Chaos, Solitons & Fractals

House hunting of ant, such as Temnothorax albipennis, has been shown to be a distributed dynamical system. Such a system includes agent-based algorithm [1], with agents in different roles including nest exploration, nest assessment, quorum sensing, and brood item transportation. Such an algorithm, if used properly, can be applied on artificial intelligent system, like robotic swarms. Despite of its complexity, we are focusing on the quorum sensing mechanism, which is also observed in bacteria model. In bacterial model, multiple biochemical networks co-exist within each cell, including binding of autoinducer and cognate receptors, and phosphorylation-dephosphorylation cycle. In ant hunting, we also have ant commitment to the nest, mimicking binding between autoinducer and cognate receptors. We also have assessment ant specific to one nest and information exchange between two assessment ants corresponding to different nests, which is similar process to the phosphorylation-dephosphorylation cycle in bacteria quorum sensing network. Due to the similarity between the two models, we borrow the idea from bacteria quorum sensing to clarify the definition of quorum threshold through biological plausible mechanism related to limited resource model. We further made use of the contraction analysis to explore the trade-off between decision split and decision consensus within ant population. Our work provides new generation model for understanding how ant adapt to the changing environment during quorum sensing.

In this study, we analyze the number of infected positive cases of COVID-19 outbreak with concern to lockdown in India in the time window of February 11th 2020 to Jun 30th 2020. The first case in India was reported in Kerala on January 30th 2020. To break the chain of spreading, Government announced a nationwide lockdown on March 24th 2020, which is increased two times. The Ongoing lockdown 3.0 is over on May 18th, 2020. We derived how the lockdown relaxation is going to impact on containment of the outbreak. Here the Exponential Growth Model has been used to derive the epidemic curve based on the data collected from February 11th 2020, to May 11th 2020, and the Machine Learning based Linear Regression model that gives the epidemic curve to predict the cases with the continuous flow of the lockdown. We estimate that if the lockdown is continuing with more relaxation, then the estimated infected cases reach up to 1.16 crores by June 30th 2020, and the lockdown would persist with current restriction, then the expected predicted infected cases are 5.69 lacs. The Exponential Growth Model and the Linear Regression Model are advantageous to predict the number of affected cases of COVID-19. These models can be used for forecasting in long term intervals. It shows from our result that lockdown with certain restriction has a vital role in preventing the spreading of this epidemic in this current situation.

India is one of the most harshly affected countries due to COVID epidemic. Early implementation of lockdown protocols were useful to control certain parameters of transmission dynamics, but the numbers are consistently increasing in later months. Indias population is divided into different clusters on the basis of population density and population mobility, even varying resource availability and since the recent cases are coming from throughout the country, it allows us to model an overall average of the country. In this study, we try to prove the efficiency of using the SEIR epidemiological model for different rate study analysis for COVID epidemic in India. Along with it we derived newer components for better forecast of the pandemic in India. We found that there is a decrease in R0 value, but still the epidemic is not under control. The percentage of infected patients being admitted into ICU for critical care is around 9.986%, while the chances of recovery of critical patients being admitted to the ICU seem to be slim at 79.9% of the admitted being dead.

Following power law, Farrs law and IDEA model, we analyze the data of COVID-19 pandemic for India up to 2 May, 2020 and for Germany, France, Italy, the USA, Singapore, China and Denmark up to 26 April, 2020. The cumulative total number of infected persons as a function of elapsed time has been fitted with power law to find the scaling exponent ({gamma}). The reduction in{gamma} in different countries signals the reduction in the growth of infection, possibly, due to long-term Government intervention. The extent of infection and reproduction rate R0 of the same are also examined using Farrs law and IDEA model. The new cases per day with time assume Gaussian bell shaped curve, obeying the rule that faster rise follows faster decay. In India and Singapore, the peak of the bell shaped curve is still elusive. It is found that, till date, countries such as Denmark and India implementing sooner lockdown have underwent lower number of new cases of infection. Daily variation shows, R0 of all the countries is reducing, ushering in fresh hopes to combat COVID-19. Finally, we try to make a prediction as to the date on which the different countries will come down to daily cases of infection as low as one hundred (100).

CoVID-19 is spreading throughout the world at an alarming rate. So far it has spread over 200 countries in the whole world. Mathematical modeling of an epidemic like CoVID-19 is always useful for strategic decision making, especially it is very useful to gain some understanding of the future of the epidemic in densely populous countries like India. We use a simple yet effective mathematical model SIR(D) to predict the future of the epidemic in India by using the existing data. We also estimate the effect of lock-down/social isolation via a time-dependent coefficient of the model. The model study with realistic parameters set shows that the epidemic will be at its peak around the end of June or the first week of July with almost 108 Indians most likely being infected if the lock-down relaxed after May 3, 2020. However, the total number of infected population will become one-third of what predicted here if we consider that people only in the red zones (approximately one-third of Indias population) are susceptible to the infection. Even in a very optimistic scenario we expect that at least the infected numbers of people will be [Formula].

ObjectivesOur primary objective is to predict the dynamics of COVID-19 epidemic in India while adjusting for the effects of various progressively implemented containment measures. Apart from forecasting the major turning points and parameters associated with the epidemic, we intend to provide an epidemiological assessment of the impact of these containment measures in India. MethodsWe propose a method based on time-series SIR model to estimate time-dependent modifiers for transmission rate of the infection. These modifiers are used in state-space SIR model to estimate reproduction number R0, expected total incidence, and to forecast the daily prevalence till the end of the epidemic. We consider four different scenarios, two based on current developments and two based on hypothetical situations for the purpose of comparison. ResultsAssuming gradual relaxation in lockdown post 17 May 2020, we expect the prevalence of infecteds to cross 9 million, with at least 1 million severe cases, around the end of October 2020. For the same case, estimates of R0 for the phases no-intervention, partial-lockdown and lockdown are 4.46 (7.1), 1.47 (2.33), and 0.817 (1.29) respectively, assuming 14-day (24-day) infectious period. ConclusionsEstimated modifiers give consistent estimates of unadjusted R0 across different scenarios, demonstrating precision. Results corroborate the effectiveness of lockdown measures in substantially reducing R0. Also, predictions are highly sensitive towards estimate of infectious period.

This paper focuses on the development and analysis of the endemic model for disease control in an aged-structured population in Nigeria. Upon the model framework development, the model equations were transformed into proportions with rate of change of the different compartments forming the model, thereby reducing the model equations from twelve to ten homogenous ordinary differential equations. The model exhibits two equilibria, the endemic state and the disease-free equilibrium state while successfully achieving a Reproductive Number R0 = 0. The deterministic endemic susceptible-exposed-infected-removed-undetectable=untransmissible-susceptible (SEIRUS) model is analyzed for the existence and stability of the disease-free equilibrium state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0 [&le;] R0 < 1. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect treatment rate and the net transmission rate on recovery for both juvenile and adult sub-population in an age-structured population.

This paper questions various claims from the paper "Social distancing strategies for curbing the COVID-19 epidemic" by Kissler, Tedijanto, Lipsitch, and Grad: most importantly, the claim that Chinas "intense" distancing measures achieved only a 60% reduction in R0.

This paper analyses the trend in daily reported confirmed cases of COVID-19 in India using joinpoint regression analysis. The analysis reveals that there has been little impact of the nation-wide lockdown and subsequent extension on the progress of the COVID-19 pandemic in the country and there is no empirical evidence to suggest that relaxations under the third and the fourth phase of the lockdown have resulted in a spike in the reported confirmed cases. The analysis also suggests that if the current trend continues, in the immediate future, then the daily reported confirmed cases of COVID-19 in the country is likely to increase to 21 thousand by 15 June 2020 whereas the total number of confirmed cases of COVID-19 will increase to around 422 thousand. The analysis calls for a population-wide testing approach to check the increase in the reported confirmed cases of COVID-19.

COVID-19 pandemic has impacted people all across the world. As a result, there has been a collective effort to monitor, predict, and control the spread of this disease. Among this effort is the development of mathematical models that could capture accurately the available data and simulate closely the futuristic scenarios. In this paper, a fractional-order memory-dependent model for simulating the spread of COVID-19 is proposed. In this model, the impact of governmental action and public perception are incorporated as part of the time-varying transmission rate. The model simulation is performed using the two-step generalized exponential time-differencing method and tested for data from Wuhan, China. The mean-square errors demonstrate the merit of the fractional-order model and provide a good estimate of the optimal order.

The outbreak of COVID-19 has an undeniable global impact, both socially and economically. March 11th, 2020, COVID-19 was declared as a pandemic worldwide. Many governments, worldwide, have imposed strict lockdown measures to minimize the spread of COVID-19. However, these measures cannot last forever; therefore, many countries are already considering relaxing the lockdown measures. This study, quantitatively, investigated the impact of this relaxation in the United States, Germany, the United Kingdom, Italy, Spain, and Canada. A modified version of the SIR model is used to model the reduction in lockdown based on the already available data. The results showed an inevitable second wave of COVID-19 infection following loosening the current measures. The study tries to reveal the predicted number of infected cases for different reopening dates. Additionally, the predicted number of infected cases for different reopening dates is reported.

AO_SCPLOWBSTRACTC_SCPLOWWe use publicly available timeline data on the Covid-19 outbreak for nine indian states to calculate the important quantifier of the outbreak, the sought after Rt or the time varying reproduction number of the outbreak. This quantity can be measured in in several ways, e.g. by application of Stochastic compartmentalised SIR (DCM) model, Poissonian likelihood based (ML) model & the exponential growth rate (EGR) model. The third one is known as the effective reproduction number of an outbreak. Here we use, mostly, the second one. It is known as the instantaneous reproduction number for an outbreak. This number can faithfully tell us the success of lockdown measures inside indian states, as containment policy for the spread of Covid-19 viral disease. This can also, indirectly yield notional value of the generation time inteval in different states. In doing this work we employ, pan India serial interval of the outbreak estimated directly from data from January 30th to April 19th, 2020. Simultaneously, in conjunction with the serial interval data, our result is derived from incidences data between March 14th, 2020 to June 1st, 2020, for the said states. We find the lockdown had marked positive effect on the nature of time dependent reproduction number in most of the Indian states, barring a couple. The possible reason for such failures have been investigated.

As we calculate analytic to link the coefficient of third-order polynomial equations from raw data of an Asean to the SEIR model. The Reproductive index depending on the average incubation period and the average infection period and the coefficient polynomial equations fitted from raw are derived. We also consider the difference of the average incubation period as 5 days and 3 days with the average infection period as 10 day of an Asean. We find that the value of R0 are Indonesia (7.97), Singapore (6.22), Malaysia (3.86), Thailand (2.48), respectively. And we also find that Singapore has 2 values of R0 as 1.54 (16 Feb to 37 March) and 6.22 (31 March-4 April).The peak of infection rate are not found for Singapore and Indonesia at the time of consideration. The model of external stimulus is added into raw data of Singapore and Indonesia to find the maximum rate of infection. We find that Singapore need more magnitude of external stimulus than Indonesia. And the external stimulus for 14 days can stimulate to occur the peak of infected daily case of both country.

In this paper, a data-driven adaptive model for infection of COVID-19 is formulated to predict the confirmed total cases and active cases of an area over 4 weeks. The parameter of the model is always updated based on daily observations. It is found that the short term prediction of up to 3-4 weeks can be possible with good accuracy. Detailed analysis of predicted value and the actual value of confirmed total cases and active cases for India from 1st June to 3rd July is provided. Prediction over 7, 14, 21, 28 days has the accuracy about 0.73% {+/-} 1.97%, 1.92% {+/-} 2.95%, 4.34% {+/-} 3.91%, 6.40% {+/-} 9.26% of the actual value of confirmed total cases. Similarly, the 7, 14, 21, 28 days prediction has the accuracy about 1.24% {+/-} 6.57%, 3.04% {+/-} 10.00%, 6.33% {+/-} 16.12%, 10.20% {+/-} 24.14% of the actual value of confirmed active cases.

New variants of SARS-COV-2 have been found in various countries. Especially, the UK has been attacked by Indias Delta Plus, and the spread of infection has been very rapid, since it is extremely infectious. Fortunately, however, the number of deaths has been stayed flat, where deaths are reported to be those who are not yet received a shot of COVID-19 vaccine. In this short not, we would like to consider why the number of deaths is so small, compared with high cases, around the infection peak, when the basic reproduction number is very large.

The COVID-19 infections in Pakistan are spreading at an exponential rate and a point may soon be reached where rigorous prevention measures would need to be adopted. Mathematical models can help define the scale of an epidemic and the rate at which an infection can spread in a community. I used ARIMA Model, Diffusion Model, SIRD Model and Prophet Model to forecast the magnitude of the COVID-19 pandemic in Pakistan and compared the numbers with the reported cases on the national database. Results depicts that Pakistan could hit peak number of infectious cases between June 2020 and July, 2020.

The novel coronavirus disease (namely COVID-19) has taken attention because of its deadliness across the globe, causing a massive death as well as critical situation around the world. It is an infectious disease which is caused by newly discovered coronavirus. Our study demonstrates with a nonlinear model of this devastating COVID-19 which narrates transmission from human-to-human in the society. Pontryagins Maximum principle has also been applied in order to obtain optimal control strategies where the maintenance of social distancing is the major control. The target of this study is to find out the most fruitful control measures of averting coronavirus infection and eventually, curtailed of the COVID-19 transmission among people. The model is investigated analytically by using most familiar necessary conditions of Pontryagins maximum principle. Furthermore, numerical simulations have been performed to illustrate the analytical results. The analysis reveals that implementation of educational campaign, social distancing and developing human immune system are the major factors which can be able to plunge the scenario of becoming infected.

Newly proposed SIQR model defines exponent{lambda} of exponential function expressing daily number of isolated persons as linear equation of isolation rate q and social distancing ratio x. In order to dynamically analyze the process of COVID-19 epidemic in seven countries by means of regression analyses of{lambda} , increasing rate of cumulative isolated persons(cases), IRCC, is proposed as practical index for the isolation rate q. IRCC is correlated with q in the form of q=C {middle dot} IRCC, where C is a normalizing coefficient. At first, C is formulated in two modes, one is simple and the other complex, under the constraint conditions by definition 0[&le;]x, q[&le;]1, which give allowable narrow path of C between upper and lower boundaries. Then, the dynamic locus of q-x relation is analyzed for each of seven countries including Japan and the United States using formulated isolation rate q, and characteristic q-x behavior for each country is derived. At the same time, it is shown that specific path selection of C gives almost same linear loci of q-x relation derived by mathematical sequential method imitating a bipedal walk. In addition, increasing rates of cumulative PCR tests, IRCT, for six countries are discussed in relation with IRCC, and are shown that IRCT contributes to the promotion of the isolation rate via IRCC.

In this paper, we estimate the reproductive number R0 of COVID-19 based on Wallinga and Lipsitch framework [11] and a novel statistical time delay dynamic system. We use the observed data reported in CCDCs paper to estimate distribution of the generation interval of the infection and apply the simulation results from the time delay dynamic system as well as released data from CCDC to fit the growth rate. The conclusion is: Based our Fudan-CCDC model, the growth rate r of COVID-19 is almost in [0.30, 0.32] which is larger than the growth rate 0.1 estimated by CCDC [9], and the reproductive number R0 of COVID-19 is estimated by 3.25 [&le;] R0 [&le;] 3.4 if we simply use R = 1 + r * Tc with Tc = 7.5, which is bigger than that of SARS. Some evolutions and predictions are listed.

There are standard computational and statistical techniques of forecasting the spread pattern of a pandemic. In this article, we are going to show how close the forecasts can be if we use a simple numerical approach that can be worked out using just a scientific calculator. Using a few recent data, short term forecasts can be found very easily. In this numerical technique, we need not make any assumptions, unlike in the cases of using computational and statistical methods. Such numerical forecasts would be nearly perfect unless the pandemic suddenly starts retarding during the period of the forecasts naturally or otherwise.