ABSTRACT
In this paper, a mathematical model of the COVID-19 pandemic with lockdown that provides a more accurate representation of the infection rate has been analyzed. In this model, the total population is divided into six compartments: the susceptible class, lockdown class, exposed class, asymptomatic infected class, symptomatic infected class, and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method and presented graphically based on different progression rates and effective contact rates of infective individuals. The COVID-19 epidemic model exhibits the disease-free equilibrium and endemic equilibrium. The local and global stability analysis has been done at the disease-free and endemic equilibrium based on R0. The stability analysis of the model shows that the disease-free equilibrium is both locally and globally stable when R0<1, and the endemic equilibrium is locally and globally stable when R0>1 under some conditions. A control strategy including vaccination and treatment has been studied on this pandemic model with an objective functional to minimize. Finally, numerical simulation of the COVID-19 outbreak in India is carried out using MATLAB, highlighting the usefulness of the COVID-19 pandemic model and its mathematical analysis.
ABSTRACT
In this study, we developed and analyzed a mathematical model for explaining the transmission dynamics of COVID‐19 in India. The proposed SIuIkR model is a modified version of the existing SIR model. Our model divides the infected class I of SIR model into two classes: Iu (unknown infected class) and Ik (known infected class). In addition, we consider R a recovered and reserved class, where susceptible people can hide them due to fear of the COVID‐19 infection. Furthermore, a non‐monotonic incidence function is deemed to incorporate the psychological effect of the novel coronavirus diseases on India's community. The epidemiological threshold parameter, namely the basic reproduction number, has been formulated and presented graphically. With this threshold parameter, the local and global stability analysis of the disease‐free equilibrium and the endemic proportion equilibrium based on disease persistence have been analyzed. Lastly, numerical results of long‐run prediction using MATLAB show that the fate of this situation is very harmful if people are not following the guidelines issued by the authority.
ABSTRACT
BACKGROUND: Despite NICE/AUGIS recommendations, the practice of early laparoscopic cholecystectomy (ELC) has been particularly poor in the UK offered only by 11%-20% surgeons as compared to 33%-67% internationally, possibly due to financial constraints, logistical difficulties and shortage of expertise, thus, reflecting the varied provision of emergency general surgical care. To assess whether emergency general surgeons (EGS) could provide a 'Hot Gall Bladder Service' (HGS) with an acceptable outcome. PATIENTS AND METHODS: This was a prospective HGS observational study that was protocol driven with strict inclusion/exclusion criteria and secure online data collection in a district general hospital between July 2018 and June 2019. A weekly dedicated theatre slot was allocated for this list. RESULTS: Of the 143 referred for HGS, 86 (60%) underwent ELC which included 60 (70%) women. Age, ASA and body mass index was 54* (18-85) years, II* (I-III) and 27* (20-54), respectively. 86 included 46 (53%), 19 (22%), 19 (22%) and 2 (3%) patients presenting with acute calculus cholecystitis, gallstone pancreatitis, biliary colic, and acalculus cholecystitis, respectively. 85 (99%) underwent LC with a single conversion. Grade of surgical difficulty, duration of surgery and post-operative stay was 2* (1-4) 68* (30-240) min and 0* (0-13) day, respectively. Eight (9%) required senior surgical input with no intra-operative complications and 2 (2%) 30-day readmissions. One was post-operative subhepatic collection that recovered uneventfully and the second was pancreatitis, imaging was clear requiring no further intervention. CONCLUSION: In the current climate of NHS financial crunch, COVID pandemic and significant pressure on inpatient beds: Safe and cost-effective HGS can be provided by the EGS with input from upper GI/HPB surgeons (when required) with acceptable morbidity and a satisfactory outcome. *Median.