doi: 10.3934/dcdsb.2022110
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Modelling Trypanosoma cruzi-Trypanosoma rangeli co-infection and pathogenic effect on Chagas disease spread

1. 

Colleges of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China

2. 

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

3. 

Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322, United States

4. 

Department of Mathematics and Statistics, York University, Toronto, ON, M3J1P3, Canada

*Corresponding author: Jianhong Wu

Received  July 2021 Revised  April 2022 Early access June 2022

Fund Project: The work is supported by NSF of China (12071300), NSF of Shanghai (20ZR1440600), and NSERC of Canada and the Canada Research Chair program

A mathematical model is developed to investigate the impact of Trypanosoma cruzi and Trypanosoma rangeli co-infection and Trypanosoma rangeli-induced pathogenicity of triatomine bugs on the spread of Chagas disease. Due to the presence of two parasites, basic reproduction numbers of one parasite in the absence of the other parasite ($ \mathcal{R}_{10} $ and $ \mathcal{R}_{20} $) and invasion reproduction numbers of one parasite invading the other parasite ($ \mathcal{R}_{12} $ and $ \mathcal{R}_{21} $) are derived to determine the dynamics of the co-infection system. With a simple case of two parasites' independent transmission, we have found that both parasites go extinct if both $ \mathcal{R}_{i0}<1\,(i=1,2) $, thus no Chagas disease spread. Nevertheless, the condition of $ \mathcal{R}_{i0}>1\,(i=1,2) $ is not sufficient to cause Chagas disease persistence, the invasion reproduction number of Trypanosoma cruzi invading Trypanosoma rangeli transmission $ \mathcal{R}_{12} $ plays an important role. Specifically, Chagas disease could go extinct if $ \mathcal{R}_{12}<1 $, and uniformly persistent if $ \mathcal{R}_{12}>1 $. Moreover, due to pathogenicity, oscillation pattern of Chagas disease is observed, which is different from other mechanisms such as maturation delay, seasonality and regular spraying with insecticides for vector control. In conclusion, we have found that the presence of Trypanosoma rangeli infection leads to the risk reduction of Chagas disease infection. Our findings are beneficial to the prevention and control of Chagas disease.

Citation: Xiaotian Wu, Daozhou Gao, Zilong Song, Jianhong Wu. Modelling Trypanosoma cruzi-Trypanosoma rangeli co-infection and pathogenic effect on Chagas disease spread. Discrete and Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2022110
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show all references

References:
[1]

M. A. Acuña-ZegarraD. Olmos-Liceaga and J. X. Velasco-Hernández, The role of animal grazing in the spread of Chagas disease, J. Theor. Biol., 457 (2018), 19-28.  doi: 10.1016/j.jtbi.2018.08.025.

[2]

N. Añez, M. Molero, E. Valderrama, D. Nieves, et al., Studies on Trypanosoma rangeli Tejera, 1920 X- Its comparison with Trypanosoma cruzi Chagas, 1909. Infection in different stages of Rhodnius prolixus Stal, 1859, KASMERA, 20 (1992), 35-51.

[3]

B. BassoI. CastroV. IntroiniP. GilbC. Truyensc and E. Morettia, Vaccination with Trypanosoma rangeli reduces the infectiousness of dogs experimentally infected with Trypanosoma cruzi, Vaccine, 25 (2007), 3855-3858.  doi: 10.1016/j.vaccine.2007.01.114.

[4]

B. BassoE. Moretti and R. Fretes, Vaccination with epimastigotes of different strains of Trypanosoma rangeli protects mice against Trypanosoma cruzi infection, Mem. Inst. Oswaldo Cruz., 103 (2008), 370-374.  doi: 10.1590/S0074-02762008000400010.

[5]

B. BassoE. Moretti and R. Fretes, Vaccination with Trypanosoma rangeli induces resistance of guinea pigs to virulent Trypanosoma cruzi, Vet. Immunol. Immunopathol., 157 (2014), 119-123.  doi: 10.1016/j.vetimm.2013.10.011.

[6]

B. BassoE. Moretti and E. Votrero-cima, Immune response and Trypanosoma cruzi infection in Trypanosoma rangeli-immunized mice, Am. J. Trop. Med. Hyg., 44 (1991), 413-419.  doi: 10.4269/ajtmh.1991.44.413.

[7]

C. Barbu, E. Dumonteil and S. Gourbiére, Optimization of control strategies for nondomiciliated Triatoma dimidiata, Chagas disease vector in the Yucatan Peninsula, Mexico, PLoS. Negl. Trop. Dis., 3 (2009), e416. doi: 10.1371/journal. pntd. 0000416.

[8]

G. Cruz-PachecoL. Esteva and C. Vargas, Control measures for Chagas disease, Math. Biosci., 237 (2012), 49-60.  doi: 10.1016/j.mbs.2012.03.005.

[9]

A. B. B. de Oliveira, K. C. C. Alevi, C. H. L. Imperador, et al., Parasite-vector interaction of Chagas disease: A mini-review, Am. J. Trop. Med. Hyg., 98 (2018), 653-655. doi: 10.4269/ajtmh. 17-0657.

[10]

O. DiekmannJ. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.  doi: 10.1007/BF00178324.

[11]

O. DiekmannJ. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, J. R. Soc. Interface, 7 (2010), 873-885.  doi: 10.1098/rsif.2009.0386.

[12]

D. Erazo, et al., Modelling the influence of host community composition in a sylvatic Trypanosoma cruzi system, Parasitology, 144 (2017), 1881-1889. doi: 10.1017/S0031182017001287.

[13]

C. A. Eva, P. S. Katia, R. B. Giselle, et al., Nanocarriers for effective delivery of benznidazole and nifurtimox in the treatment of chagas disease: A review, Acta. Tropica, 198 (2019), 105080. doi: 10.1016/j. actatropica. 2019.105080.

[14]

M. R. Fellet, M. G. Lorenzo, S. L. Elliot, et al., Effects of infection by Trypanosoma cruzi and Trypanosoma rangeli on the reproductive performance of the vector Rhodnius prolixus, PLoS One, 9 (2014), e105255. doi: 10.1371/journal. pone. 0105255.

[15]

R. C. Ferreira, C. F. Teixeira, V. F. A. de Sousa and A. A. Guarneri, Effect of temperature and vector nutrition on the development and multiplication of Trypanosoma rangeli in Rhodnius prolixus, Parasitol. Res., 117 (2018), 1737–1744. doi: 10.1007/s00436-018-5854-2.

[16]

D. GaoT. C. Porco and S. Ruan, Coinfection dynamics of two diseases in a single host population, J. Math. Anal. Appl., 442 (2016), 171-188.  doi: 10.1016/j.jmaa.2016.04.039.

[17]

N. Gottdenker, L. Chaves, J. Calzada, et al., Trypanosoma cruzi and Trypanosoma rangeli co-infection patterns in insect vectors vary across habitat types in a fragmented forest landscape, Parasitology, 2 (2016), E10. doi: 10.1017/pao. 2016.9.

[18]

M. J. Grijalva, V. Suarez-Davalos, A. G. Villacis et al., Ecological factors related to the widespread distribution of sylvatic Rhodnius ecuadoriensis populations in southern Ecuador, Parasit. Vectors, 5 (2012), 17. doi: 10.1186/1756-3305-5-17.

[19]

A. A. Guarneri and M. G. Lorenzo, Triatomine physiology in the context of trypanosome infection, J. Insect Physiol., 97 (2017), 66-76.  doi: 10.1016/j.jinsphys.2016.07.005.

[20]

F. Guhl, L. Hudson, C. J. Marinkelle, et al., Clinical Trypanosoma rangeli infection as a complication of Chagas' disease, Parasitology, 94 (1987), 475-484. doi: 10.1017/S0031182000055827.

[21]

R. E. Gürtler, L. A. Ceballos, P. Ordóñez-Krasnowski et al., Strong host-feeding preferences of the vector Triatoma infestans modified by vector density: Implications for the epidemiology of Chagas disease, PLoS Negl. Trop. Dis., 3 (2009), e447. doi: 10.1371/journal. pntd. 0000447.

[22]

R. E. G¨urtler, U. Kitron, M. C. Cecere, et al., Sustainable vector control and management of Chagas disease in the Gran Chaco, Argentina, Proc. Natl. Acad. Sci. USA., 104 (2007), 16194-16199. doi: 10.1073/pnas. 0700863104.

[23]

C. M. Kribs and C. Mitchell, Host switching vs. host sharing in overlapping sylvatic Trypanosoma cruzi transmission cycles, J. Biol. Dyn., 9 (2015), 247-277.  doi: 10.1080/17513758.2015.1075611.

[24]

C. Kribs-Zeleta, Vector Consumption and Contact Process Saturation in Sylvatic Transmission of T. cruzi, Mathematical Population Studies, 13 (2006), 135-152.  doi: 10.1080/08898480600788576.

[25]

C. Kribs-Zeleta, Estimating Contact Process Saturation in Sylvatic Transmission of Trypanosoma cruzi in the United States, PLoS. Negl. Trop. Dis., 4 (2010), e656. doi: 10.1371/journal. pntd. 0000656.

[26]

M. Z. Levy, F. S. Malaga Chavez, J. G. Cornejo Del Carpio, et al., Rational spatio-temporal strategies for controlling a Chagas disease vector in urban environments, J. R. Soc. Interface., 7 (2010), 1061-1070. doi: 10.1098/rsif. 2009.0479.

[27]

B. Y. Lee, K. M. Bacon, A. R. Wateska, et al., Modeling the economic value of a Chagas disease therapeutic vaccine, Hum. Vaccin. Immunother., 8 (2012), 1293-1301. doi: 10.4161/hv. 20966.

[28]

B. Y. LeeK. M. BaconM. E. Bottazzi and P. J. Hotez, Global economic burden of Chagas disease: A computational simulation model, Lancet. Infect. Dis., 13 (2013), 342-348.  doi: 10.1016/S1473-3099(13)70002-1.

[29]

B. Y. Lee, S. M. Bartsch, L. Skrip, et al., Are the London Declaration's 2020 goals sufficient to control Chagas disease?: Modeling scenarios for the Yucatan Peninsula, PLoS Negl. Trop. Dis., 12 (2018), e0006337. doi: 10.1371/journal. pntd. 0006337.

[30]

K. C. F. Lidani, F. A. Andrade, L. Bavia, et al., Chagas disease: From discovery to a worldwide health problem, Front. Public Health, 7 (2019), 166. doi: 10.3389/fpubh. 2019.00166.

[31]

Y. LouJ. Wu and X. Wu, Impact of biodiversity and seasonality on Lyme-pathogen transmission, Theor. Biol. Med. Model., 11 (2014), 50.  doi: 10.1186/1742-4682-11-50.

[32]

N. P. Marliére, M. G. Lorenzo and A. A. Guarneri, Trypanosoma rangeli infection increases the exposure and predation endured by Rhodnius prolixus, Parasitology, 149 (2022) 155–160. doi: 10.1017/S0031182021001682.

[33]

M. Martcheva and S. S. Pilyugin, The role of coinfection in multidisease dynamics, SIAM J. Appl. Math., 66 (2006), 843-872.  doi: 10.1137/040619272.

[34]

J. K. PetersonS. M. BartschB. Y. Lee and A. P. Dobson, Broad patterns in domestic vector-borne Trypanosoma cruzi transmission dynamics: Synanthropic animals and vector control, Parasites Vectors, 8 (2015), 537.  doi: 10.1186/s13071-015-1146-1.

[35]

J. K. PetersonA. L. GrahamR. J. ElliottA. P. Dobson and O. T. Chávez, Trypanosoma cruzi-Trypanosoma rangeli co-infection ameliorates negative effects of single trypanosome infections in experimentally infected Rhodnius prolixus, Parasitology, 143 (2016), 1157-1167.  doi: 10.1017/S0031182016000615.

[36]

J. E. RabinovichJ. A. Leal and D. Feliciangeli de Piñero, Domiciliary biting frequency and blood ingestion of the Chagas's disease vector Rhodnius prolixus Stahl (Hemiptera: Reduviidae), in Venezuela, Trans. R. Soc. Trop. Med. Hyg., 73 (1979), 272-283.  doi: 10.1016/0035-9203(79)90082-8.

[37]

A. Requena-Méndez, E. Aldasoro, E. de Lazzari, et al., Prevalence of Chagas disease in Latin-American migrants living in Europe: A systematic review and meta-analysis, PLoS Negl. Trop. Dis., 9 (2015), e0003540. doi: 10.1371/journal. pntd. 0003540.

[38]

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Figure 1.  (Color online) A schematic diagram of co-infection transmission in the host population

Here $ S_h $ represents the subpopulation of susceptible hosts, and $ I_{hi}/I_{vi}\, (i=1,2,3) $ represents the subpopulation of infected hosts/vectors with subscript $ i $ denoting the parasite infectious status, respectively. Subscript 0–no parasites; 1–single T. cruzi parasites; 2–single T. rangeli parasites; 3–both T. cruzi and T. rangeli parasites

Figure 2.  (Color online) A schematic diagram of co-infection in the triatomine bug population

Here $ S_v $ is the number of susceptible triatomine bugs and $ I_{vi}/I_{hi}\,\,(i=1,2,3) $ represents the number of infected triatomine bugs/hosts with subscript $ i $ denoting the infectious status with parasite-$ i $, respectively. Subscript 0–no parasites; 1–single T. cruzi parasites; 2–single T. rangeli parasites; 3–both T. cruzi and T. rangeli parasites

Figure 3.  (Color online) Impact of biting rate per bug per unit time on basic/invasive reproduction numbers

Here, $ a\in[1,30] $, $ N_h = 400 $, $ b^{h1}_{1\rightarrow0} = 0.003 $, $ b^{h2}_{2\rightarrow0} = 0.0027 $, $ b^{v1}_{1\rightarrow0} = 0.00032 $, $ b^{v2}_{2\rightarrow0} = 0.0026 $, $ \mu_h = 0.0005 $, $ \mu_v = 0.005 $, $ r =0.03 $, $ \sigma = 0.0009 $, $ \theta = 0.01 $, $ \delta_v=0.006 $ are used

Figure 4.  (Color online) Impact of T. rangeli presence on the spread of Chagas disease if $ \mathcal{R}_{20}>1 $ and $ \mathcal{R}_{10}>1>\mathcal{R}_{12} $ are satisfied

(a) and (b) are simulated from the model of T. cruzi-infection alone, and (c) and (d) are simulated from the co-infection model (2). Here, $ a = 0.8 $, $ N_h = 400 $, $ b^{h1}_{1\rightarrow0} = 0.003 $, $ b^{h2}_{2\rightarrow0} = 0.0027 $, $ b^{v1}_{1\rightarrow0} = 0.00032 $, $ b^{v2}_{2\rightarrow0} = 0.0026 $, $ \mu_h = 0.0005 $, $ \mu_v = 0.005 $, $ r =0.03 $, $ \sigma = 0.0009 $, $ \theta = 0.01 $, $ \delta_v=0.006 $ are used for the simulations

Figure 5.  (Color online) Impact of T. cruzi and T. rangeli co-infection on the risk of Chagas disease if $ \mathcal{R}_{20}>1 $ and $ \mathcal{R}_{10}>\mathcal{R}_{12}>1 $ are satisfied

(a) Solutions of T. cruzi-infected hosts with/without co-infection; (b) solutions of susceptible vectors with/without co-infection; (c) solutions of T. cruzi-infected vectors with/without co-infection. Model parameters are $ a = 0.3 $, $ N_h = 400 $, $ b^{h1}_{1\rightarrow0} = 0.03 $, $ b^{v1}_{1\rightarrow0} = 0.03 $, $ b^{h2}_{2\rightarrow0} = 0.012 $, $ b^{v2}_{2\rightarrow0} = 0.2 $, $ \mu_h = 0.001 $, $ \mu_v = 0.005 $, $ r =0.0274 $, $ \sigma = 0.001 $, $ \theta = 0.9 $, $ \delta_v=0.03 $. Particularly, $ b^{h2}_{2\rightarrow0}=b^{v2}_{2\rightarrow0}=\delta_v=0 $ and $ \theta=1 $ in the case of no T. rangeli co-infection

Figure 6.  (Color online) The effect of $ \theta $, $ \delta_v $ and $ \mu_h $ on the oscillation pattern of Chagas disease

All simulations run until the steady state. Apart from the varied parameters in each subfigure, other associated parameters are fixed as $ a = 0.6 $, $ b^{h1}_{1\rightarrow0} = 0.06 $, $ b^{v1}_{1\rightarrow0} = 0.2 $, $ b^{h2}_{2\rightarrow0} = 0.05 $, $ b^{v2}_{2\rightarrow0} = 0.2 $, $ N_h = 400 $, $ \mu_v = 0.005 $, $ r =0.0274 $, $ \sigma = 0.001 $, $ \delta_v=0.0347 $, $ \theta=0.1 $, $ \mu_h = 0.001 $

Figure 7.  (Color online) Numerical illustration of bifurcation diagram with the variation of $ \theta $ and $ \delta_v $

(a) Maximum/minimum sizes of $ I_{h1} $ at steady state with respect to $ \theta\in[0,1] $; (b) maximum/minimum sizes of $ I_{h1} $ at steady state with respect to $ \delta_v\in[0,0.05] $. Here, $ a = 0.6,\, b^{h1}_{1\rightarrow0} = 0.06,\, b^{v1}_{1\rightarrow0} = 0.2,\, b^{h2}_{2\rightarrow0} = 0.05,\, b^{v2}_{2\rightarrow0} = 0.2,\, N_h = 400,\, \mu_h = 0.001,\, \mu_v = 0.005,\, r =0.0274,\, \sigma = 0.001 $ and $ \delta_v = 0.0347 $ for (a), $ \theta = 0.1 $ for (b) are used

Table 1.  Parameter description and justification
Parameter Description Range/Value Source
$ N_h $ total number of hosts 400 [29, 50]
$ a $ number of bites per bug per unit time $ (0.2,33)\, day^{-1} $ [36]
$ b_{i\rightarrow j}^{hk} $ transmission probability of parasite-$ k $ per contact, from triatomine bugs who are infected with parasite-$ i $ to hosts who are already infected with parasite-$ j $ [0.00271, 0.06] [29, 44]
$ \beta_{i\rightarrow j}^{hk} $ transmission rate of parasite-$ k $ per host per vector, from triatomine bugs who are infected with parasite-$ i $ to hosts who are already infect with parasite-$ j $ $ (ab^{hk}_{i\rightarrow j})/N_h $ calculated
$ b_{i\rightarrow j}^{vk} $ transmission probability of parasite-$ k $ per contact, from hosts who are infected with parasite-$ i $ to vectors who are already infected with parasite-$ j $ [0.00026, 0.49] [1, 44]
$ \beta_{i\rightarrow j}^{vk} $ transmission rate of parasite-$ k $ per host per vector, from hosts who are infected with parasite-$ i $ to vectors who are already infected with parasite-$ j $ $ (ab^{vk}_{i\rightarrow j})/N_h $ calculated
$ \mu_h $ host mortality rate $ [0.000038,0.0025]\, day^{-1} $ [1, 44]
$ \mu_v $ vector mortality rate $ [0.0045,0.0083]\, day^{-1} $ [1, 44]
$ r $ the intrinsic birth rate of vectors $ [0.0274,0.7714]\, day^{-1} $ [1, 29, 50]
$ \sigma $ density-dependency strength measuring the reproduction of bugs $ [0,\infty) $ [50]
$ \theta_i (i=2,3) $ T. rangeli-induced reproduction reduction of traitomine bugs who are infected with parasite-$ i $ [0, 1] assumed
$ \delta_{vi} (i=2,3) $ T. rangeli-induced mortality rate of traitomine bugs who are infected with parasite-$ i $ $ (0, 0.05]\, day^{-1} $ [2, 50]
Parameter Description Range/Value Source
$ N_h $ total number of hosts 400 [29, 50]
$ a $ number of bites per bug per unit time $ (0.2,33)\, day^{-1} $ [36]
$ b_{i\rightarrow j}^{hk} $ transmission probability of parasite-$ k $ per contact, from triatomine bugs who are infected with parasite-$ i $ to hosts who are already infected with parasite-$ j $ [0.00271, 0.06] [29, 44]
$ \beta_{i\rightarrow j}^{hk} $ transmission rate of parasite-$ k $ per host per vector, from triatomine bugs who are infected with parasite-$ i $ to hosts who are already infect with parasite-$ j $ $ (ab^{hk}_{i\rightarrow j})/N_h $ calculated
$ b_{i\rightarrow j}^{vk} $ transmission probability of parasite-$ k $ per contact, from hosts who are infected with parasite-$ i $ to vectors who are already infected with parasite-$ j $ [0.00026, 0.49] [1, 44]
$ \beta_{i\rightarrow j}^{vk} $ transmission rate of parasite-$ k $ per host per vector, from hosts who are infected with parasite-$ i $ to vectors who are already infected with parasite-$ j $ $ (ab^{vk}_{i\rightarrow j})/N_h $ calculated
$ \mu_h $ host mortality rate $ [0.000038,0.0025]\, day^{-1} $ [1, 44]
$ \mu_v $ vector mortality rate $ [0.0045,0.0083]\, day^{-1} $ [1, 44]
$ r $ the intrinsic birth rate of vectors $ [0.0274,0.7714]\, day^{-1} $ [1, 29, 50]
$ \sigma $ density-dependency strength measuring the reproduction of bugs $ [0,\infty) $ [50]
$ \theta_i (i=2,3) $ T. rangeli-induced reproduction reduction of traitomine bugs who are infected with parasite-$ i $ [0, 1] assumed
$ \delta_{vi} (i=2,3) $ T. rangeli-induced mortality rate of traitomine bugs who are infected with parasite-$ i $ $ (0, 0.05]\, day^{-1} $ [2, 50]
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