increased engagement of amygdala at aversive retrieval (P < 0.05 FDR corrected, cluster size > 50).
Rural or urban childhoods appear associated with physiological and behavioural differences, particularly in the neural processing of aversive episodic memory at medial temporal and striatal brain regions. It remains to be explored the extent to which these effects relate to individual risk for neuropsychiatric or stress-related disorders.
Disclosure of interest
The authors have not supplied their declaration of competing interest.
Chlamydia trachomatis (CT) infection has been a major public health threat globally. Monitoring and prediction of CT epidemic status and trends are important for programme planning, allocating resources and assessing impact; however, such activities are limited in China. In this study, we aimed to apply a seasonal autoregressive integrated moving average (SARIMA) model to predict the incidence of CT infection in Shenzhen city, China. The monthly incidence of CT between January 2008 and June 2019 in Shenzhen was used to fit and validate the SARIMA model. A seasonal fluctuation and a slightly increasing pattern of a long-term trend were revealed in the time series of CT incidence. The monthly CT incidence ranged from 4.80/100 000 to 21.56/100 000. The mean absolute percentage error value of the optimal model was 8.08%. The SARIMA model could be applied to effectively predict the short-term CT incidence in Shenzhen and provide support for the development of interventions for disease control and prevention.
This study evaluated the effects of rumen-protected folic acid (RPFA) and betaine (BT) on growth performance, nutrient digestion and blood metabolites in bulls. Forty-eight Angus bulls were blocked by body weight and randomly assigned to four treatments in a 2 × 2 factorial design. BT of 0 or 0·6 g/kg DM was supplemented to diet without or with the addition of 6 mg/kg DM of folic acid from RPFA, respectively. Average daily gain increased by 25·2 and 6·29 % for addition of BT without RPFA and with RPFA, respectively. Digestibility and ruminal total volatile fatty acids of neutral-detergent fibre and acid-detergent fibre increased, feed conversion ratio and blood folate decreased with the addition of BT without RPFA, but these parameters were unchanged with BT addition in diet with RPFA. Digestibility of DM, organic matter and crude protein as well as acetate:propionate ratio increased with RPFA or BT addition. Ruminal ammonia-N decreased with RPFA addition. Activity of carboxymethyl cellulase, cellobiase, xylanase, pectinase and protease as well as population of total bacteria, protozoa, Fibrobacter succinogenes and Ruminobacter amylophilus increased with RPFA or BT addition. Laccase activity and total fungi, Ruminococcus flavefaciens and Prevotella ruminicola population increased with RPFA addition, whereas Ruminococcus albus population increased with BT addition. Blood glucose, total protein, albumin, growth hormone and insulin-like growth factor-1 increased with RPFA addition. Addition of RPFA or BT decreased blood homocysteine. The results indicated that addition of BT stimulated growth and nutrient digestion in bulls only when RPFA was not supplemented.
The Square Kilometre Array (SKA) is a planned large radio interferometer designed to operate over a wide range of frequencies, and with an order of magnitude greater sensitivity and survey speed than any current radio telescope. The SKA will address many important topics in astronomy, ranging from planet formation to distant galaxies. However, in this work, we consider the perspective of the SKA as a facility for studying physics. We review four areas in which the SKA is expected to make major contributions to our understanding of fundamental physics: cosmic dawn and reionisation; gravity and gravitational radiation; cosmology and dark energy; and dark matter and astroparticle physics. These discussions demonstrate that the SKA will be a spectacular physics machine, which will provide many new breakthroughs and novel insights on matter, energy, and spacetime.
In order to map quantitative trait loci (QTLs) for allometries of body compositions and metabolic traits in chicken, we phenotypically characterize the allometric growths of multiple body components and metabolic traits relative to BWs using joint allometric scaling models and then establish random regression models (RRMs) to fit genetic effects of markers and minor polygenes derived from the pedigree on the allometric scalings. Prior to statistically inferring the QTLs for the allometric scalings by solving the RRMs, the LASSO technique is adopted to rapidly shrink most of marker genetic effects to zero. Computer simulation analysis confirms the reliability and adaptability of the so-called LASSO-RRM mapping method. In the F2 population constructed by multiple families, we formulate two joint allometric scaling models of body compositions and metabolic traits, in which six of nine body compositions are tested as significant, while six of eight metabolic traits are as significant. For body compositions, a total of 14 QTLs, of which 9 dominant, were detected to be associated with the allometric scalings of drumstick, fat, heart, shank, liver and spleen to BWs; while for metabolic traits, a total of 19 QTLs also including 9 dominant be responsible for the allometries of T4, IGFI, IGFII, GLC, INS, IGR to BWs. The detectable QTLs or highly linked markers can be used to regulate relative growths of the body components and metabolic traits to BWs in marker-assisted breeding of chickens.
Each species is subject to various biotic and abiotic factors during growth. This paper formulates a deterministic model with the consideration of various factors regulating population growth such as age-dependent birth and death rates, spatial movements, seasonal variations, intra-specific competition and time-varying maturation simultaneously. The model takes the form of two coupled reaction–diffusion equations with time-dependent delays, which bring novel challenges to the theoretical analysis. Then, the model is analysed when competition among immatures is neglected, in which situation one equation for the adult population density is decoupled. The basic reproduction number
is defined and shown to determine the global attractivity of either the zero equilibrium (when
) or a positive periodic solution (
) by using the dynamical system approach on an appropriate phase space. When the immature intra-specific competition is included and the immature diffusion rate is neglected, the model is neither cooperative nor reducible to a single equation. In this case, the threshold dynamics about the population extinction and uniform persistence are established by using the newly defined basic reproduction number
as a threshold index. Furthermore, numerical simulations are implemented on the population growth of two different species for two different cases to validate the analytic results.