COVID-19 in Kerala: analysis of measures and impacts


 In the absence of an effective vaccine or drug therapy, non-Pharmaceutical Interventions are the only option for control of the outbreak of the coronavirus disease 2019, a pandemic with global implications. Each of the over 200 countries affected1 has followed its own path in dealing with the crisis, making it difficult to evaluate the effectiveness of measures implemented, either individually, or collectively. In this paper we analyse the case of the south Indian state of Kerala, which received much praise in the international media for its success in containing the spread of the disease in the early months of the pandemic, but is now in the grips of a second wave. We use a model to study the trajectory of the disease in the state during the first four months of the outbreak. We then use the model for a retrospective analysis of measures taken to combat the spread of the disease, to evaluate their impact. Because of the unusual aspects of the Kerala case, we argue that it is a model worthy of a place in the discussion on how the world might best handle this and other, future, pandemics.

Kerala reference model predicts a total of 7 deaths between 30 th January 2020 and 30 th May 98 2020 (compared with 9 reported). The model admits that a proportion of infected people may 99 not have been identified; and the 2,461 cumulative modelled cases (Table 1a)   Currently the state has 1,280 public hospitals and 2,062 private hospitals, giving a state-wide 111 total of 99,227 hospital beds, of which 4,961 are intensive care unit beds, with 2,481 112 ventilators 16 . As of 30 th May 2020, Kerala had not reached any of these thresholds. However, 113 it shows a worrying trend, with the number of cases increasing from day 99, indicating both 114 an increase in transmission rate as well as the intake of already-infected people into the state.

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Though the basic reproduction number ℛ 0 had dropped to 0.21 by 24 th March, a value well 116 below the threshold of one required for the number of cases to decline, it had risen far above 117 the threshold value by 20 th April, reaching 2.1 (close to its initial value 2.2 at the beginning of 118 simulation, see Supplementary Material, Table SM-3). This is consistent with recent reports 119 in mid-July, according to which community transmission was responsible for more newly-120 reported cases than the influx of infected people.
In the simulations which considered the impact of government measures, removing inhospital quarantine had the most effect, with only the removal of all modelled government 123 actions yielding a higher number of cases and deaths (see Table 1a and Figure 3 and Figure   124 SM-2). Removing out-of-hospital measures also had a high impact on both death and cases.
Due to the success of the initial actions taken by the government, with excellent response 136 from the community, only a small proportion of the community had the virus (2,461) by 30 th 137 May, according to the reference model. These low numbers do not come close to the rate 138 required for herd immunity (60% for an ℛ 0 of 2.5 17 , or 55% for an ℛ 0 of 2.2 which occurs 139 with track-and-trace) so that population immunity cannot be relied upon to slow infection.

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Without further decrease in the transmission rate, the outbreak, which was successfully 141 stalled, has the potential to return in full force. For comparison with other countries, a 142 snapshot at the end of May (Table 1b) shows a high level of success in Kerala, in keeping the 143 number of infections down. But it is evident from the inferred ℛ 0 that relaxation came too 144 early, and that longer-term control strategies are needed to prevent further escalation through 145 community transmission 18 .

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This work would not have been possible without the meticulous book-keeping followed by 149 all the health-care sectors of Kerala. The leadership response at various levels of government 150 was well-coordinated and prompt, and benefitted from a strong reputation built on a track 151 record of successfully dealing with previous health emergencies 19  The data and the model show remarkably low cases and fatalities (a total of three) till 7 th 159 May, when the lock-down was eased in districts with low case numbers and repatriation of 160 Keralites stranded outside the state began, which has been followed by a period of 161 exponentially growing infection, continuing into July.   The first part of the study period also demonstrates a cost-effective path that would be viable 215 for developing societies. Now, and in the wake of the pandemic, many analyses will be 216 undertaken to determine whether various governments took the right path to dealing with 217 COVID-19. Several strategies will no doubt be examined. The Kerala COVID-19 response is 218 worthy of consideration in the comparisons, not only because it flattened the curve in the 219 early days against all odds, but also, sadly, because of the secondary period of exponential 220 growth of cases in the subsequent, post-lock-down months.

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The Kerala COVID-19 model presented here is based on the generic class of susceptible-224 exposed-infected-recovered (SEIR) models, with additional partitioning of the population 225 into compartments dealing with hospitalised (h); out-of-hospital (o) and travel into state (δ).

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Symbols and definitions used here for all model variables are listed in

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In the model, the rate of change in the out-of-hospital, susceptible population (S o ) is 232 expressed as: where δ T = δ S + δ E + δ I + δ R .
The dynamics of the exposed population in the out-of-hospital compartment, E o , are given 246 by: in which a part of the out-of-hospital susceptible population S o is transferred to E o when 250 exposed to the disease, but prior to developing any symptoms, as represented by the term The rate of change in the infected, but out-of-hospital pool I o is computed as:

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where I o increases when people from the out-of-hospital exposed compartment become 259 infectious, at a rate p. The pool size also increases when travellers who do not test positive 260 for COVID-19 enter the state ((1 − μ se )δ I ). This pool decreases when people recover from the 261 disease at a rate r, the recovery rate, progressing to the out-of-hospital recovered population.

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The out-of-hospital infected population also decrease when members move to the The compartment S h , representing hospitalised people who have not been exposed to the 276 virus, is modelled as: in which the pool increases when travellers come into the state, and test positive for COVID- The change in the hospitalised, infected, population (I h ) is modelled as: 289 where this pool increases when the hospitalised exposed population becomes infectious expected to be severe enough to be detectable prior to patient mortality.

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Finally, the hospitalised recovered population (R h ) is modelled as: testing delays affect every afflicted area.

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The model is run from 30 th January 2020 to 30 th May 2020, assuming an initial population of The susceptible-infected-recovered (SIR) modelling framework, of which the model above is It is assumed here that the identification of people entering the state is complete, and that 339 testing is carried out on all people entering the state. This is unlikely to be true: there are 340 always limits to testing capacity, such that numbers entering the state above the limit cannot 341 be tested. This could have occurred prior to the travel ban implemented on 24 th March 2020.

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People entering the state may also go unidentified when checkpoints are avoided, or provide 343 incomplete information on travel history. The potential for a contagion to spread is often expressed as ℛ 0 , the basic reproduction 372 number, which represents the expected number of cases that might be infected by a single 373 case, given all the members of the population are susceptible 20 . The ℛ 0 number can be 374 computed given three of the SEIR parameters -λ, r and σas:   Reduced testing 405 To model reduced testing of people entering the state, a testing parameter a was introduced 406 such that the equations become: The testing rate a was 100% in the reference run and was then reduced to 10% in the 417 hypothetical case considered here, to represent a highly inefficient testing system.

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This presumes that in the reference run, the system in place is 100% effective, and that all 419 people entering the state are tested. Note that a lower testing rate in the reference run would 420 also change the fit, resulting in a higher value of λ and consequently a higher ℛ 0 number. carried out a simulation in which the initial ℛ 0 value was raised somewhat arbitrarily to 3, 450 and the subsequent ℛ 0 values were increased by the same proportion (see Table SM-3). We 451 also ran a simulation in which ℛ 0 of 3 was maintained throughout the simulation period, as      Eh Hospitalised exposed population. -

Eo
Out-of-hospital exposed population.