The impact of an African swine fever outbreak on endemic
tuberculosis in wild boar populations
Running head: African swine fever impact on endemic tuberculosis
Xander O’Neill1,*; Andrew White1;
Francisco Ruiz-Fons2; Christian
Gortázar2
1 - Maxwell Institute for Mathematical Sciences, Department of
Mathematics, Heriot-Watt University, Edinburgh, UK, EH14 4AS
2 - SaBio, Instituto de Investigación en Recursos Cinegéticos IREC (UCLM
& CSIC), 13005 Ciudad Real, Spain
*Corresponding Author
September 18, 2020
Key Words: disease control; infectious disease model, multiple pathogens
Abstract
Animal tuberculosis (TB) is a widespread infectious disease caused by
bacteria belonging to the Mycobacterium tuberculosis complex(MTC), mainly M. bovis and M. caprae , that can persist in
wildlife reservoir hosts. Wild boar (Sus scrofa ) are a key
reservoir for MTC on the Iberian Peninsula and an increasing trend in
wild boar density is expected to lead to an increase in TB prevalence
with spill-over to livestock. MTC infection is presently controlled
through a variety of strategies, including culling. African swine fever
(ASF) is a virulent, viral infection which affects wild boar and is
spreading across Eurasia and Oceania. ASF infection leads to near 100%
mortality at the individual level, can cause a dramatic decrease in
population density and may therefore, paradoxically, contribute to TB
control. In this study we develop a mathematical model to examine the
impact of ASF introduction into a wild boar population that supports
endemic TB. Our model results indicate that an ASF infection will reduce
wild boar population density and lead to a decrease in the prevalence of
TB. If ASF persists in the local host population the model predicts the
long-term decline of TB prevalence in wild boar. If ASF is eradicated,
or fades-out in the local host population, the model predicts a slower
recovery of TB prevalence in comparison to wild boar density after an
ASF epidemic. This may open a window of opportunity to apply TB
management to maintain low TB prevalence.
1 Introduction
Animal tuberculosis (TB) is a widespread multi-host disease caused by
infection with Mycobacterium bovis and closely related members of
the M. tuberculosis complex (MTC) and leads to increased host
mortality [Barasona et al., 2016]. TB has a significant economic
impact on the livestock industry due to test and slaughter schemes and
movement restrictions [Gortázar et al., 2015], [Picasso-Risso et
al., 2020], [Schiller et al., 2011] and within the European Union
there has been funding and a long-term policy to reduce and eradicate TB
in cattle [Kubik et al., 2016]. Other intervention measures include
reducing indirect contacts among host species [Barasona et al.,
2013], [Wilber et al., 2019], vaccinating wildlife [Díez-Delgado
et al., 2018], and culling wildlife [Boadella et al., 2012],
[Tanner et al., 2019a]. Nevertheless, there is an increasing
prevalence of infection among cattle herds in Europe, with the EU herd
prevalence at 0.4% in 2008 and at 0.9% in 2018 [EFSA and ECDC,
2019]. A key issue for the control of TB is its persistence in
wildlife reservoirs from which it can spill-over to livestock
[Barasona et al., 2019]. The primary reservoir species vary with
location and include European badgers (Meles meles ) in the
British Isles, cervids in North America, brushtail possums
(Trichosurus vulpecula ) in New Zealand and buffalo
(Syncerus caffer ) in South Africa, among others [Fitzgerald and
Kaneene, 2013], [Gortázar et al., 2015]. In mainland Europe, and
in particular on the Iberian Peninsula, wild ungulates such as the
Eurasian wild boar (Sus scrofa ) and red deer (Cervus
elaphus ) act as the primary reservoir of infection [Gortázar et al.,
2015], [Gortázar et al., 2012], [Naranjo et al., 2008],
[Santos et al., 2020]. Due to increasing habitat suitability and
decreasing hunting pressure, the density of wild ungulates has seen an
unprecedented increase over the last decades [Burbaitė and Csányi,
2010], [Massei et al., 2015], [Milner et al., 2006] and this
presents a challenge for TB management.
Wildlife species can harbour multiple infectious agents and this can be
facilitated by the increase in density of wild ungulates. In wild boar,
the spread of African swine fever (ASF) is a cause for current concern
as it leads to high levels of mortality and has the potential to
spill-over to domestic pigs resulting in subsequent losses in pig
production [Barongo et al., 2016], [Sánchez-Vizcaíno et al.,
2013]. As such, ASF is listed as a notifiable disease by the World
Organisation for Animal Health (OIE) [Jurado et al., 2018],
[Vergne et al., 2016]. Outbreaks are currently causing global
concern; in Europe an outbreak in Georgia and the Russian Federation in
2007 had spread to Ukraine, Belarus, Estonia, Latvia, Lithuania and
Poland [Depner et al., 2017] and recent outbreaks have been reported
in the Czech Republic, Belgium, Slovakia and several south-east European
countries [Miteva et al., 2020]. Germany, the EU’s largest pork
producer, is the most recently affected country [Kość and Standaert,
2020]. ASF is likely to continue to spread and therefore have a
widespread global impact on domestic pig production and wild boar
abundance.
The persistence of infectious disease is known to be linked to host
population density with the potential for disease eradication if the
host population decreases below a threshold density [Anderson and May,
1979]. This has underpinned the use of culling as a management
strategy to control wildlife diseases [Barlow, 1996], [Tanner et
al., 2019b], [Woodroffe, 1999]. Since ASF outbreaks typically lead
to significant reductions in host population density this is likely to
have impacts for the prevalence and persistence of co-circulating
pathogens, such as MTC. With the continued spread of ASF it is therefore
important to examine the potential impact of an ASF outbreak on the
persistence of TB.
Mathematical models have played a key role in understanding the
processes that drive epidemiological dynamics in wildlife populations
[Anderson and May, 1979], [Keeling and Rohani, 2008]. In this
study we develop a mathematical model for a wild boar host population
that can be co-infected with MTC and ASF. Given the marked effect of ASF
on wild boar population density and knowing that wild boar culling can
contribute to TB control, we hypothesize that ASF emergence will have a
significant impact on wild boar TB. Therefore, our aim is to understand
the consequences of an ASF outbreak on the prevalence and persistence of
endemic TB in wild boar. To do this we incorporate the disease dynamics
for ASF, detailed in O’Neill et al. [O’Neill et al., 2020], into a
model of TB in wild boar [Tanner et al., 2019a]. Our model system is
parameterised to be representative of the wild boar TB system in
different regions in Spain. However, the findings apply in general as we
examine the impact of ASF in regions of high density and high endemic TB
prevalence and in regions of low density and low endemic TB prevalence.
Degradation of ASF in wild boar carcasses can play a key role in the ASF
epidemiological dynamics [Berg et al., 2015], [O’Neill et al.,
2020], [Probst et al., 2017], and so we explore the outcome with
two different rates of degradation, a high and a low rate. In
particular, the high rate represents the rapid degradation of the
pathogen as seen in places with high temperatures or with abundant
obligate scavengers, such as vultures. We then consider how disease
control measures introduced to eradicate ASF will impact the dynamics of
TB. Beyond assessing the potential impact of ASF on the epidemiological
dynamics of TB our findings add new perspective to the theory on the
interaction and co-existence of multiple pathogens in a single host
species.
2 Methodology
We intend to extend the model seen in Tanner et al. 2019 [Tanner et
al., 2019a], which represents the dynamics of tuberculosis in wild
boar, to include co-infection of African swine fever, as represented in
O’Neill et al. 2020 [O’Neill et al., 2020]. A full model description
is presented in the supplementary information. Here we describe the key
infection processes for TB, in section 2.1, and for ASF, in section 2.2.
2.1 The Wild Boar Tuberculosis Model
The model of Tanner et al. 2019 [Tanner et al., 2019a] considers a
wild boar host population that is split into three age-classes: piglets
(P ), yearlings (Y ) and adults (A ). The
three different age classes are required as each class has distinct
properties in terms of their demographic and infection dynamics. The
age-classes are further split into susceptible (subscript S ),
infected (subscript I ) and generalised (subscript G )
classes to reflect the TB disease status of the population. Generalised
individuals can also release free-living TB pathogen particles, with
density F , into the environment. The model is given below:
Here, N = P +Y +A represents the total wild boar population,
where P=PS +PI +PG; Y=YS +YI+YG; A = AS+AI+AG and G is the
total number of generalised individuals, G = PG+YG+AG . Yearlings
and adults give birth to susceptible piglets at rate b . This
takes two values, b = log 4 and b = log 7 , for scenarios
representative of low and high TB prevalence regions, respectively. The
total population is regulated through a crowding parameter, q ,
that acts on the birth rate, and is related to the carrying capacity,K , since . We choose the values, K = 5.95 or K =
27 , for low and high prevalence TB regions, respectively. Maturity from
piglets to yearlings and yearlings to adults occurs at rate m and
piglets, yearlings and adults may die of natural causes at rate d. This
set-up for the demographic dynamics has previously been used to assess
wild boar TB interactions [Díez-Delgado et al., 2018], [Tanner et
al., 2019b].
The model assumes infection can occur through direct frequency-dependent
interactions (since wild boar tend to congregate in social groups)
between susceptible and generalised individuals with transmission
coefficients βDP, βDY andβDA , for piglets, yearling and adults
respectively, or through environmental contact with the free-living MTC,
with transmission coefficients βFP,βFY and βFA . Piglets and
yearlings are assumed to be three times more susceptible to infection
than adults [Martín-Hernando et al., 2007]. Infected individuals are
not infectious but can progress to the generalised (infectious) class at
rates εP, εY andεA , for the different age-classes, respectively.
In low prevalence regions, where resources are not limited, it is
assumed that εP = εY =
εA [Tanner et al., 2019a]. However, for high
prevalence regions, where resources (particularly water) are scarce and
overall health is impaired (similar to conditions in central and
southern Spain), it is assumed that piglets and yearlings progress from
the infected to the generalised class at three times the rate of adults
(εP = εY = 3εA )
[Tanner et al., 2019a]. The model assumes that free-living MTC is
shed from generalised wild boar at rate λ and decays at rateμF . The level of environmental transmission is
scaled through the parameter ω which increases when environmental
conditions become more severe to reflect, for example, aggregation at
limited water holes. Finally, it is assumed that all wild boar in the
generalised class suffer disease induced mortality at rate α and
that all adult and yearling classes are culled due to hunting at
constant rate c .
In this study we consider two parameter sets that include a range of
wild boar densities and TB prevalences found in Spain: (i) where the
wild boar density is 4km-2 and TB is endemic
with a prevalence of 10% , representative of regions in northern
Spain, or similar, where water is not a limiting factor and no feeding
takes place [Muñoz Mendoza et al., 2013] and (ii) where the wild
boar density is 12km-2 and TB is endemic with a
prevalence of 60% , representative of regions in central Spain,
or similar, where wild boar are supplementary fed but where water
resources are scarce in summer [Vicente et al., 2013]. A full
description of the parameters and their values (which are taken from
Tanner et al. 2019 [Tanner et al., 2019a], except where stated) is
given in the supplementary information.
2.2 The Wild Boar African Swine Fever and Tuberculosis Model
We extend the wild boar TB dynamics to include co-infection with ASF
following the methodology presented in O’Neill et al. 2020 [O’Neill et
al., 2020] that develops a wild boar ASF model. For the ASF
epidemiological dynamics we consider the following classes: S ,
uninfected and susceptible to infection; I , infected and able to
transmit the virus; C , survivor individuals which do not transmit
the virus but can revert to the infected (I ) class and D ,
infected carcasses which can transmit the virus. The definition of
survivor individuals arises from the type 1 ‘survivors’ definition used
in Ståhl et al. [Ståhl et al., 2019] where such individuals will
invariably die but have the potential to excrete virus in association
with the resurgence of viraemia. An overview of the ASF infection
dynamics is shown schematically in Figure 1.
ASF infection is assumed to affect all age-classes of wild boar equally
[O’Neill et al., 2020]. It is assumed a susceptible can become
infected with ASF due to direct contact with an infected individual via
frequency dependent transmission, βF or due to
environmental transmission through contact with an infected carcass,βE . A proportion, ρ , of infected
individuals suffer disease induced mortality at rate γ = 365/5 ,
reflecting an average lifespan of 5 days for an individual with
ASF [Gallardo et al., 2015]. A proportion, 1 - ρ , of infected
individuals can instead enter the survivor class, which does not incur
disease induced mortality. Survivor individuals can revert to the
infected class at rate κ = 12/6 implying that on average
individuals remain survivors for 6 months [Gallardo et al.,
2015]. Host individuals that die due to the infection become infected
carcasses which degrade at rate μC . Further
details of the wild boar ASF model can be found in O’Neill et al. 2020
[O’Neill et al., 2020] and the combined TB and ASF infection model
is shown in full in the supplementary information with details of the
parameter values. Note, in the TB and ASF full model we do not assume
direct interference between competing pathogens. However, there will be
indirect interference due to parasite induced changes in host population
density.
In this study we consider ASF control measures in the form of culling
and the removal of carcasses. Culling is applied at ratebC , across all age and infection classes whilst
the removal of carcasses is applied at rate r . The valuebC corresponds to a culling proportion equal to
1- e- bC, per year, of the total
population and the value r corresponds to an average time till
the removal of a carcass of 1/r years.
3 The Impact of African Swine Fever on endemic Tuberculosis
We undertake model simulations for the introduction of ASF into the TB
endemic system, for scenarios that are representative of TB infection
status found in wild boar in Spain, including regions of high and low TB
prevalence and scenarios that represent high and low ASF infected
carcass degradation rates.
For the scenario with high TB prevalence and a high rate of ASF infected
carcass degradation the introduction of ASF leads to a rapid population
reduction of 85% (Figure 2). There is a peak in ASF infection
around 3 months after its introduction and in the model ASF persists at
low prevalence (0.8% ) in the long-term. The impact and
persistence of ASF leads to a reduction in the host population density
which in turn leads to a decrease in TB prevalence. Note, the decrease
in TB prevalence is slow and in the long-term TB prevalence stabilises
to a reduced level. For the scenario with high TB prevalence and a low
rate of ASF infected carcass degradation the introduction of ASF leads
to a near eradication of the host population, with a 99%reduction in the host population density (Figure 3). The impact of ASF
is more severe as the low rate of carcass degradation increases the
potential for ASF transmission. ASF infection peaks after 2 months and
persists for 2 years but the model results indicate local disease
fade-out. In the long-term this allows the host population to return to
the density prior to the ASF outbreak. The impact on TB is a gradual
reduction in prevalence from 60% to less than 20% within
8 years, and then an increase in TB prevalence back to 60% at a
rate that lags behind the increase in population density.
Although ASF leads to near eradication of the population, the TB
prevalence does not drop below 20% . TB is not eradicated in the
model as the component of the effective reproductive ratio that arises
through the frequency dependent transmission is independent of host
density and is greater than 1 (see supplementary information,
section S3, for more details).
In the low TB prevalence (and lower initial host density), high carcass
degradation rate scenario ASF establishes slowly and becomes endemic at
low prevalence (Figure 4). This leads to a slow decrease in the host
population of around 35% which then leads to a slow decrease in
TB prevalence. In the long-term TB would be eradicated as the TB
infection parameters for this scenario mean that the reduction in host
population density due to endemic ASF is sufficient to reduce the
effective reproductive ratio for TB below 1 (see supplementary
information, section S3). The low TB prevalence and low carcass
degradation rate scenario (Figure 5) is similar to the equivalent high
TB prevalence case with an ASF outbreak followed by rapid population
crash and fade out of ASF before the population then recovers. There is
a reduction in TB prevalence to low levels and a slow increase in TB
prevalence following population recovery. The slow decrease and then
increase in TB prevalence is due to the effective reproductive ratio for
TB dropping below 1 for low host population densities and
increasing above 1 as the host population returns to its density
prior to the ASF outbreak. A common finding across all scenarios is that
the epidemiological dynamics of ASF are rapid whereas those of TB are
slow and highlights a difference between acute and chronic infections.
4 Applying ASF control
Due to the economic and population impact of ASF on farmed hosts control
measures to eradicate ASF are applied following its detection. In ASF
endemic regions, such as the Baltic countries, infected wild boar are
recorded for several years after the initial introduction and suggest
there could be poorly understood pathways that facilitate the
persistence of the virus at very low densities [Miteva et al.,
2020], [O’Neill et al., 2020]. ASF maintenance could also be
caused by continued new introductions of the virus from adjacent
affected regions and countries [Miteva et al., 2020]. Recommended
measures under these epidemiological circumstances include continued
active and passive disease surveillance, intense efforts of carcass
detection and removal, and continuous and intensive hunting of wild boar
to maintain low population densities, both to slow down the speed of
infection spread and to monitor progress through active disease
surveillance [Miteva et al., 2020]. We repeat the scenarios outlined
in section 3 but with the inclusion of ASF control measures. We consider
two control measures: the culling of the host population (with culling
rate bC ) and the removal of ASF infected
carcasses (with removal rate r ). The measures are implemented as
soon as ASF enters the population, and cease when ASF has been
eradicated from the population (defined as the time when the total
number of ASF infected and survivor individuals, I + C , is less
than 0.1% of the initial host density).
For control that focuses on carcass removal (a high carcass removal
rate, r = 200 and low culling rate bC =
0.2 ) the results are similar regardless of the ASF and TB scenario. We
show results for the high TB prevalence and low carcass degradation rate
scenario (Figure 6). Results for other scenarios can be found in the
supplementary information (Figure S1). ASF control prevents a severe ASF
infectious outbreak and ASF is eradicated within 3 years. There is an
approximate 40% drop in total population and only 10%drop in TB prevalence. This method of control eradicated ASF without a
significant drop in host population density and therefore will have
little impact on TB prevalence.
For the culling-based control measure (a low carcass removal rate,r = 26 and high culling rate bC = 0.7 ) the
outcome depends on whether the initial TB prevalence is high or low but
is independent of the natural carcass degradation rate. We show results
representative of a low carcass degradation rate with results
representative of a high carcass degradation rate given in the
supplementary information (Figure S2). For scenarios representative of a
high TB prevalence region there is a rapid reduction in host population
density, of approximately 95% , and a more gradual reduction in
TB prevalence (Figure 7). Once ASF is eradicated the total population
recovers but the increase in prevalence of TB to its original value lags
behind that of the increase in host population. For scenarios
representative of a low TB prevalence region (Figure 7), there is an
approximate drop of 80% in the total population and slow
decrease in TB prevalence. Following ASF eradication the host population
recovers to its original density but TB prevalence increases slowly.
5 Discussion
The insight gained from our mathematical model confirmed the hypothesis
that the emergence of ASF could have a significant impact on the
prevalence of TB in wild boar, with a reduction in TB prevalence in
response to an ASF outbreak. If ASF persists in the local host
population the model predicts the long-term decline of TB prevalence in
wild boar. If ASF fades-out in the local host population the model
predicts a slower recovery of TB prevalence in comparison to wild boar
density after an ASF epidemic. This may open a window of opportunity to
apply TB management to maintain low TB prevalence. Whilst there are
ongoing efforts to prevent ASF re-emergence in Spain, after its
successful eradication in 1995 [Mur et al., 2012], and elsewhere
across the globe, the ongoing ASF spread in Eurasia [Nielsen et al.,
2019], [Jo and Gortázar, 2020] makes such an unfortunate scenario
more practical.
Our model study adds new perspective to the theory on the co-existence
of multiple pathogens. Classical infectious disease model studies
[Anderson and May, 1979], [Bremermann and Thieme, 1989], that
include multiple pathogens which exclusively infect the host and that
consider density dependent infection transmission, indicate that the
pathogen with the greatest reproductive ratio can out-compete other
pathogen. Exclusion of competing pathogens occurs as disease-induced
mortality suppresses the host density to levels where only one pathogen
can persist [Bowers and Boots, 2003]. Coexistence of multiple
pathogens requires co-infection or super-infection mechanisms that
include trade-offs balancing the pathogens ability to transmit the
infection against disease-induced mortality [Begon and Bowers,
1995], [Hochberg and Holt, 1990], [Nowak and May, 1994],
[Levin and Pimentel, 1981]. Our study includes co-infection of the
host population by different pathogens that infect the host through
density-dependent and frequency-dependent mechanisms. In particular, the
component of the pathogen reproductive ratio arising through
frequency-dependent transmission does not depend on host density (see
supplementary information, section S3) and we show that this
transmission mechanism can promote pathogen coexistence and prevent the
pathogen exclusion that arises due to disease-induced suppression of the
host density.
ASF infection leads to high levels of disease-induced mortality in wild
boar and an ASF outbreak can cause a rapid and significant decline in
population density [O’Neill et al., 2020], [Depner et al.,
2017], [Gallardo et al., 2015], [Korennoy et al., 2014],
[Simulundu et al., 2017]. Therefore, an ASF outbreak in wild boar
populations that support endemic TB will act in a similar manner to host
population culling and can have an impact on TB prevalence and MTC
infection levels [Tanner et al., 2019a], [Tanner et al., 2019b].
Our model results indicate that an ASF infection will reduce wild boar
population density and lead to a decrease in the prevalence of TB. The
decrease in population density leads to a rapid decrease in the number
of TB infected individuals but with the decrease in TB prevalence
occurring on a longer time scale. This is due to ASF infecting all TB
classes equally, TB being a chronic long-lived infection compared to ASF
and due to the direct, frequency dependent transmission of TB at low
wild boar density. When ASF persists in the host population a reduction
in wild boar population density is seen due to the increase in
population level mortality. This leads to a long-term reduction in TB
prevalence and the potential for TB eradication. In some model scenarios
where ASF transmission in the environment (from infected carcasses) is
high, the ASF outbreak causes a severe reduction in host population
density and while ASF persists in the medium term it can fade-out, in
the local host population, in the long-term. This further highlights the
importance of environmental transmission from infected carcasses in the
persistence of ASF and the role obligate scavengers may play in reducing
environmental transmission [Berg et al., 2015], [O’Neill et al.,
2020], [Probst et al., 2017]. Infection fade-out is common for
highly virulent, acute infections [Chenais et al., 2019], [Cross
et al., 2005], [Macpherson et al., 2015], [White et al., 2014]
and may occur locally for ASF but is unlikely to do so over a regional
scale due to the spatial spread of infection (for example, ASF has
persisted at the regional scale in Baltic countries since 2014,
[Nurmoja et al., 2020]). Model results indicate that following ASF
fade-out the local wild boar population density will increase and slowly
return to pre-ASF infection levels. The increase in MTC infection lags
behind the increase in population density and therefore the return to
pre-ASF infection levels of TB is predicted to occur on a longer time
scale. This should not be misinterpreted for TB control as TB will still
increase in the long-term. However, the slow increasing rate of TB
infection may open a window of opportunity to apply TB management and
maintain low TB prevalence. This could include bio-safety measures that
reduce wildlife-cattle contact rates [Barasona et al., 2013], the
culling of wild boar [Boadella et al., 2012] or the introduction of
TB vaccinations for wild boar [Díez-Delgado et al., 2018]. We
recognise that our model only considers a single host system and in a
natural system there are several species that can act as a TB reservoir
[Gortázar et al., 2015], [Gortázar et al., 2012], [Naranjo et
al., 2008]. Therefore, there is the potential for inter-species
transmission which could accelerate the increase in TB prevalence during
the wild boar population recovery phase. However, there is evidence that
wild boar are the key reservoir species for TB in Spain [Naranjo et
al., 2008], [Santos et al., 2020] and that a decrease in wild boar
TB infection levels leads to a reduction in TB prevalence in other
wildlife [Tanner et al., 2019a], [Boadella et al., 2012].
ASF infection has widespread and severe impacts on wild boar and
domestic pig production [Barongo et al., 2016], [Sánchez-Vizcaíno
et al., 2013] and is listed as a notifiable disease by the World
Organisation of Animal Health (OIE) [Jurado et al., 2018], [Vergne
et al., 2016]. Control measures to manage ASF are likely to be
introduced following detection [Bellini et al., 2016], [Jurado et
al., 2018] and while these would diminish the impact of an ASF
outbreak they may also limit host population mortality and therefore the
impact of ASF on TB control. Furthermore, resources that are used to
target TB control may be redistributed to focus on ASF management and
this could have unforeseen consequences for TB management. A consequence
of the Foot-and-Mouth outbreak in the UK in 2001 [Vial et al., 2013]
and a likely consequence of the effort to tackle COVID-19 [Gortázar
and de la Fuente, 2020], is a shift in resources to control the
emerging disease at the expense of a reduction in the direct efforts to
control endemic disease. Therefore, any efforts to control emerging
pathogens should be considered as part of a joint strategy to control
the multiple pathogens that share a host.
In this study we have used a mathematical modelling framework to assess
the potential impact of an ASF outbreak on the epidemiological dynamics
of wild boar. We have made particular reference to the situation in
Spain where wild boar are the key reservoir host for TB. However, the
key findings that ASF can lead to a marked reduction in host density and
hence a rapid reduction in TB infected individuals but a more gradual
reduction in TB prevalence generalise beyond the system in Spain. Our
results highlight the interaction and impact of co-infecting pathogens
on the population and epidemiological dynamics of their host and the
need to consider multiple pathogens when attempting to control a primary
infectious outbreak.
Acknowledgements
Xander O’Neill was supported by The Maxwell Institute Graduate School in
Analysis and its Applications, a Centre for Doctoral Training funded by
the UK Engineering and Physical Sciences Research Council (grant
EP/L016508/01), the Scottish Funding Council, Heriot-Watt University and
the University of Edinburgh. The authors would like to acknowledge the
contribution of the COST Action ASF-STOP CA15116, from the MCIU Plan
Nacional project CGL2017-89866-R.
Author Contributions
X.O. and A.W. performed mathematical analysis. All authors contributed
to the production of the manuscript. All authors gave final approval for
publication.
Competing Interests
The authors declare no competing interests.
Data Availability Statement
Data sharing is not applicable to this article as no new data was
created or analysed in this study.
Ethical Statement
The authors confirm that the ethical policies of the journal, as noted
on the journal’s author guidelines page, have been adhered to. No
ethical approval was required as this is a research article with no
original data.
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Figure 1: A visual representation of the wild boar ASF model presented
in O’Neill et al. 2020 [O’Neill et al., 2020]. The nodes represent
the different ASF infection classes: S , ASF susceptible,I , ASF infected, C , ASF survivor individuals and D ,
infected carcasses. The arrows show the possible entry and exit routes
into and out of each respective class.
Figure 2: Population densities and prevalence for the model described by
the equations (S1-S5), in the supplementary information, for the
scenario with high carcass degradation rate and a high tuberculosis
prevalence. Results are shown over a 25-year period. (A) shows total
host density (blue), hosts susceptible to TB (green), hosts infected
with TB (magenta), hosts with generalised TB infection (red) and the
combined infected and generalised hosts (black). (B) shows the total
host density (blue), hosts susceptible to ASF (green), hosts infected
with TB (magenta), ASF survivor density (red) and the infected carcass
density (black). (C) shows TB prevalence with infected prevalence,ITB/N , (dotted); generalised prevalence,G/N , (dot-dash) and total prevalence, (ITB+ G)/N , (solid). We used default parameter values and K = 27, b =
ln 7, cε = 3, ω = 1 and d = 52 .
Figure 3: Population densities and prevalence for the model described by
the equations (S1-S5), in the supplementary information, for the
scenario with low carcass degradation rate and a high tuberculosis
prevalence. Results are shown over a 25-year period. (A) shows total
host density (blue), hosts susceptible to TB (green), hosts infected
with TB (magenta), hosts with generalised TB infection (red) and the
combined infected and generalised hosts (black). (B) shows the total
host density (blue), hosts susceptible to ASF (green), hosts infected
with TB (magenta), ASF survivor density (red) and the infected carcass
density (black). (C) shows TB prevalence with infected prevalence,ITB/N , (dotted); generalised prevalence,G/N , (dot-dash) and total prevalence, (ITB+ G)/N , (solid). We used default parameter values and K = 27, b =
ln 7, cε = 3, ω = 1 and d = 13 .
Figure 4: Population densities and prevalence for the model described by
the equations (S1-S5), in the supplementary information, for the
scenario with high carcass degradation rate and a low tuberculosis
prevalence. Results are shown over a 25-year period. (A) shows total
host density (blue), hosts susceptible to TB (green), hosts infected
with TB (magenta), hosts with generalised TB infection (red) and the
combined infected and generalised hosts (black). (B) shows the total
host density (blue), hosts susceptible to ASF (green), hosts infected
with TB (magenta), ASF survivor density (red) and the infected carcass
density (black). (C) shows TB prevalence with infected prevalence,ITB/N , (dotted); generalised prevalence,G/N , (dot-dash) and total prevalence, (ITB+ G)/N , (solid). We used default parameter values and K = 5.95, b
= ln 4, cε = 1, ω = 0.1 and d = 52 .
Figure 5: Population densities and prevalence for the model described by
the equations (S1-S5), in the supplementary information, for the
scenario with low carcass degradation rate and a low tuberculosis
prevalence. Results are shown over a 25-year period. (A) shows total
host density (blue), hosts susceptible to TB (green), hosts infected
with TB (magenta), hosts with generalised TB infection (red) and the
combined infected and generalised hosts (black). (B) shows the total
host density (blue), hosts susceptible to ASF (green), hosts infected
with TB (magenta), ASF survivor density (red) and the infected carcass
density (black). (C) shows TB prevalence with infected prevalence,ITB/N , (dotted); generalised prevalence,G/N , (dot-dash) and total prevalence, (ITB+ G)/N , (solid). We used default parameter values and K = 5.95, b
= ln 4, cε = 1, ω = 0.1 and d = 13 .
Figure 6: Population densities and prevalence for the model described by
the equations (S1-S5), in the supplementary information, for the
scenario with low carcass degradation rate and a high tuberculosis
prevalence under specific ASF control measures. Results are shown over a
25-year period. (A) shows total host density (blue), hosts susceptible
to TB (green), hosts infected with TB (magenta), hosts with generalised
TB infection (red) and the combined infected and generalised hosts
(black). (B) shows the total host density (blue), hosts susceptible to
ASF (green), hosts infected with TB (magenta), ASF survivor density
(red) and the infected carcass density (black). (C) shows TB prevalence
with infected prevalence, ITB/N , (dotted);
generalised prevalence, G/N , (dot-dash) and total prevalence,(ITB + G)/N , (solid). Parameters are as in Figure
3, with the culling parameter bC = 0.2 and
carcass removal rate r = 200 .
Figure 7: Population densities and prevalence for the model described by
the equations (S1-S5), in the supplementary information, for the
scenario with low carcass degradation rate and either a high
tuberculosis prevalence (A-C) or a low tuberculosis prevalence (D-F),
under specific ASF control measures. Results are shown over a 25-year
period. (A&D) show total host density (blue), hosts susceptible to TB
(green), hosts infected with TB (magenta), hosts with generalised TB
infection (red) and the combined infected and generalised hosts (black).
(B&E) show the total host density (blue), hosts susceptible to ASF
(green), hosts infected with TB (magenta), ASF survivor density (red)
and the infected carcass density (black). (C&F) show TB prevalence with
infected prevalence, ITB/N , (dotted); generalised
prevalence, G/N , (dot-dash) and total prevalence,(ITB + G)/N , (solid). For A-C parameters are as
in Figure 3 and for D-F parameters are as in Figure
5. For all plots, the culling parameter bC = 0.7and carcass removal rate r = 26 are used.