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The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain restrictions. The mathematical model has been numerically simulated using the predictor-corrector method to highlight the role played by fractional order in controlling the disease spread. Numerical simulations signify the fact that a vital role has been played by fractional order model over integer order model in determining the transmission of COVID-19. It can be visualized that the increment rate in the infectives is lower by taking into consideration the memory effect due to a previous exposure to COVID-19. [ABSTRACT FROM AUTHOR]

The absence of reliable registration of Covid-19 deaths in India has prevented proper assessment and monitoring of the coronavirus pandemic. In addition, India's relatively young age structure tends to conceal the severity of Covid-19 mortality, which is concentrated in older age groups. In this paper, we present four different demographic samples of Indian populations for which we have information on both their demographic structures and death outcomes. We show that we can model the age distribution of Covid-19 mortality in India and use this modeling to estimate Covid-19 mortality in the country. Our findings point to a death toll of approximately 3.2–3.7 million persons by early November 2021. Once India's age structure is factored in, these figures correspond to one of the most severe cases of Covid-19 mortality in the world. India has recorded after February 2021 the second outbreak of coronavirus that has affected the entire country. The accuracy of official statistics of Covid-19 mortality has been questioned, and the real number of Covid-19 deaths is thought to be several times higher than reported. In this paper, we assembled four independent population samples to model and estimate the level of Covid-19 mortality in India. We first used a population sample with the age and sex of Covid-19 victims to develop a Gompertz model of Covid-19 mortality in India. We applied and adjusted this mortality model on two other national population samples after factoring in the demographic characteristics of these samples. We finally derive from these samples the most reasonable estimate of Covid-19 mortality level in India and confirm this result using a fourth population sample. Our findings point to a death toll of about 3.2–3.7 million persons by late May 2021. This is by far the largest number of Covid-19 deaths in the world. Once standardized for age and sex structure, India's Covid-19 mortality rate is above Brazil and the USA. Our analysis shows that existing population samples allow an alternative estimation of deaths due to Covid-19 in India. The results imply that only one out of 7–8 deaths appear to have been recorded as a Covid-19 death in India. The estimates also point to a very high Covid-19 mortality rate, which is even higher after age and sex standardization. The magnitude of the pandemic in India requires immediate attention. In the absence of effective remedies, this calls for a strong response based on a combination of non-pharmaceutical interventions and the scale-up of vaccination to make them accessible to all, with an improved surveillance system to monitor the progression of the pandemic and its spread across India's regions and social groups. [ABSTRACT FROM AUTHOR]

Modern mathematics, and modern science in general, was embraced enthusiastically in the Indian subcontinent quite early, thanks to a large extent to the tradition of learning going back to the ancient times. By the early decades of the 20th century the Indian mathematical community had made important research contributions in diverse areas of mathematics, including number theory, real and complex analysis, diffrential geometry, diffrential equations, algebra, combinatorial mathematics and applied mathematics. Interaction with world leaders in the field, reforms in the educational system, establishment of societies for actively pursuing study and discussion of mathematics, publication of mathematical journals, were some of the major progressive steps taken. Apart from the indigenous leadership, participation of a few enlightened foreigners in the process also paved the way for the advancement of the subject in the country. We recount here the story of the early developments of the mathematical scene in India, and of the various players involved. [ABSTRACT FROM AUTHOR]

Background: The VL elimination strategy requires cost-effective tools for case detection and management. This intervention study tests the yield, feasibility and cost of 4 different active case detection (ACD) strategies (camp, index case, incentive and blanket approach) in VL endemic districts of India, Nepal and Bangladesh. Methodology/Principal Findings: First, VL screening (fever more than 14 days, splenomegaly, rK39 test) was performed in camps. This was followed by house to house screening (blanket approach). An analysis of secondary VL cases in the neighborhood of index cases was simulated (index case approach). A second screening round was repeated 4–6 months later. In another sub-district in India and Nepal, health workers received incentives for detecting new VL cases over a 4 month period (incentive approach). This was followed by house screening for undetected cases. A total of 28 new VL cases were identified by blanket approach in the 1st screening round, and used as ACD gold standard. Of these, the camp approach identified 22 (sensitivity 78.6%), index case approach identified 12 (sensitivity – 42.9%), and incentive approach identified 23 new VL cases out of 29 cases detected by the house screening (sensitivity – 79.3%). The effort required to detect a new VL case varied (blanket approach – 1092 households, incentive approach – 978 households; index case approach – 788 households had to be screened). The cost per new case detected varied (camp approach $21 – $661; index case approach $149 – $200; incentive based approach $50 – $543; blanket screening $112 – $629). The 2nd screening round yielded 20 new VL cases. Sixty and nine new PKDL cases were detected in the first and second round respectively. Conclusions/Significance: ACD in the VL elimination campaign has a high yield of new cases at programme costs which vary according to the screening method chosen. Countries need the right mix of approaches according to the epidemiological profile, affordability and organizational feasibility. Author Summary: For the elimination of any infectious disease (i.e., reduction of the burden of a serious public health problem to a minor problem which can be managed by the general health services) the right mix of public health tools has to be identified for the early detection and successful treatment of new cases as well as effective vector control (in the case of vector borne diseases) at affordable costs. The paper provides a powerful example of evidence building for cost-effective early case detection in the visceral leishmaniasis elimination initiative of Bangladesh, India and Nepal. It compares the camp approach (mobile teams testing in chronic fever camps for spleen enlargement and rapid diagnostic tests) with the index case approach (screening for new cases in the neighbourhood of reported visceral leishmaniasis patients) and the incentive based approach (where basic health workers receive an allowance for detecting a new case) using subsequent house-to-house screening for the identification of the real number of un-detected cases. By applying a mix of different study methods and an itinerate research process to identify the most effective, feasible and affordable case detection method, under different environmental conditions, recommendations could be developed which help governments in shaping their visceral leishmaniasis elimination strategy. [ABSTRACT FROM AUTHOR]