Center's Guideline Implemented To Stop Corona In Bihar, Home Department Order Issued ?Containment Efficiency And Control Strategies For The Corona Pandemic Costs Lecture On Anti Corona Preventive Measures Conducted In Mizoram

New Delhi: Guidelines issued by the Centre to prevent the spread of corona epidemic infections will be implemented in Bihar. Additional Chief Secretary of the Home Department, Chaitanya Prasad has issued an order in this regard on Friday. The authorities have been asked to ensure strict adherence to the guidelines. The guidelines were issued by the Ministry of Home Affairs on 23rd March to prevent the spread of coronavirus infection. The order will be effective by April 30. The state government has decided that the guidelines issued by the Ministry of Home Affairs will be applicable in Bihar. The Home Department has ordered all officials of the departments and regional administration to ensure strict compliance. The period of the guideline issued for not spreading the corona infection was ending on 31st March. The new guidelines issued by the Ministry of Home Affairs have given a number of guidelines on the increasing cases of the corona. It has been asked to conduct more and more tests to identify the infection, to identify the infected, and to detect the people who have been in contact. In public places, instructions have been issued to strictly adhere to the use of masks and social distancing. Other activities have not been allowed except the necessary services in the container zone. Further, the States have also been asked to take precautionary measures. New Delhi: Guidelines issued by the Centre to prevent the spread of corona epidemic infections will be implemented in Bihar. Additional Chief Secretary of the Home Department, Chaitanya Prasad has issued an order in this regard on Friday. The authorities have been asked to ensure strict adherence to the guidelines. The guidelines were issued by the Ministry of Home Affairs on 23rd March to prevent the spread of coronavirus infection. The order will be effective by April 30. The state government has decided that the guidelines issued by the Ministry of Home Affairs will be applicable in Bihar. The Home Department has ordered all officials of the departments and regional administration to ensure strict compliance. The period of the guideline issued for not spreading the corona infection was ending on 31st March. The new guidelines issued by the Ministry of Home Affairs have given a number of guidelines on the increasing cases of the corona. It has been asked to conduct more and more tests to identify the infection, to identify the infected, and to detect the people who have been in contact. In public places, instructions have been issued to strictly adhere to the use of masks and social distancing. Other activities have not been allowed except the necessary services in the container zone. Further, the States have also been asked to take precautionary measures. Also read:
Controlled-SIR model In the following we introduce the model. At a given time t we denote with \(S=S(t)\) the fraction of susceptible (non-infected) individuals and \(I=I(t)\) the fraction of the population that is currently ill (active cases). Infected individuals can either recover or die as a consequence of the infection, here we subsume both outcomes under \(R=R(t)\), which denotes hence the fraction of recovered or deceased individuals. Normalization demands \(S+I+R=1\) at all times. The continuous-time SIR model34 $$\beginaligned \tau \dotS = -gSI, \quad \quad \tau \dotI = (gS-1)I, \quad \quad \tau \dotR = I \endaligned$$ (1) describes an isolated epidemic outbreak characterized by a timescale \(\tau\) and a dimensionless reproduction factor g. Social and political reactions reduce the reproduction factor below its intrinsic (medical disease-growth) value, \(g_0\). We describe this functionality as $$\beginaligned g = \fracg_01+\alpha _X X, \qquad \quad X=1-S\,, \endaligned$$ (2) where we generalized standard epidemiological approaches to nonlinear incidence rates35,36. The reaction to the epidemic is taken to be triggered by the total fractional case count X (i.E. The sum of active, recovered and deceased cases), with \(\alpha _X\) encoding the reaction strength. In the Methods section we show how this functionality is validated by COVID-19 data, see also Fig. 2. In this view \(\alpha _X\) sums up the effects of an extended number of social processes and political action taking. Further below we will examine in addition strategies for which the response is based on the fraction of actual active cases, I. We note that containment due to a reduction in the reservoir of susceptible S, is of minor importance, given that COVID-19 infection cases are generally small with respect to the overall population size. The inverse functionality in Eq. (2) captures the law of diminishing returns, namely that it becomes progressively harder to reduce g when increasing social distancing. In this view, small reductions of g are comparatively easy, however a suppression by several orders of magnitude requires a near to total lockdown. We denote Eq. (1) together with (2) the controlled-SIR model. Key to our investigation is the observation that one can integrate the controlled-SIR model analytically, as shown in the Methods section, to obtain the phase-space relation $$\beginaligned I = \frac\alpha _X+g_0g_0\,X+ \frac1+\alpha _Xg_0\,\log (1-X)\,. \endaligned$$ (3) This relation, which we denote the ?XI representation?, is manifestly independent of the time scale \(\tau\). The medical peak load \(I_\mathrmpeak\) of actual infected cases is reached at a total fractional case count \(X= X_\mathrmpeak\), which is given by $$\beginaligned gS=1, \qquad \quad X_\mathrmpeak =\fracg_0-1g_0+\alpha _X\,, \endaligned$$ (4) For the case that \(\alpha _X=0\) (no control), \(X_\mathrmpeak\) reduces to the well-known result \(X_\mathrmpeak =(g_0-1)/g_0\). For finite \(\alpha _X\), \(I_\mathrmpeak\) is obtained from Eqs. (3) and (4), $$\beginaligned I_\mathrmpeak = \fracg_0-1g_0 + \frac1+\alpha _Xg_0\,\log \left( \frac1+\alpha _Xg_0+\alpha _X\right) \,. \endaligned$$ (5) For \(\alpha _X=0\), \(I_\mathrmpeak\) is sometimes called the ?herd immunity point?. The XI representation can be parameterized consequently either by \(g_0\) and \(\alpha _X\), as in Eq. (3), or indirectly by \(X_\mathrmpeak\) and \(I_\mathrmpeak\), which are measurable (modulo undercounting). In Fig. 1a an illustration of the XI-representation is given. For \(g_0=3\) and \(\alpha _X=0\) one has \(X_\mathrmpeak=2/3\) and \(I_\mathrmpeak\approx 0.3\). The total fraction of infected \(X_\mathrmtot\) is 94%, which implies that only about 6% of the population remains unaffected. Containment policies, \(\alpha _X>0\), reduce these values. Fig. 1a and Eq. (5) illustrate a sometimes encountered misconception regarding the meaning of the herd immunity point, which we have labeled simply \(I_\mathrmpeak\). The epidemic doesn?t stop at \(I_\mathrmpeak\) since infections continue beyond this point, albeit at a declining rate. Figure 2 Validation of controlling feedback loop. The fraction of newly infected at time t and at \(t-4\) is used to estimate the time dependent reproduction factor \(R_t = \overlineI_t / \overlineI_t-4\), when assuming a serial interval of four days (compare37). Note that a seven-day centred moving average \(\overlineI_t = \sum _s=t - 3^t+3 I_s\) is utilised. (a) \(R_t\) as a function of the relative cumulative number \(X / X_\mathrmpeak\) of cases. A fit to the same functional form as in Eq. (2) is given (grey line). (b) correlation of \(R_t\) and \(g_t\). The estimated reproduction factor \(R_t\) is compared to the effective reproduction factor \(g_t\) as defined in Eq. (2). In (a) and (b) only data between \(0.1 \le X / X_\mathrmpeak \le 2\) is shown, with the lower bound discarding the strong fluctuations in the early stages of the pandemic. The upper bound is used to define the termination of the first wave. XI representation of COVID-19 outbreaks In Fig. 1b,c we show for a representative choice of countries, regions and cities that COVID-19 outbreaks are described by the controlled-SIR model to an remarkable degree of accuracy. For the analysis presented in Fig. 1b,c we divided, as described in the Methods section, the official case counts by the nominal population size of the respective region or country. Seven-day centered averages are performed in addition. The country- and region-specific XI representations are then fitted by Eq. (3). The fact that the outbreaks are well described by the model, independently of the size of the country, region or city, evidences the applicability of the controlled-SIR model. It has been widely discussed that official case counts are affected by a range of factors, which include the availability of testing facilities and the difficulty to estimate the relative fraction of unreported cases38,39. For example, as of mid-March 2020, the degree of testing for COVID-19, as measured by the proportion of the entire population, varied by a factor of 20 between the United States (340 tests per million) and South Korea (6100 tests per million)40. The true incidence might be, according to some estimates41 higher by up-to a factor of ten than the numbers reported in the official statistics as positive. Case counts enter the XI representation in both the \(x-\) and \(y-\) axis. Scaling both I and X with a constant factor allows therefore to compensate for the undercounting problem. At the same time the control strength \(\alpha _X\) needs to be rescaled, a procedure implicitly implemented for the fits shown in Fig. 1b,c. The XI framework is in this sense robust. Renormalization becomes however invalid if the undercounting of infection cases changes abruptly at a certain point during the epidemics, f.I. As a result of substantially increased testing. We will come back to this point further below. A fundamental change in the strategy followed by the government, e.G. From laissez faire to restrictive, would lead likewise to a change in \(\alpha _X\), which is not captured in the current framework. In the analysis presented in Fig. 1 daily case counts were taken as proxies for the number (relative fraction), of infected individuals \(I=I(t)\). This assumption holds only up to a rescaling factor, which implies that the \(g_0\) extracted for a given country or region is not the native, but an effective reproduction factor. To see this consider, e.G., the initial slope, \(I\sim X(g_0-1)/g_0\), as given by Eq. (15). Rescaling daily case counts in order to obtain estimates for the number of infected individuals changes the slope and hence \(g_0\). Given that the appropriate rescaling of daily case counts can only be estimated, and that we are interested here in a simple but accurate effective modeling of COVID-19 outbreaks, and not in the extraction of the native reproduction factor, we did not pursue this route. In Table 1 we present for a number of countries and regions the obtained effective growth factors \(g_0\) and the corresponding doubling times \(\tau _2\), where \(\tau _2=\log (2)/\log (g_0)\) defines the number of time units \(\tau\) needed to double case numbers. As expected, according to the description above, one finds that the values of \(g_0\) are substantially lower than the consensus estimates 2-3 for the native reproduction number42,43,44,45,46. The observed doubling times \(\tau _2\) are however retained when adapting the effective time scale \(\tau\) accordingly. For a robustness check we evaluated the parameters of the controlled-SIR model assuming that only a fraction f of the nominal population of the country or region in question could be potentially infected, possibly due to the presence of social or geographical barriers to the disease spreading. Only marginal differences were found for \(f=1/3\). The data presented in Table 1 suggest most countries followed in the first wave of the COVID-19 pandemic strict containment policies, as measured in terms of the CEI index. This insight is of particular relevance for the discussion of the costs incurring for the various containment strategies presented further below. Data collapse for COVID-19 Given that the XI representation is determined solely by two quantities, \(X_\mathrmpeak\) and \(I_\mathrmpeak\), universal data collapse can be attained by plotting field data normalized with regard to the respective peak values, viz by plotting \(I/I_\mathrmpeak\) as a function of \(X/X_\mathrmpeak\). It is remarkable, to which degree the country- and region specific official case counts coincide in relative units, see Fig. 1c. It implies that the controlled-SIR model constitutes a faithful phase-space representation of epidemic spreading subject to socio-political containment efforts. Table 1 COVID-19 containment efficiency index. Asymmetry of up/down time scales For the controlled SIR model an explicit analytic expression for the \(X-I\) phase space representation can be derived, as given by Eq. (3), but not for the complete timeline X(t) and I(t). Exploiting the fact that case counts are generally small with respect to the population for real-world epidemic outbreaks, the universal relation $$\beginaligned \frac\text time \text down \text from \text the \text peak \text time \text up \text to \text the \text peak = 2g_0-1 \endaligned$$ (6) between the time the outbreak needs to retreat from the peak, and to reach it in first place, can however be found, as shown in the Methods section. Interestingly, the ratio of down-/ and up-times is independent of the control strength \(\alpha _X\) (if and only if \(X\ll 1\)), which suggests that Eq. (6) is valid for epidemic outbreaks in general. For COVID-19, typical values of the effective \(g_0\) are of the order of 1.2-1.3, as listed in Table 1, which implies that outbreaks take of the order of 40-60% longer to retreat than to ramp up. Containment efficiency index The control strength \(\alpha _X\) enters the reproduction factor as \(\alpha _X X\), see Eq. (2). Data collapse suggest that regional and country-wise data is comparable on a relative basis. From \(\alpha _X X=(\alpha _X X_\mathrmpeak)(X/X_\mathrmpeak)\) it follows that \(\alpha _X X_\mathrmpeak=\alpha _X(g_0-1)/(g_0+\alpha _X)\) is a quantity that measures the combined efficiency of socio-political efforts to contain an outbreak. Dividing by \(g_0-1\) results in a normalized index, the ?Containment Efficiency Index? (CEI): $$\beginaligned \text CEI = \frac\alpha _X X_\mathrmpeakg_0-1 = \frac\alpha _Xg_0+\alpha _X\,, \endaligned$$ (7) with \(\text CEI \in [0,1]\). The index is unbiased, being based solely on case count statistics, and not on additional socio-political quantifiers. Our estimates are given in Table 1. The values for the evaluated regions/ countries are consistently high, close to unity, the upper bound, indicating that the near-to-total lockdown policies implemented by most countries have been effective in containing the spread of COVID-19. A somewhat reduced CEI value is found for the particularly strongly affected Italian region of Bergamo. For South Korea the CEI is so high that its deviation from unity cannot be measured with confidence. Figure 3 Control of epidemic peak. (a) Shown is the timeline of actual infected cases during an epidemic outbreak with an intrinsic reproduction factor of \(\rho _0=3.0\) defined in the discrete model, which is close to COVID-19 estimates47. The simulation is obtained by iterating Eq. (9), with one iteration corresponding to two weeks, taken as the average duration of the illness. Short-term control, when responding to the actual number of cases, see Eq. (8), is able to reduce the peak strain on the hospital system, but only by prolonging substantially the overall duration. Long-term control, which takes the entire history of the outbreak into account, is able to reduce both the peak and the duration of the epidemic. (b) Increasing testing by a factor two (arrow), reduces the undercounting factor which increases, in turn, the effective response strength for both, the peak number of actual cases and the duration of the outbreak. Here \((\alpha _X,\alpha _I)=(400,0)\,/\,(0,400)\) has been used respectively for long- / short-term control. Long-term versus short-term control So far, in Eq. (2) it was assumed that society and policy makers react to the total case count of infected X. This reaction pattern, which one may denote as ?long-term control?, describes field data well. It is nevertheless of interest to examine an alternative, short-term control: $$\beginaligned g = \left\ \beginarraylcl g_0/(1+\alpha _I I) && \text(short-term) \\ g_0/(1+\alpha _X X) && \text(long-term) \\ \endarray\right. \endaligned$$ (8) For short-term control the relevant yardstick is given by the actual case number of infected I. In reality, people will react to officially reported case counts, which are affected by the undercounting problem. For the terms \(\alpha _I I\) and \(\alpha _X X\) in Eq. (8) this corresponds to a renormalization of reaction parameters \(\alpha _I\) and \(\alpha _X\). Figure 4 Cost of epidemic control strategies including value of life. Shown are the costs in terms of GDP\(_\mathrmp.C.\), for long-term and short-term control, as defined by Eq. (8), both as a function of \(\alpha _X\) and the CEI values (7), as indicated by the additional axis at the bottom. Given are the costs incurring from social distancing, Eq. (10) with \(m=0.25\) (lower panel), the pure medical costs with value of life costs (middle panel), and the sum of social and medical costs (upper panel). It is assumed that the containment policy switches from mass control to individual tracking when the fraction of actual cases \(I_t\) drops below a threshold of \(I_\mathrmmin=10^-5\). The starting \(I_0=2\cdot 10^-5\). Both control types, short- and long-term, can be employed either for the continuous-time SIR model, Eq. (1), or for the discrete-time variant, $$\beginaligned I_t+1 = \rho _t I_t (1-X_t), \quad \quad X_t = \sum _k=0^\infty I_t-k\,, \endaligned$$ (9) The time-dependent reproduction factor has been denoted here as \(\rho _t\), in order to make clear that discrete times are used. Short- and long-term control is then equivalent to \(\rho _t=\rho _0/(1+\alpha _I I)\) and \(\rho _t=\rho _0/(1+\alpha _X X)\). One time step corresponds for the discrete-time SIR model to the mean infectious period. The simulations of Eq. (9) presented in Fig. 3 illustrate the capability of short-term and long-term reaction policies to contain an epidemic. While both strategies are able to lower the peak of the outbreak with respect to the uncontrolled (\(\alpha _X=\alpha _I=0\)) case, the disease will become close to endemic when the reaction is based on the actual number of cases, \(I_t\), and not on the overall history of the outbreak. Also included in the lower panel of Fig. 3 is a protocol simulating an increase of testing by a factor of two. Here \((\alpha _X,\alpha _I)=(400,0)\) and \((\alpha _X,\alpha _I)=(0,400)\) have been used as the starting reaction strengths, respectively for long- and short-term control, which are increased by a factor of two when testing reduces the undercounting ratio by one half. One observes that long-term control is robust, in the sense that increased testing contributes proportionally to the containment of the outbreak. Strategies reacting to daily case number are in contrast likely to produce an endemic state. The framework developed here, Eqs. (1) and (2), describes mass control strategies, which are necessary when overly large case numbers do not allow to track individual infections. The framework is not applicable once infection rates are reduced to controllable levels by social distancing measures. The horizontal ?tail? evident in the data from South Korea in Fig. 1b can be taken as evidence of such a shift from long-term mass control to the tracking of individual cases. Costs of controlling the COVID-19 pandemic As shown above, the controlled-SIR model allows for a faithful modeling of the entire course of an isolated outbreak. We apply it now to investigate how distinct policies and societal reaction patterns, as embedded in the parameter \(\alpha _X\), influence the overall costs of the epidemic. This is an inter-temporal approach since the cost of restrictions today to public life (lockdowns, closure of schools, etc.) must be set against future gains in terms of lower infections (less intensive hospital care, fewer deaths). Four elements dominate the cost structure: (i) The working time lost due to an infection, (ii) the direct medical costs of infections, (iii) the value of life costs, and (iv) the cost related to ?social distancing?. The first three are medical or health-related. All costs can be scaled in terms of GDP per capita (GDP\(_\mathrmp.C.\)). This makes our analysis applicable not only to the US, but to most countries with similar GDP\(_\mathrmp.C.\), e.G. Most OECD countries. Overall cost estimates The cost estimates, which are given in detail in the Supplementary Information, can be performed disregarding discounting. With market interest rates close to zero and the comparatively short time period over which the epidemic plays out, a social discount rate between 3% and 5% would make little difference over the course of one year48. Total health costs \(C^\mathrmmedical\) incurring over the duration of the epidemic are proportional to the overall fraction \(X_\mathrmtot=X_t\rightarrow \infty \) of infected, with a factor of proportionality k. We hence have \(C^\mathrmmedical =kX_tot\). We estimate \(k\approx 0.305\) in terms of GDP\(_\mathrmp.C.\) when all three contributions (working-time lost, direct medical cost, value of life) are taken into account, and \(k\approx 0.14\) when value of life costs are omitted. The economic costs induced by social-distancing measures, \(C^\mathrmsocial\), depend in a non-linear way on the evolution of new cases (short-term control) or the percentage of the population infected (long-term control). To be specific, we posit that the reduction of economic activity is percentage-wise directly proportional to the relative reduction in the reproduction factor49, viz to \((\rho _0-\rho _t)/\rho _0\): $$\beginaligned C^\mathrmsocial = \sum _I_t>I_\mathrmmin \text c_t^\mathrms, \quad \quad \text c_t^\mathrms = m\ \frac\rho _0-\rho _t\rho _0\,\frac252\,, \endaligned$$ (10) where 2/52 is the per year fraction of 2-week quarantine period. The epidemic is considered to be under control when the fraction of new infections \(I_t\) falls below a minimal value \(I_\mathrmmin\). As detailed out in the Supplementary Information, a comprehensive analysis yields \(m\approx 0.25\) in terms of GDP\(_\mathrmp.C.\). Note that the ansatz Eq. (10) holds only when mass control is operative, viz when large case numbers do not allow the tracking of individual infections. Once k and m are known, one can compare the total costs incurring as the result of distinct policies by computing the sum of future costs for different values for \(\alpha _X\) in Eq. (2). This is illustrated in Fig. 4 with the value of life costs included (\(k=0.305\)), and in Fig. 5, without value of life costs (\(k=0.14\)). Given are the total cumulative costs for the two strategies considered, long-term and short-term control, both as a function of the respective implementation strength, as expressed by the value of \(\alpha _X\) and \(\alpha _I\). The middle panel of Fig. 4 shows that a society focused on short-term successes will incur substantially higher medical costs, because restrictions are relaxed soon after the peak. By contrast, if policy (and individual behavior) is influenced by the total number of all cases experienced so far, restrictions will not be relaxed prematurely and the medical costs will be lower for all values of \(\alpha _X\). The bottom panel shows the social distancing costs as a fraction of GDP\(_\mathrmp.C.\), which represent a more complicated trade-off between the severity of the restrictions and the time they need to be maintained. If neither policy, nor individuals react to the spread of the disease (\(\alpha _X=0\)) the epidemic will take its course and costs are solely medical. This changes as soon as society reacts, i.E. As \(\alpha _X\) increases. Social distancing costs increase initially (i.E. For small values of \(\alpha _X\)), somewhat stronger for the long-term than for the short-term reaction framework. The situation reverses for higher values of \(\alpha _X\) and \(\alpha _I\) with \(\alpha _X, \alpha _I \approx 30\) being the turning point. From there on, the distancing cost from a long-term based reaction falls below that of the short-term strategy. The sum of the two costs is shown in the uppermost panel. For large values of \(\alpha _X\), \(\alpha _I\) short-term policies result in systematically higher costs. Figure 5 Cost of epidemic control without value of life. As in Fig. 4 (bottom panels are identical), but without the value of life costs. A long-term strategy with intermediate reaction strength is costlier than a hands-off policy. Supplementary Figure 1 of the Supplementary Information shows that short-term control cannot explain observed COVID-19 outbreaks per se. Our estimates for the incurring costs suggest that economic cost considerations may have caused countries to follow predominantly long-term control strategies during the first wave of the COVID-19 outbreak.
Facebook Twitter Pinterest WhatsApp Lunglei Battalion of Headquarter 23 Sector Assam Rifles under the aegis of Headquarter Inspector General Assam Rifles (East), conducted a lecture on ?Anti Corona Preventive Measures? at Siahatla ? I Community Hall by Lunglei Battalion on Saturday. A total of 36 civilians attended the same. The aim of the lecture was to spread awareness about preventive measures against COVID-19 and imparting knowledge regarding social distancing and necessary precautionary measures. Facebook Twitter Pinterest WhatsApp
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