Human Immunodeficiency Virus (HIV) dynamics in Africa are purely characterised by sparse sampling of DNA sequences for individuals who are infected. There are some sub-groups that are more at risk than the general population. These sub-groups have higher infectivity rates. We came up with a likelihood inference model of multi-type birth-death process that can be used to make inference for HIV epidemic in an African setting. We employ a likelihood inference that incorporates a probability of removal from infectious pool in the model. We have simulated trees and made parameter inference on the simulated trees as well as investigating whether the model distinguishes between heterogeneous and homogeneous dynamics. The model makes fairly good parameter inference. It distinguishes between heterogeneous and homogeneous dynamics well. Parameter estimation was also performed under sparse sampling scenario. We investigated whether trees obtained from a structured population are more balanced than those from a non-structured host population using tree statistics that measure tree balance and imbalance. Trees from non-structured population were more balanced basing on Colless and Sackin indices.
References
[1]
UNAIDS (2017) Unaids Data. Technical Report, Joint United Nations Programme on HIV/AIDS.
[2]
UNDESA (2017) United Nations Department of Economic and Social Affairs, Population Division. World Population Prospects: The 2017 Revision, Key Findings and Advance Tables. Technical Report, United Nations, New York.
[3]
UNAIDS (2011) Unaids Terminology Guidelines. Technical Report, Joint United Nations Programme on HIV/AIDS.
[4]
UAC (2016) Uganda HIV and Aids Country Progress Report. Technical Report, Uganda AIDS Commission.
[5]
UAC (2014) Uganda HIV and Aids Country Progress Report. Technical Report, Uganda AIDS Commission.
[6]
Kiwanuka, N., Ssetaala, A., Nalutaaya, A., Mpendo, J., Wambuzi, M., Nanvubya, A., Sigirenda, S., Kitandwe, P.K., Nielsen, L.E. and Balyegisawa, A. (2014) High Incidence of HIV-1 Infection in a General Population of Fishing Communities around Lake Victoria, Uganda. PLoS ONE, 9, e94932. https://doi.org/10.1371/journal.pone.0094932
[7]
Kribs-Zaleta, C.M., Lee, M., Rom an, C., Wiley, S. and Hernandez-Suarez, C.M. (2005) The Effect of the HIV/AIDS Epidemic on Africa’s Truck Drivers. Mathematical Biosciences and Engineering: MBE, 2, 771-788. https://doi.org/10.3934/mbe.2005.2.771
[8]
Gouws, E. and Cuchi, P. (2012) Focusing the HIV Response through Estimating the Major Modes of HIV Transmission: A Multi-Country Analysis. Sexually Transmitted Infections, 88, i76-i85. https://doi.org/10.1136/sextrans-2012-050719
[9]
Bbosa, N., Ssemwanga, D., Nsubuga, R.N., Salazar-Gonzalez, J.F., Salazar, M.G., Nanyonjo, M., Kuteesa, M., Seeley, J., Kiwanuka, N., Bagaya, B.S., et al. (2019) Phylogeography of HIV-1 Suggests that Ugandan Fishing Communities Are a Sink for, Not a Source of, Virus from General Populations. Scientific Reports, 9, 1051. https://doi.org/10.1038/s41598-018-37458-x
[10]
UPHIA (2017) Uganda Population Based HIV Impact Assessment. Technical Report, Government of Uganda.
[11]
Pillay, D., Herbeck, J., Cohen, M.S., Tulio de Oliveira, Fraser, C., Ratmann, O., Leigh Brown, A. and Kellam, P. (2015) The Pangea-HIV Consortium: Phylogenetics and Networks for Generalised HIV Epidemics in Africa. The Lancet Infectious Diseases, 15, 259. https://doi.org/10.1016/S1473-3099(15)70036-8
[12]
Stadler, T., Kouyos, R., von Viktor, W., Yerly, S., Boni, J., Burgisser, P., Klimkait, T., Joos, B., Rieder, P., Xie, D., et al. (2011) Estimating the Basic Reproductive Number from Viral Sequence Data. Molecular Biology and Evolution, 29, 347-357. https://doi.org/10.1093/molbev/msr217
[13]
Kuhnert, D., Stadler, T., Vaughan, T.G. and Drummond, A.J. (2014) Simultaneous Reconstruction of Evolutionary History and Epidemiological Dynamics from Viral Sequences with the Birth-Death Sir Model. Journal of the Royal Society Interface, 11, Article ID: 20131106. https://doi.org/10.1098/rsif.2013.1106
[14]
Stadler, T. and Bonhoeffer, S. (2013) Uncovering Epidemiological Dynamics in Heterogeneous Host Populations Using Phylogenetic Methods. Philosophical Transactions of the Royal Society B: Biological Sciences, 368, Article ID: 20120198. https://doi.org/10.1098/rstb.2012.0198
[15]
Gavryushkina, A., Welch, D., Stadler, T. and Drummond, A.J. (2014) Bayesian Inference of Sampled Ancestor Trees for Epidemiology and Fossil Calibration. PLoS Computational Biology, 10, e1003919. https://doi.org/10.1371/journal.pcbi.1003919
[16]
Stadler, T. (2012) How Can We Improve Accuracy of Macroevolutionary Rate Estimates? Systematic Biology, 62, 321-329. https://doi.org/10.1093/sysbio/sys073
[17]
Stadler, T. (2014) Treesim: Simulating Trees under the Birth-Death Model. R Package Version 2.0.
[18]
Stadler, T. and Maintainer Stadler, T. (2015) Estimating Birth and Death Rates Based on Phylogenies. R Package Version 3.3.
[19]
Gascuel, O. (2005) Mathematics of Evolution and Phylogeny. OUP, Oxford.
[20]
Ota, R., Waddell, P.J., Hasegawa, M., Shimodaira, H. and Kishino, H. (2000) Appropriate Likelihood Ratio Tests and Marginal Distributions for Evolutionary Tree Models with Constraints on Parameters. Molecular Biology and Evolution, 17, 798-803. https://doi.org/10.1093/oxfordjournals.molbev.a026358
[21]
Yebra, G., Hodcroft, E.B., Ragonnet-Cronin, M.L., Pillay, D., Leigh Brown, A.J., Fraser, C., Kellam, P., De Oliveira, T., Dennis, A., Hoppe, A., et al. (2016) Using Nearly Full-Genome HIV Sequence Data Improves Phylogeny Reconstruction in a Simulated Epidemic. Scientific Reports, 6, 39489. https://doi.org/10.1038/srep39489
[22]
Drummond, A.J. and Rambaut, A. (2007) Beast: Bayesian Evolutionary Analysis by Sampling Trees. BMC Evolutionary Biology, 7, 214. https://doi.org/10.1186/1471-2148-7-214
[23]
Blum, M.G.B. and Francois, O. (2005) On Statistical Tests of Phylogenetic Tree Imbalance: The Sackin and Other Indices Revisited. Mathematical Biosciences, 195, 141-153. https://doi.org/10.1016/j.mbs.2005.03.003
[24]
Pybus, O.G. and Harvey, P.H. (2000) Testing Macro-Evolutionary Models Using Incomplete Molecular Phylogenies. Proceedings of the Royal Society of London B: Biological Sciences, 267, 2267-2272. https://doi.org/10.1098/rspb.2000.1278
[25]
Blum, M.G.B., Francois, O. and Janson, S. (2006) The Mean, Variance and Limiting Distribution of Two Statistics Sensitive to Phylogenetic Tree Balance. The Annals of Applied Probability, 16, 2195-2214. https://doi.org/10.1214/105051606000000547
[26]
Shao, K.T. (1990) Tree Balance. Systematic Zoology, 39, 266-276. https://doi.org/10.2307/2992186
[27]
Bortolussi, N., Durand, E., Blum, M. and Francois, O. (2005) Aptreeshape: Statistical Analysis of Phylogenetic Tree Shape. Bioinformatics, 22, 363-364. https://doi.org/10.1093/bioinformatics/bti798
[28]
Maddison, W.P., Midford, P.E. and Otto, S.P. (2007) Estimating a Binary Character’s Effect on Speciation and Extinction. Systematic Biology, 56, 701-710. https://doi.org/10.1080/10635150701607033
[29]
Rabosky, D.L (2010). Extinction Rates Should Not Be Estimated from Molecular Phylogenies. Evolution: International Journal of Organic Evolution, 64, 1816-1824. https://doi.org/10.1111/j.1558-5646.2009.00926.x
[30]
Beaulieu, J.M. and O’Meara, B.C. (2015) Extinction Can Be Estimated from Moderately Sized Molecular Phylogenies. Evolution, 69, 1036-1043. https://doi.org/10.1111/evo.12614
[31]
Rabosky, D.L. (2016) Challenges in the Estimation of Extinction from Molecular Phylogenies: A Response to Beaulieu and O’Meara. Evolution, 70, 218-228. https://doi.org/10.1111/evo.12820
