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Asia-Pacific Journal of Public Health, November 14, 2011
Pandemic Influenza and Health System Resource Gaps in Bali: An Analysis Through a Resource Transmission Dynamics Model
Wiku Adisasmito, Benjamin M. Hunter, Ralf Krumkamp, Kamal Latief, James W. Rudge, Piya Hanvoravongchai, and Richard J. Coker, MD
Asia-Pacific Journal of Public Health, November 14, 2011
Pandemic Influenza and Health System Resource Gaps in Bali: An Analysis Through a Resource Transmission Dynamics Model
Wiku Adisasmito, Benjamin M. Hunter, Ralf Krumkamp, Kamal Latief, James W. Rudge, Piya Hanvoravongchai, and Richard J. Coker, MD
Asia-Pacific Journal of Public Health, November 14, 2011
Pandemic Influenza and Health System Resource Gaps in Bali: An Analysis Through a Resource Transmission Dynamics Model
Wiku Adisasmito, Benjamin M. Hunter, Ralf Krumkamp, Kamal Latief,
James W. Rudge, Piya Hanvoravongchai, and Richard J. Coker, MD
Asia-Pacific Journal of Public Health XX(X) 1 –21
© 2011 APJPH Reprints and permission:
sagepub.com/journalsPermissions.nav DOI: 10.1177/1010539511421365 http://aph.sagepub.com
1Universitas Indonesia, Depok, Indonesia
2London School of Hygiene & Tropical Medicine
3Hamburg University of Applied Sciences, Hamburg, Germany
Corresponding Author:
Richard J. Coker, Communicable Disease Policy Research Group, London School of Hygiene & Tropical Medicine, Mahidol University, Satharanasukwisit Building, 420/1 Rajvithi Road, Bangkok 10400, Thailand
Email: [email protected]
Pandemic Influenza and Health System Resource Gaps in Bali:
An Analysis Through a Resource Transmission Dynamics Model
Wiku Adisasmito, PhD
1, Benjamin M. Hunter, MSc
2, Ralf
Krumkamp, MSc
3, Kamal Latief, MEpid
1, James W. Rudge, PhD
2, Piya Hanvoravongchai, PhD
2, and Richard J. Coker, MD
2Abstract
The failure to contain pandemic influenza A(H1N1) 2009 in Mexico has shifted global attention from containment to mitigation. Limited surveillance and reporting have, however, prevented detailed assessment of mitigation during the pandemic, particularly in low- and middle-income countries. To assess pandemic influenza case management capabilities in a resource-limited setting, the authors used a health system questionnaire and density-dependent, determinis- tic transmission model for Bali, Indonesia, determining resource gaps. The majority of health resources were focused in and around the provincial capital, Denpasar; however, gaps are found in every district for nursing staff, surgical masks, and N95 masks. A relatively low patho- genicity pandemic influenza virus would see an overall surplus for physicians, antivirals, and antimicrobials; however, a more pathogenic virus would lead to gaps in every resource except antimicrobials. Resources could be allocated more evenly across Bali. These, however, are in short supply universally and therefore redistribution would not fill resource gaps.
Keywords
Bali, health system resources, Indonesia, pandemic influenza, resource gaps, mathematical model
Introduction
In March 2009, outbreaks of influenza-like illness began to appear in otherwise healthy young adults in Mexico.1 By April, the virus had spread to the United States and was identified, both
in patients there and in samples from Mexico, as a novel influenza A subtype,2 pandemic influ- enza A(H1N1) 2009 (denoted here as H1N1v). Rapidly spreading both within North America and internationally, a pandemic was declared by the World Health Organization on June 11, 2009, by which time almost 29 000 cases had been reported across 74 countries.3
Completed just prior to the emergence of the pandemic subtype in Mexico, an evaluation of national plans for pandemic influenza in Latin America showed Mexico to be one of the better prepared Latin American countries, although no country in the region had considered contain- ment.4 Yet the virus spread rapidly and it was not until late June 2009, months after the first cases had begun to appear, that emergency laws and wide-ranging public facility closures were implemented in an attempt to reduce transmission.5 The experience of North America suggests that containment may not be a feasible strategy to pursue and so research assessing pandemic influenza preparedness may need to assume an emergent subtype will advance quickly to assume pandemic status.
Transmission models have been widely used to inform pandemic influenza planning and policy; however, until recently many were used to assess the feasibility of containing a novel emergent influenza subtype.6-8 The failure of policies based on these models has renewed inter- est in the use of models in mitigation planning, such as critical care demand.9-11 These have, however, been limited to high-income countries, reflecting, in part, ready access to information on health system resources and data on population contact patterns that are needed for adequate modelling.12,13 Gaps in operational capacity have previously been determined as a measure of pandemic influenza preparedness in Thailand at a provincial level.14,15 Our research builds on this previous work by introducing population density as a determinant of transmission and simulating spread at a district level for Bali, Indonesia. Bali, in addition to being a site of previ- ous human cases of avian influenza, stands as one of the few places in the world where a full- scale exercise to contain a suspected outbreak of a high-pathogenicity influenza virus has been undertaken.16 The availability of detailed health system resource data for Bali will allow resource gaps to be determined in order to support future pandemic influenza preparedness planning.
Methods
The Transmission Model
The model we used to describe pandemic influenza outbreak progression was based on a deter- ministic SEAIR (susceptible, exposed, asymptomatic, infectious, recovered) model described in detail elsewhere.14 The model had been parameterized for pandemic H1N1v and was run sepa- rately for each district (assuming no mixing between districts) in MS Excel (Microsoft Corporation, Redmond, WA). We altered the daily contact rate between individuals to reflect the differences in population density between the districts of Bali. Individuals in more densely populated districts were assumed to have higher contact rates whereas individuals in less densely populated districts were assumed to have lower contact rates (Table A2 in the appen- dix). Infected cases were stratified by disease severity and individuals in each disease severity strata were divided into a number of treatment strata.
Pandemic Scenarios
Estimates for H1N1v-associated hospitalization and mortality vary widely and most data are from developed countries.17-19 We explored 2 different scenarios in the research by using 2 sets of hospitalization and mortality rates for H1N1v pandemic influenza: lower (scenario 1) and
higher (scenario 2; Table A2 in the appendix). Other than the proportion of cases requiring hospitalization and the mortality rates for different treatment strata, the virus transmission dynamics simulated in the 2 scenarios were identical.
Resource Calculator
There is a lack of data from developing countries on resource use for the isolation and treatment of cases of pandemic H1N1v. Instead, average resource requirements were based on estimates formed by Putthasri et al,15 who collected data on the treatment of H5N1 avian influenza from the retrospective analysis of H5N1 case notes in Thailand and interviews with clinical and sur- veillance personnel involved in the management of cases. The transmission model described previously was linked to a resource calculator by Krumkamp et al,14 to determine resource needs during the simulated outbreak (details of the resource calculator are provided in the appendix).
We expanded the resources under investigation to explicitly determine the need and calculate gaps for hospital beds, mechanical ventilators, antimicrobials, and antivirals, using bed occu- pancy and resource depletion rates (Table A4 and Table A5 in the appendix). Needs for person- nel, mechanical ventilators, and hospital beds were calculated at the peak of the simulated outbreak whereas needs for personal protective equipment (PPE), antivirals, and antimicrobials were based on the total number of cases in each of the specific treatment strata.
Health System Resources
Information on specific health system resources in Bali was collected in a questionnaire as part of the AsiaFluCap project.20 This included hospital- and district-level data on a range of resources, though data for numbers of physicians, nursing staff, and surveillance and rapid response teams (SRRT) were only collected at a district level to account for staff registered at multiple facilities. Other resources include PPE, antivirals, antimicrobials, hospital beds, and mechanical ventilators. Hospital resources, both public and private, within a district were com- bined with district health authority resources to give aggregated district data. Data for health resources were mapped to Bali using ArcGIS 9.2 (ESRI Inc, Redlands, CA) at a district and hospital level.
Gaps in Operational Capacity
Resource gaps/surpluses were calculated by subtracting resource needs from available resources.
Available resources were assumed to be the surge capacity within Bali—resources that can be taken from other uses during exceptional circumstances. In comparable contexts this has been assumed to be 12% of total resources (an aggregation of the resources of all hospitals and the health authority),15 the other 88% is assumed to be unavailable. Antivirals and SRRT are the only exception to this as they are assumed to be a resource dedicated to the treatment of pan- demic influenza.
Results
Pandemic Influenza Without Intervention
The proportion of the population infected would vary between districts, reflecting the population size and density of each district—these are detailed in Table A6 in the appendix. In both sce- narios, districts with higher population densities (Badung, Denpasar, Gianyar and Klungkung)
Table 1. Pandemic Influenza in Each of the 9 Districts of Bali if There Is No Interventiona
District R0
Duration (Days)
Peak (Days)
Final Number of Symptomatic
Infections
Population Infected (%)
Total
Critically Ill Deaths Panel A
Badung 1.42 145 83 116 859 43.0 334 134
Bangli 1.32 161 92 52 622 36.0 150 60
Buleleng 1.32 189 102 151 359 36.0 432 173
Denpasar 1.47 139 80 186 983 46.5 534 214
Gianyar 1.47 133 78 137 003 46.5 391 157
Jembrana 1.32 166 94 62 372 36.1 178 71
Karangasem 1.32 177 98 95 046 36.0 272 109
Klungkung 1.37 140 83 45 059 39.4 129 51
Tabanan 1.32 178 98 100 519 36.0 287 115
Smallest 1.32 133 78 45 059 36.0 129 51
Largest 1.47 189 102 186 983 46.5 534 214
Panel B
Badung 1.42 145 83 119 610 44.0 2563 1128
Bangli 1.33 160 92 53 887 36.9 1155 508
Buleleng 1.33 188 101 155 028 36.9 3322 1462
Denpasar 1.47 138 79 191 038 47.5 4094 1801
Gianyar 1.47 132 77 139 990 47.5 3000 1320
Jembrana 1.33 165 93 63 865 36.9 1369 602
Karangasem 1.33 176 97 97 341 36.9 2086 918
Klungkung 1.37 139 83 46 181 40.4 990 435
Tabanan 1.33 177 98 102 941 36.9 2206 971
Smallest 1.33 132 77 46 181 36.9 990 435
Largest 1.47 188 101 191 038 47.5 4094 1801
aScenario 1 (panel A) assumes lower hospitalization and mortality rates than scenario 2 (panel B).
could expect to suffer larger outbreaks (a greater proportion of the population is infected) that are shorter in duration (Table 1). A pandemic influenza virus associated with increased rates of mortality (scenario 2) would cause a higher proportion of cases to become critically ill and there would be many more deaths as a result of infection. In comparison with a less pathogenic virus (scenario 1), there would be an almost 7-fold increase in the number of critically ill cases in each district, whereas the number of deaths due to influenza infection would be 7.5 times larger. The duration of the outbreak and the proportion of people affected would remain largely unchanged by the increased pathogenicity.
Resource needs
A more pathogenic influenza virus (scenario 2) would require a greater level of all resources than a less pathogenic virus (scenario 1; see Table A7 in the appendix). Combining peak require- ments for the treatment of critically ill patients in all districts during scenario 1 shows that more than 500 hospital beds and approximately 140 mechanical ventilators would be needed (15 and 4 per 100 000, respectively), while this would increase 6-fold to more than 3700 hospital beds and more than 1000 ventilators for scenario 2 (110 and 31 per 100 000, respectively). Relative increases for antivirals and N95 masks are similar whereas the increase in requirements for other resources is smaller.
Health System Resources
The majority of health resources in Bali are concentrated on the south of the island, in and around Denpasar, though the highest per capita rates of SRRT, antivirals, and N95 masks are not found in Denpasar (Figures 1 and 2). Within each district, resources are generally highly focused in the major health facility of the primary settlement. The outermost districts (farthest from Denpasar) Buleleng, Karangasem, and Jembrana have much lower proportions of much of the island’s health resources (eg, 21% of hospital beds and 21% of ventilators), despite contain- ing more than one third of the island’s population. The referral hospital for suspected cases of pandemic influenza in Bali is situated in Denpasar and contains the largest numbers of most resources for the treatment and control of pandemic influenza in the province. Denpasar is also the site of 3 secondary-level hospitals and a fourth one is found in the Bangli district.
Gaps in Operational Capacity
Gaps in operational capacity would be expected in Bali for all resources except physicians, antimicrobials, and antivirals in scenario 1 and all resources except antimicrobials in scenario 2 (Table 2).
There is some variation between districts, for example, Bangli, Denpasar, and Klungkung would be expected to have surpluses of hospital beds in scenario 1, though in scenario 2 there would be a shortage of hospital beds in all districts (Figure 3). Ventilators would be in short sup- ply in both scenarios, though this shortage would be much greater in scenario 2. The health outcome of ventilator shortages was measured through deaths due to lack of ventilators: almost 330 across Bali in scenario 1 and approaching 2300 in scenario 2. Although antiviral stocks are sufficient in all districts to treat every critically ill influenza case for scenario 1, this would only be the case for Bangli and Karangasem in scenario 2.
Discussion
This research shows that health system resource gaps are likely to exist in many districts across Bali in the event of pandemic influenza. This reflects similarities to resource shortages identified in Thailand.15 The scale of resource requirements leading to these gaps would depend on the pathogenicity of the influenza subtype. For example, a more pathogenic influenza virus would increase the proportion of cases requiring hospitalization and thus increase the needs for physi- cians, nursing staff, hospital beds, and ventilators. Subsequent resource gaps would have broader public health implications with shortages in the numbers of hospital beds and ventilators leading to an increase in number of deaths.
Further public health implications can be inferred from gaps in other health system resources and one particular concern is the shortage in PPE for health care workers (HCWs). This would potentially increase transmission within hospitals, drive up the perceived threat of infection, and provoke HCW absenteeism.21 Qualitative studies in Australia and the United Kingdom high- lighted the perceived importance of adequate PPE supply to HCW22,23; however, absenteeism is highly context specific and further research would be needed to determine the effect in a resource- limited environment such as Bali. Even discarding unforced absenteeism, adherence to guide- lines for PPE is not guaranteed and infection of HCWs could lead to HCW absenteeism though illness.24 It is not beyond reason that during an influenza pandemic in Bali the overstretched, underresourced health care workforce may be tempted to ignore guidelines.25
Patients can be expected to seek treatment at hospitals with perceived surpluses or the smallest gaps, assuming equal access to these. Given the current distribution of health system resources in
Figure 1. Maps of selected health system resources in Bali (chosen to highlight institutional capacity) against the population density of the districts
A, Hospitals. B, Hospital beds. C, Ventilators (adult and paediatric). Denpasar has been expanded to aid visualization.
Figure 2. Maps displaying the distribution of district level health system resources per 100,000 inhabitants
A, Physicians. B, Nursing staff. C, Surveillance and rapid response team (SRRT). D, Antivirals. E, Surgical masks. F, N95 masks.
Bali, it would be reasonable to expect a migration of pandemic influenza cases to the secondary and tertiary hospitals in Denpasar and Bangli. “Mismatching” (districts with more resources lying adjacent to those with less) appears to be present, for example, Denpasar with Badung, or Bangli with Karangasem; however, no provision was made for it in the model. It is very likely that because of the “mismatching” of certain resources, patients living in resource-limited districts may, in real- ity, seek health care at (or be referred to) health facilities in adjacent, relatively resource-rich dis- tricts. The movement of patients may affect transmission as was seen during the 2003 severe acute respiratory syndrome (SARS) epidemic in Toronto, where transmission within and between hospi- tals occurred through the movement of patients with undiagnosed SARS infection.26
Tourists were ignored because of the seasonal nature of tourism and relative short durations of stay (normally less than the duration of the outbreak). However, tourists can contribute to transmission and are often used as an important form of surveillance.27 The exclusion of tourists from the study underestimated population size for each district, thereby underestimating popula- tion density (a determinant of transmission). Access to health care was not addressed either, and
Table 2. A Summary of Gaps/Surpluses for Selected Health System Resources During Pandemic Influenza in Bali, as a Total for All Districtsa
Scenario 1 Scenario 2
Human resources
Physicians 151 −589
Nurses −3943 −5264
SRRT −8460 −8573
PPE
Surgical masks −9 000 231 −10 750 698
N95 masks −74 912 −168 956
Treatment
Hospital beds −11 −3127
Ventilators −130 −1112
Amoxicillin 521 410 335 672
Co-trimoxazole 44 791 −190 024
Antivirals 89 305 −52 185
Abbreviations: SRRT, surveillance and rapid response team; PPE, personal protective equipment.
aA positive total reflects an overall surplus of the resource in Bali, whereas a negative total reflects a resource gap.
it was assumed that all hospitals within a district were accessible to all cases within that district.
Although many people may not be able to access health care at the private hospitals in Bali, twice as much national GDP is spent on private rather than public health care in Indonesia and we felt this warranted the inclusion of private hospitals.28
The model, like any other, was limited by the parameter assumptions and simplifications used to program it, such as the assumption of 12% surge capacity in all of the resources for health under investigation. Very limited data are available on surge capacity in Bali (or indeed else- where). Homogenous mixing of populations was also assumed in the model, despite evidence for age-dependent contact rates and social mixing patterns in Europe.13 Although it is possible that there are some differences in contact rates between age groups in Southeast Asia, the exact degree to which European patterns can be applied is at present unknown. Geographical barriers to transmission were also ignored and it is possible transmission was overestimated in certain districts such as Klungkung (because of its 3 islands) or those containing mountainous areas.
The model also had no link between PPE and transmission or the numbers of physicians and nursing staff with deaths. Surgical and N95 masks have been shown to be effective in reducing transmission,29 while it is logical that insufficient physicians or nursing staff to manage the criti- cally ill could increase the number dying as a result of infection. In addition to a lack of feedback of PPE shortages in the model, PPE needs are calculated assuming 100% adherence of HCWs to hospital PPE usage policy, which is unlikely.24 If adherence is less than 100%, the calculated need for PPE in the model would be an overestimation.
Finally, preexisting immunity to pandemic influenza was not considered in the transmission model used in the project. Some preexisting immunity to the current pandemic influenza has been shown in older age groups, probably because of exposure to previous influenza pandem- ics.30 Depending on the prevalence of cross-reactive antibodies to the pandemic virus in the population, a proportion of the population in each district may suffer less severe disease than expected. Although a significant proportion of cases were assumed to be asymptomatic, it is still possible that figures for the number of critically ill and possibly even mild cases would have been overestimated. Future transmission models could account for this by stratifying by age or incorporating a proportion of the population with reduced rates of severe illness.
Figure 3. The geographical distribution of gaps in the operational capacity for Bali during scenario 1 (left) and scenario 2 (right)
A, Hospital beds. B, Ventilators. C, Antiviral doses.
Investment in health system resources should focus on increasing the operational capacity of resources on the island and the growing focus on mitigation during pandemics supports this.
There are particularly large resource gaps to consider for ventilators, nursing staff, PPE, and hospital beds. Although current levels of antivirals are sufficient for the treatment of critically ill cases during an outbreak of a less pathogenic subtype, health authorities should recognize that shelf-life is finite and the risks associated with relying on the susceptibility of the pandemic virus to oseltamivir.31 Finally, although policies for vaccination were not explored in the research, there is likely to be much discussion in the future about increasing vaccine stocks for developing countries in preparation for the next pandemic.32
It is clear from the gaps in provincial health system resources that resources are insufficient to stop all preventable deaths in an influenza pandemic. Current policy is for the transfer of pan- demic influenza cases in Bali to the referral hospital in Denpasar. Capacity in this facility is, however, insufficient to manage all predicted hospitalized cases in the province. If a pandemic influenza subtype displays higher pathogenicity, tertiary and secondary public hospitals in Denpasar and Bangli may be highly constrained by resource shortages. There are advantages and
disadvantages to the centralization of resources in Denpasar and to support evidence-based deci- sion making, these should be considered when health system resource allocation occurs in future.33
Although we have addressed the extent of resource gaps for pandemic influenza mitigation in Bali and whether resources can be better allocated, further research is needed to elucidate the cost and feasibility of filling gaps in resource-limited settings such as Bali. The development of frameworks to assess surge capacity in the health systems of Southeast Asian counties would also benefit studies on operational capacity in the region. In addition, there have, to date, been no published studies of contact rates in Southeast Asia that would, among other things, give an indication whether models should stratify the population by age.
Conclusion
A focus on producing national strategic plans aimed at containment in Southeast Asia has left, it could be argued, mitigation strategically neglected. Gaps in operational capacity and resource mobilization have the potential to result in otherwise preventable deaths in Bali during an influ- enza pandemic. Whereas pandemic influenza A (H1N1) 2009 has been relatively mild in a clinical sense, H5N1 has maintained a high mortality rate in humans, particularly in Indonesia, and still poses a pandemic threat. Insufficient resources for mitigation during a pandemic of a more pathogenic subtype places Bali, and other resource-limited provinces, at risk of a public health disaster. Future investment—in Bali and other provinces—that is focused on addressing resource shortages identified here could help prevent unnecessary loss of lives.
Appendix
Transmission Model
The deterministic model is based on an SEAIR model. It comprises distinct compartments for the stages of infection with unidirectional movement of individuals from the susceptible to the recovered compartments (Figure A1). An individual may only be present in one compartment at a time and the sum of all individuals is the total population size. Importantly, the model assumes no preexisting immunity in the population.
Requirements for the number of physicians and nurses per case (bed occupancy rates) were based on the number of patients that can be treated by a single physician or nurse at any one time during a shift (of which there are 3 in a day: 2 daytime and 1 nighttime; Table A2). Doctors are only required for the treatment and isolation of cases, but nurses are also used in the investigation of cases. Depletion rates of resources are based on the average requirements for the treatment of a single case of pandemic H1N1v. Furthermore, the need for physicians and nurses was assumed to be linked to the number of hospitalized cases, which in turn may be limited by the number of hospital beds available. Only individuals in critically ill treatment strata can be considered to die as a direct result of infection by pandemic H1N1v, in particular hospitalized patients requiring but not receiving mechanical ventilation are assumed to die.
The effects of different control measures and treatment are incorporated into the model in a number of ways. First, it is assumed that available hospital beds will be used for critically ill patients and that the critically ill patients become outpatients if beds are unavailable. Cases that are hospitalized will have reduced contact rates to account for infection control proce- dures while death rates and infectious periods are assumed to differ between critically ill hospitalized patients and critically ill outpatients. Contact rates are also reduced within the
(continued) Figure A1. Diagrammatic representation of the transmission model
Adapted from Krumkamp et al.14
entire population (by 10% for 45 days) during the outbreak to account for the natural ten- dency of individuals to increase social distances when an infectious disease is known to be spreading rapidly.
Antiviral treatment is considered by altering the infectious period for mild symptomatic patients and the infectious period and death rate for critically ill outpatients. Although the period of infectiousness varies between treatment strata, it is assumed infectiousness at any one time during infection is equal for all infected individuals. The transmission parameters used in the model were chosen by Krumkamp et al14 based on a review of pandemic H1N1v literature; the values assumed are listed in the appendix tables along with the reason(s) for choice of value.
The basic differential equations used to describe the movement between compartments are listed in the below:
dS dt
S N I A
= −β ( + ) dE
dt S
N I A E
=β ( + )− σ
dA
dt =Eσ−Aδ dI
dt =Aδ−Iγ dR
dt = γI The initial conditions for the model are
S( )0 = −N E( )0 −A( )0 −I( )0 −R( )0
E( )0 =0 A( )0 =0 I( )0 =0 R( )0 =0
Further differential equations (taken from Krumkamp et al14) governing the model are listed below:
dN
dtAV = −Imτ(pma)−Icτ(ph + −(1 ph)pca) dN
dtbed =Ih2γh +V2γv−ϕ τIc (1−pv)−ϕω τI pc v dN
dtvent =V2γv−ϕω τI pc v dS
dt S v q p S
N D A I I I I
I I I I q
= − − −
− + + + +
+ + + + −
ρ κ( α κ) (
) (
m m
1 2 2
2
a a
ma c c ca 11−
− +
p S
N D I V
qh)κh ( h )
Appendix (continued)
dE
dt q p S
N D A I I I I
I Ic I I q p
= −
− + + + +
+ + + + + −
κ( α κ) (
) (
1
1
2 2
2
a a m m
ma c ca qh))κh S ( h ) σ
N D I V E
− + −
dA
dt =Eσ−Aδ dI
dta =A pδ a −Iaτ dI
dta2 =Iaτ−Ia2γa dI
dtm =A pδ m−Imτ dI
dtma =ε τIm pma −Ima maγ dI
dtm2 =ε τIm (1−pma) (+ −1 ε)Imτ−Im2γm dI
dtc =A pδ c−Icτ dI
dth =ϕ τIc (1−pv)−ε γIh ca − −(1 ε γ)Ih c dI
dth2 =ε γIh ca+ −(1 ε γ)Ih c −Ih2γh dI
dtca =ε τIc (1−ϕ)(1−pv)pca−Ica caγ dI
dtc2 =ε τIc (1−ϕ)(1−pv)(1−pca) (+ −1 ε τ)Ic (1−ϕ)(1−pv)pca −Ic2γc dV
dt =ϕω τI pc v −ε γV ca− −(1 ε γ)V c dV
dt2 =ε γV ca + −(1 ε γ)V c −V2γv
(continued)
dD
dt I d I d I d
I d V d
= + +
+ − + + −
c c c ca ca ca h h ha
h h h v v
2 2
2 2
1 1
γ γ ε γ
ε γ γ ϕ
( ) ( )((1− ϖ τ)I pc v dR
dt S v I I I I d
I d I
= + + + + −
+ − +
ρ γ γ γ γ
γ ε
a a m m ma ma c c c
ca ca ca h
2 2 2
2
1 1
( )
( ) γγh(1−dha) (+ −1 ε)Ih2γh(1−dh)+V2γv(1−dv)
Symptomatic point prevalence, pp(t), is used in the model to determine if and when indi- viduals in the population will increase social distances as a result of an influenza epidemic. It is calculated at a single point in time as
pp m ma m c ca
c h h
( ) ( ( ) ( ) ( ) ( ) ( )
( ) ( )
t I t I t I t I t I t
I t I t I V
= + + + +
+ + + +
2
2 2 (( )t +V t2( )) /100( ( )N t −D t( ))
R0, the basic reproduction number, is calculated by weighting the infectious periods by the pro- portion of cases within each infectious compartment:
R q q
p q
p q
p p q
p p q
0 = κ+ + + + 1− +
δ κ τ
κ γ
κ γ
κ γ
κ
a γ
a m
m
c h
c
c h h
c
( ) .
Appendix (continued)
Table A1. Definitions of the Variables Used in the Model
Variable Definition
S(t) Number of individuals at time t who are susceptible to infection
E(t) Number of individuals at time t who are exposed and infected but not infectious
A(t) Number of individuals at time t who are infectious and asymptomatic but can, and may yet, develop symptoms
I(t) Number of individuals at time t who are infectious and have either developed symptoms, or remain asymptomatic and will not develop any symptoms
R(t) Number of individuals at time t who have recovered from infection NAV(t) Number of antiviral doses available for use at time t
NBED(t) Number of hospital beds available for use at time t NVENT(t) Number of mechanical ventilators available at time t
Ia(t) Number of infectious individuals at time t who are asymptomatic, can no longer develop symptoms, and have not been detected
Ia2(t) Number of infectious individuals at time t who are asymptomatic, can no longer develop symptoms, and have been detected
Im(t) Number of infectious individuals with mild clinical symptoms at time t and who have not been detected
Ima(t) Number of infectious individuals with mild clinical symptoms at time t who are detected and treated with antivirals
(continued)
Variable Definition
Im2(t) Number of infectious individuals with mild clinical symptoms at time t who are detected but not given antivirals
Ic(t) Number of infectious individuals who are critically ill at time t and who have not been detected
Ih(t) Number of infectious individuals who are critically ill at time t and are detected and hospitalized
Ih2(t) Number of individuals at time t who are critically ill and have been hospitalized but are no longer infectious
Ica(t) Number of infectious individuals who are critically ill at time t then are detected and treated at home with antivirals
Ic2(t) Number of infectious individuals who are critically ill at time t then are detected and treated at home without antivirals
V(t) Number of infectious individuals who are critically ill at time t and are detected, hospitalized, and require mechanical ventilation
V2(t) Number of individuals at time t who are critically ill, have been detected, hospitalized, required mechanical ventilation, and are no longer infectious
D(t) Cumulative number of critically ill cases that have died at time t pp(t) Symptomatic point prevalence
Table A1. (continued)
(continued) Table A2. Definitions and Values Assumed for Parameters Used in the Modela
Parameter Definition Value Assumed
κ Rate of contact between individuals per day at population density d inhabitants per square kilometer. Derived from Krumkamp et al14 for use in the AFC simulator produced by National Institute for Public Health and the Environment, Netherlands
d < 50 50 ≤ d < 100 100 ≤ d < 250 250 ≤ d < 500 500 ≤ d < 750 750 ≤ d < 1000
d ≥ 1000
6.25 6.50 6.75 7.00 7.25 7.50 7.75 q Probability that a contact between an infectious and
a susceptible individual results in transmission14
0.09 β Rate of spread of the infection between individuals κq σ Rate at which exposed (preinfectious) individuals
become infectious but asymptomatic8,34,35
1/1 δ Rate at which asymptomatic, infectious individuals
become symptomatic34,35
1/0.4
τ Rate at which cases are detected14 1/1
pca Proportion of critically ill cases treated with antivirals
1 pma Proportion of mild cases treated with antivirals 0 pqh Proportion of hospital transmission prevented by
isolation measures
0.7 pκ Proportion of overall population contacts reduced
by social distancing. Assumed, as in Krumkamp et al14 and Duerr et al36
0.1
Table A3. Definitions for Parameters Reflecting Variation in Health System Resources Between Districtsa
Parameter Definition
ε Availability of antiviral drugs
ε = >
=
⎧⎨
⎪
⎩⎪
1 0
0 0
, ( )
, ( )
N t
N t
AV AV
ϕ Availability of hospital beds
ϕ = >
=
⎧⎨
⎪
⎩⎪
1 0
0 0
, ( )
, ( )
N t
N t
bed bed
ω Availability of mechanical ventilators
ω = >
=
⎧⎨
⎪
⎩⎪
1 0
0 0
, ( )
, ( )
N t
N t
vent vent
aWhen the parameter equals 1, there is surplus resource available for use, and 0 indicates there is no surplus available for use.
Parameter Definition Value Assumed
pi Proportion of cases that are asymptomatic (i = a), mild (i = m), or hospitalized (i = h) and proportion of hospitalized requiring ventilation (i = v) 8,10,11,36-43
Scenario 1:
i = a 0.3
i = m 0.698
i = h 0.002
i = v 0.2
Scenario 2:
i = a 0.3
i = m 0.685
i = h 0.015
i = v 0.2
γj Rate at which symptomatic, infectious individuals leave treatment group j: asymptomatic and untreated (j = a), mild and treated with antivirals (j = ma), mild but not treated with antivirals (j = m), critical and treated with antivirals at home (j = ca), critical but treated at home without antivirals (j = c), hospitalized (j = h), hospitalized and on a mechanical ventilator (j = v)17,34,35,37,44,45
j = a 1/1
j = ma 1/1
j = m 1/2
j = ca 1/3
j = c 1/4
j = h 1/12
j = v 1/13
dj Proportion of infectious, symptomatic individuals in treatment group j who die. Treatment groups are as above, but it is assumed that the death rate of mild or asymptomatic cases is negligible17,19,39,40,43
,45-47
Scenario 1:
j = ca 0.15
j = c 0.25
j = h 0.10
j = ha 0.05
j = v 0.25
Scenario 2:
j = ca 0.15
j = c 0.30
j = h 0.15
j = ha 0.05
j = v 0.35
α Overall population contact reduction (pκ) switch. It is active (ie, 1) for 45 days once the symptomatic
point prevalence reaches 0.5% α = ≥
<
⎧⎨
⎩
1 0 5
0 0 5
, ( ) .
, ( ) .
pp pp t t
aJustification for values assumed (taken from Krumkamp et al14) are given with the definition.
Table A2. (continued)
Table A5. Resource Depletion Rates: The Required Number of Surgical Masks, N95 Masks, Amoxicillin Capsules, Co-trimoxazole Capsules, and Oseltamivir tablets for Every Case of Pandemic Influenza at the Different Stages of Case Identification, Investigation and Treatmenta
Resource Rapid Response Case Investigation Treatment and Isolation
Surgical masks 1 10 80
N95 masks 0 0 40
Amoxicillin 0 0 1.9
Co-trimoxazole 0 0 2.4
Oseltamivir 0 0 10
aAverage requirements for amoxicillin, co-trimoxazole, and oseltamivir are based on 3 capsules per day for 5 days, 3 capsules per day for 6.33 days, and 2 doses per day for 5 days, respectively. It is assumed that 12.5% of hospitalized cases would require antimicrobials.
Table A4. Bed Occupancy Rates: The Required Number of Physician, Nursing Staff, and Surveillance and Rapid Response Teams (SRRT) for a Single Case of Pandemic Influenza at the Different Stages of Case Identification, Investigation, and Treatmenta
Treatment and Isolation
Resource Rapid Response Case Investigation Day Night
Physicians 0 0 0.1 0.025
Nurses 0 0.1 0.2 0.05
SRRT 0.1 0.1 0 0
aFor example, one physician can treat 10 patients during a daytime shift or 40 on a nighttime shift. There are assumed to be 2 daytime shifts and 1 nighttime shift during a 24-hour period.
Table A6. The Land Area, Population Size, and Density in Each of the 9 Districts of Bali
District Land Area (km2) Population Size Population Density (Inhabitants/km2)
Badung 392.9 388 548 989
Bangli 525.9 208 508 397
Buleleng 1,335.7 599 866 449
Denpasar 123.6 574 610 4650
Gianyar 364.7 421 067 1154
Jembrana 868.1 247 102 285
Karangasem 861.3 376 711 437
Klungkung 309.7 163 291 527
Tabanan 862.0 398 389 462
Total 5643.8 3 378 092 —
18
Table A7. The Needs for Selected Health System Resources During Pandemic Influenza Scenarios 1 and 2 BadungBangliBulelengDenpasarGianyarJembranaKarangasemKlungkungTabananTotal Scenario 1 Hospital level Hospital beds7024701269029432446 Ventilators196193324812612 District level Human resources Physicians85152895459 Nursing staff5932025801098784237355203384 SRRT289383110120831530453695386732 PPE Surgical masks1 294 276584 9801 682 8652 080 8051 517 069692 3831 051 179500 6881 116 97410 521 219 N95 masks7675494913 96918 02282475415554040938990 Treatment Amoxicillin15 174977127 58435 65016 25410 68110 928805917 739151 840 Co-trimoxazole19 22012 37734 93945 15620 58813 52913 84210 20822 470192 329 Antivirals285012803690476031701480223010202400 Scenario 2 Hospital level Hospital beds499172493886647203310169327 Ventilators1414814124518258894894 District level Human resources Physicians81216501165610 Nursing staff6042155911143799243364207392 SRRT1178383112020851556462710392745 PPE Surgical masks1 414 799637 1161 832 6472 267 5021 659 931754 8051 150 219544 6191 216 75911 478 397 N95 masks78 95135 544102 265127 09092 19042 01563 95630 18667 778639 975 Treatment Amoxicillin22 75035 25955 045107 06027 25120 35017 55917 35534 587337 216 Co-trimoxazole28 81744 66169 274135 61034 51725 77722 24221 98443 810426 692 Antivirals20 394605726 28132 66123 65810 77416 453771017 395161 383 Abbreviations: SRRT, surveillance and rapid response team; PPE, personal protective equipment.
Acknowledgments
We highly appreciate the Head of Provincial Health Office, Bali, Chief of Disease & Environmental Control—Provincial Health Office, Bali, for providing access to data and support during data collection.
Our thanks go to Mart Stein from the National Institute of Public Health and the Environment, Netherlands, for his assistance with transmission parameters and to research assistants from the Faculty of Public Health Universitas Indonesia: Amir Suudi, Noviyanti Liana Dewi, and Widyaningsih who have helped with field data collection in collaboration with local health officials in Bali.
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or pub- lication of this article.
Funding
The authors disclosed receipt of the following financial support for the research, authorship, and/or publi- cation of this article: This study was funded by the European Union (Grant No. Health-F3-2008-201823) and the London School of Hygiene and Tropical Medicine.
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