1
|
Huo HF, Fu T, Xiang H. Dynamics and optimal control of a Zika model with sexual and vertical transmissions. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:8279-8304. [PMID: 37161197 DOI: 10.3934/mbe.2023361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
A new transmission model of Zika virus with three transmission routes including human transmission by mosquito bites, sexual transmission between males and females and vertical transmission is established. The basic reproduction number $ R_{0} $ is derived. When $ R_{0} < 1 $, it is proved that the disease-free equilibrium is globally stable. Furthermore, the optimal control and mitigation methods for transmission of Zika virus are deduced and explored. The MCMC method is used to estimate the parameters and the reasons for the deviation between the actual infection cases and the simulated data are discussed. In addition, different strategies for controlling the spread of Zika virus are simulated and studied. The combination of mosquito control strategies and internal human control strategies is the most effective way in reducing the risk of Zika virus infection.
Collapse
Affiliation(s)
- Hai-Feng Huo
- Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
| | - Tian Fu
- Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
| | - Hong Xiang
- Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
| |
Collapse
|
2
|
Durgam L, Guruprasad L. Molecular mechanism of ATP and RNA binding to Zika virus NS3 helicase and identification of repurposed drugs using molecular dynamics simulations. J Biomol Struct Dyn 2022; 40:12642-12659. [PMID: 34516356 DOI: 10.1080/07391102.2021.1973909] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Congenital Zika virus syndrome has caused a public health emergency of international concern. So far, there are no drugs available to prevent or treat the infection caused by Zika virus. The Zika virus NS3 helicase is a potential protein target for drug discovery due to its vital role in viral genome replication. NS3 helicase unwinds the viral RNA to enable the reproduction of the viral genome by the NS5 protein. NS3 helicase has two crucial binding sites; the ATP binding site and the RNA binding site. We used molecular docking and molecular dynamics (MD) simulations to study the structural behavior of Zika virus NS3 helicase in its apo form and in the presence of ATP, single-stranded RNA, and both ATP-RNA to understand their potential implications in NS3 helicase activity. Further, we have carried out virtual screening of FDA approved drugs, followed by molecular docking to identify the ATP-competitive hit molecules as probable Zika virus NS3 helicase inhibitors. The MD simulations trajectories were analyzed using normal mode analysis and principal component analysis that reveals fluctuations in the R-loop. These findings aid in understanding the molecular mechanisms of the simultaneous binding of ATP and RNA, and guide the design and discovery of new inhibitors of the Zika virus NS3 helicase as a promising drug target to treat the Zika virus infection. Communicated by Ramaswamy H. Sarma.
Collapse
Affiliation(s)
- Laxman Durgam
- School of Chemistry, University of Hyderabad, Hyderabad, India
| | | |
Collapse
|
3
|
HONFO SEWANOUH, TABOE HEMAHOB, KAKAÏ ROMAINGLELE. Modeling COVID-19 dynamics in the sixteen West African countries. SCIENTIFIC AFRICAN 2022; 18:e01408. [PMCID: PMC9621612 DOI: 10.1016/j.sciaf.2022.e01408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Revised: 11/27/2021] [Accepted: 10/20/2022] [Indexed: 11/05/2022] Open
Abstract
The current COVID-19 pandemic has caused several damages to the world, especially in public health sector. This study considered a simple deterministic SIR (Susceptible-Infectious-Recovered) model to characterize and predict future course of the pandemic in the West African countries. We estimated specific characteristics of the disease’s dynamics such as its initial conditions, reproduction numbers, true peak, reported peak with their corresponding times, final epidemic size and time-varying attack ratio. Our findings revealed a relatively low proportion of susceptible individuals in the region and in the different countries (1.2 % across West Africa). The detection rate of the disease was also relatively low (0.9 % for West Africa as a whole) and <2 % for most countries, except for Gambia (12.5 %), Cape-Verde (9.5 %), Mauritania (5.9 %) and Ghana (4.4 %). The reproduction number varied between 1.15 (Burkina-Faso) and 4.45 (Niger) and the peak time of the pandemic was between June and July for most countries. Most generally, the peak time of reported cases came a week (7-8 days) after the true peak time. The model predicted 222,100 actual active cases in the region at peak time while the final epidemic size accounted for 0.6 % of the West African population (2,526,700 individuals). Results obtained showed that the COVID-19 pandemic has not severely affected West Africa as noticed in other regions of the world, but current control measures and standard operating procedures should be maintained over time to ensure trends observed and even accelerate the declining trend of the pandemic.
Collapse
|
4
|
Juvenile hormone analog enhances Zika virus infection in Aedes aegypti. Sci Rep 2021; 11:21062. [PMID: 34702871 PMCID: PMC8548497 DOI: 10.1038/s41598-021-00432-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 10/12/2021] [Indexed: 12/17/2022] Open
Abstract
In recent years, there has been a rise in the emergence of arboviruses of public health importance, including Zika, chikungunya, dengue, and yellow fever viruses. Insecticide-based mosquito control has been the primary method for mitigating transmission of arboviruses. The consequences for the application of insecticides include both lethal and sublethal effects, and associated development of insecticide resistance. However, little is known about the influence on arboviral transmission. Mosquitoes with phenotypes that exhibit insecticide resistance or experience sublethal effects may be associated with altered susceptibility to arbovirus infection and transmission. Juvenile hormone analogs (JHAs) are insecticides that prevent pupa to adult molting of mosquitoes by mimicking the action of their natural juvenile hormone. Here, we examined whether the JHA pyriproxyfen interacts with ambient temperature (20 °C and 30 °C) during juvenile stages to influence life-history traits, population growth (λ'), and Zika virus (ZIKV) infection in Aedes aegypti. Development time of females was lengthened at 20 °C and in the presence of JHA. Prevention of pupa to adult molting by JHA was differentially higher at elevated temperature than low temperature. Size of females was larger at 20 °C and smaller at 30 °C. Infection, disseminated infection, and transmission of ZIKV in females were enhanced by JHA at both 20 °C and 30 °C relative to the controls. These results demonstrate that mosquito life-history and vector competence parameters are strongly influenced by interactive effects of JHA and temperature. The JHA-induced enhancement of ZIKV infection in females should be a consideration when implementing JHA in vector control strategies.
Collapse
|
5
|
Bensaoud C, Martins LA, Aounallah H, Hackenberg M, Kotsyfakis M. Emerging roles of non-coding RNAs in vector-borne infections. J Cell Sci 2020; 134:134/5/jcs246744. [PMID: 33154170 DOI: 10.1242/jcs.246744] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Non-coding RNAs (ncRNAs) are nucleotide sequences that are known to assume regulatory roles previously thought to be reserved for proteins. Their functions include the regulation of protein activity and localization and the organization of subcellular structures. Sequencing studies have now identified thousands of ncRNAs encoded within the prokaryotic and eukaryotic genomes, leading to advances in several fields including parasitology. ncRNAs play major roles in several aspects of vector-host-pathogen interactions. Arthropod vector ncRNAs are secreted through extracellular vesicles into vertebrate hosts to counteract host defense systems and ensure arthropod survival. Conversely, hosts can use specific ncRNAs as one of several strategies to overcome arthropod vector invasion. In addition, pathogens transmitted through vector saliva into vertebrate hosts also possess ncRNAs thought to contribute to their pathogenicity. Recent studies have addressed ncRNAs in vectors or vertebrate hosts, with relatively few studies investigating the role of ncRNAs derived from pathogens and their involvement in establishing infections, especially in the context of vector-borne diseases. This Review summarizes recent data focusing on pathogen-derived ncRNAs and their role in modulating the cellular responses that favor pathogen survival in the vertebrate host and the arthropod vector, as well as host ncRNAs that interact with vector-borne pathogens.
Collapse
Affiliation(s)
- Chaima Bensaoud
- Institute of Parasitology, Biology Centre, Czech Academy of Sciences, 37005, Ceske Budejovice (Budweis), Czechia
| | - Larissa Almeida Martins
- Institute of Parasitology, Biology Centre, Czech Academy of Sciences, 37005, Ceske Budejovice (Budweis), Czechia
| | - Hajer Aounallah
- Université de Tunis El Manar, Institut Pasteur de Tunis, LR11IPT03, Service d'entomologie médicale, 1002, Tunis, Tunisie.,Innovation and Development Laboratory, Innovation and Development Center, Instituto Butantan, São Paulo 05503-900, Brazil
| | - Michael Hackenberg
- Dpto. de Genética, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva s/n, 18071, Granada, Spain.,Lab. de Bioinformática, Centro de Investigación Biomédica, PTS, Instituto de Biotecnología, Avda. del Conocimiento s/n, Granada 18100, Spain
| | - Michail Kotsyfakis
- Institute of Parasitology, Biology Centre, Czech Academy of Sciences, 37005, Ceske Budejovice (Budweis), Czechia
| |
Collapse
|
6
|
Zhuang J, Yin J, Lv S, Wang B, Mu Y. Advanced "lab-on-a-chip" to detect viruses - Current challenges and future perspectives. Biosens Bioelectron 2020; 163:112291. [PMID: 32421630 PMCID: PMC7215165 DOI: 10.1016/j.bios.2020.112291] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2020] [Revised: 05/02/2020] [Accepted: 05/10/2020] [Indexed: 12/28/2022]
Abstract
Massive viral outbreaks draw attention to viruses that have not been thoroughly studied or understood. In recent decades, microfluidic chips, known as "lab-on-a-chip", appears as a promising tool for the detection of viruses. Here, we review the development of microfluidic chips that could be used in response to viral detection, specifically for viruses involved in more recent outbreaks. The advantages as well as the disadvantages of microfluidic systems are discussed and analyzed. We also propose ideas for future development of these microfluidic chips and we expect this advanced technology to be used in the future for viral outbreaks.
Collapse
Affiliation(s)
- Jianjian Zhuang
- College of Life Sciences, Zhejiang University, Hangzhou, 310058, Zhejiang, China
| | - Juxin Yin
- Research Centre for Analytical Instrumentation, Institute of Cyber-Systems and Control, State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, Zhejiang Province, 310058, China; Cancer Institute (Key Laboratory of Cancer Prevention and Intervention, National Ministry of Education), The Second Affiliated Hospital, School of Medicine, Zhejiang University, Hangzhou, 310009, China; Institute of Translational Medicine, Zhejiang University, Hangzhou, 310029, China
| | - Shaowu Lv
- Key Laboratory for Molecular Enzymology and Engineering of the Ministry of Education, College of Life Science, Jilin University, Changchun, 130000, China
| | - Ben Wang
- Cancer Institute (Key Laboratory of Cancer Prevention and Intervention, National Ministry of Education), The Second Affiliated Hospital, School of Medicine, Zhejiang University, Hangzhou, 310009, China; Institute of Translational Medicine, Zhejiang University, Hangzhou, 310029, China
| | - Ying Mu
- Research Centre for Analytical Instrumentation, Institute of Cyber-Systems and Control, State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, Zhejiang Province, 310058, China; College of Life Sciences, Zhejiang University, Hangzhou, 310058, Zhejiang, China.
| |
Collapse
|
7
|
He D, Zhao S, Lin Q, Musa SS, Stone L. New estimates of the Zika virus epidemic attack rate in Northeastern Brazil from 2015 to 2016: A modelling analysis based on Guillain-Barré Syndrome (GBS) surveillance data. PLoS Negl Trop Dis 2020; 14:e0007502. [PMID: 32348302 PMCID: PMC7213748 DOI: 10.1371/journal.pntd.0007502] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2019] [Revised: 05/11/2020] [Accepted: 03/16/2020] [Indexed: 12/13/2022] Open
Abstract
BACKGROUND Between January 2015 and August 2016, two epidemic waves of Zika virus (ZIKV) disease swept the Northeastern (NE) region of Brazil. As a result, two waves of Guillain-Barré Syndrome (GBS) were observed concurrently. The mandatory reporting of ZIKV disease began region-wide in February 2016, and it is believed that ZIKV cases were significantly under-reported before that. The changing reporting rate has made it difficult to estimate the ZIKV infection attack rate, and studies in the literature vary widely from 17% to > 50%. The same applies to other key epidemiological parameters. In contrast, the diagnosis and reporting of GBS cases were reasonably reliable given the severity and easy recognition of the disease symptoms. In this paper, we aim to estimate the real number of ZIKV cases (i.e., the infection attack rate) and their dynamics in time, by scaling up from GBS surveillance data in NE Brazil. METHODOLOGY A mathematical compartmental model is constructed that makes it possible to infer the true epidemic dynamics of ZIKV cases based on surveillance data of excess GBS cases. The model includes the possibility that asymptomatic ZIKV cases are infectious. The model is fitted to the GBS surveillance data and the key epidemiological parameters are inferred by using a plug-and-play likelihood-based estimation. We make use of regional weather data to determine possible climate-driven impacts on the reproductive number [Formula: see text], and to infer the true ZIKV epidemic dynamics. FINDINGS AND CONCLUSIONS The GBS surveillance data can be used to study ZIKV epidemics and may be appropriate when ZIKV reporting rates are not well understood. The overall infection attack rate (IAR) of ZIKV is estimated to be 24.1% (95% confidence interval: 17.1%-29.3%) of the population. By examining various asymptomatic scenarios, the IAR is likely to be lower than 33% over the two ZIKV waves. The risk rate from symptomatic ZIKV infection to develop GBS was estimated as ρ = 0.0061% (95% CI: 0.0050%-0.0086%) which is significantly less than current estimates. We found a positive association between local temperature and the basic reproduction number, [Formula: see text]. Our analysis revealed that asymptomatic infections affect the estimation of ZIKV epidemics and need to also be carefully considered in related modelling studies. According to the estimated effective reproduction number and population wide susceptibility, we comment that a ZIKV outbreak would be unlikely in NE Brazil in the near future.
Collapse
Affiliation(s)
- Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Shi Zhao
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
- Division of Biostatistics, JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- Clinical Trials and Biostatistics Lab, Shenzhen Research Institute, Chinese University of Hong Kong, Shenzhen, China
| | - Qianying Lin
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
- Michigan Institute for Data Science, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Salihu S. Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Lewi Stone
- Mathematical Science, School of Science, RMIT University, Melbourne, Victoria, Australia
- Biomathematics Unit, School of Zoology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv, Israel
| |
Collapse
|
8
|
Zhao S, Stone L, Gao D, Musa SS, Chong MKC, He D, Wang MH. Imitation dynamics in the mitigation of the novel coronavirus disease (COVID-19) outbreak in Wuhan, China from 2019 to 2020. ANNALS OF TRANSLATIONAL MEDICINE 2020; 8:448. [PMID: 32395492 PMCID: PMC7210122 DOI: 10.21037/atm.2020.03.168] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Background The coronavirus disease 2019 (COVID-19) was first identified in Wuhan, China on December 2019 in patients presenting with atypical pneumonia. Although ‘city-lockdown’ policy reduced the spatial spreading of the COVID-19, the city-level outbreaks within each city remain a major concern to be addressed. The local or regional level disease control mainly depends on individuals self-administered infection prevention actions. The contradiction between choice of taking infection prevention actions or not makes the elimination difficult under a voluntary acting scheme, and represents a clash between the optimal choice of action for the individual interest and group interests. Methods We develop a compartmental epidemic model based on the classic susceptible-exposed-infectious-recovered model and use this to fit the data. Behavioral imitation through a game theoretical decision-making process is incorporated to study and project the dynamics of the COVID-19 outbreak in Wuhan, China. By varying the key model parameters, we explore the probable course of the outbreak in terms of size and timing under several public interventions in improving public awareness and sensitivity to the infection risk as well as their potential impact. Results We estimate the basic reproduction number, R0, to be 2.5 (95% CI: 2.4−2.7). Under the current most realistic setting, we estimate the peak size at 0.28 (95% CI: 0.24−0.32) infections per 1,000 population. In Wuhan, the final size of the outbreak is likely to infect 1.35% (95% CI: 1.00−2.12%) of the population. The outbreak will be most likely to peak in the first half of February and drop to daily incidences lower than 10 in June 2020. Increasing sensitivity to take infection prevention actions and the effectiveness of infection prevention measures are likely to mitigate the COVID-19 outbreak in Wuhan. Conclusions Through an imitating social learning process, individual-level behavioral change on taking infection prevention actions have the potentials to significantly reduce the COVID-19 outbreak in terms of size and timing at city-level. Timely and substantially resources and supports for improving the willingness-to-act and conducts of self-administered infection prevention actions are recommended to reduce to the COVID-19 associated risks.
Collapse
Affiliation(s)
- Shi Zhao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China.,Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen 518060, China
| | - Lewi Stone
- School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia.,Biomathematics Unit, Department of Zoology, Tel Aviv University, Ramat Aviv, Israel
| | - Daozhou Gao
- Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
| | - Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Marc K C Chong
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China.,Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen 518060, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Maggie H Wang
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China.,Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen 518060, China
| |
Collapse
|
9
|
Zhao S, Musa SS, Hebert JT, Cao P, Ran J, Meng J, He D, Qin J. Modelling the effective reproduction number of vector-borne diseases: the yellow fever outbreak in Luanda, Angola 2015-2016 as an example. PeerJ 2020; 8:e8601. [PMID: 32149023 PMCID: PMC7049463 DOI: 10.7717/peerj.8601] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2019] [Accepted: 01/19/2020] [Indexed: 01/02/2023] Open
Abstract
The burden of vector-borne diseases (Dengue, Zika virus, yellow fever, etc.) gradually increased in the past decade across the globe. Mathematical modelling on infectious diseases helps to study the transmission dynamics of the pathogens. Theoretically, the diseases can be controlled and eventually eradicated by maintaining the effective reproduction number, (R eff ), strictly less than 1. We established a vector-host compartmental model, and derived (R eff ) for vector-borne diseases. The analytic form of the (R eff ) was found to be the product of the basic reproduction number and the geometric average of the susceptibilities of the host and vector populations. The (R eff ) formula was demonstrated to be consistent with the estimates of the 2015-2016 yellow fever outbreak in Luanda, and distinguished the second minor epidemic wave. For those using the compartmental model to study the vector-borne infectious disease epidemics, we further remark that it is important to be aware of whether one or two generations is considered for the transition "from host to vector to host" in reproduction number calculation.
Collapse
Affiliation(s)
- Shi Zhao
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
- Division of Biostatistics, JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- Clinical Trials and Biostatistics Lab, Shenzhen Research Institute, Chinese University of Hong Kong, Shenzhen, China
| | - Salihu S. Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Jay T. Hebert
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Peihua Cao
- Department of Hepatobiliary Surgery II, Zhujiang Hospital, Southern Medical University, Guangzhou, China
| | - Jinjun Ran
- School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China
| | - Jiayi Meng
- School of Economics and Finance, Xi’an International Studies University, Xi’an, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Jing Qin
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
| |
Collapse
|
10
|
Musa SS, Zhao S, Gao D, Lin Q, Chowell G, He D. Mechanistic modelling of the large-scale Lassa fever epidemics in Nigeria from 2016 to 2019. J Theor Biol 2020; 493:110209. [PMID: 32097608 DOI: 10.1016/j.jtbi.2020.110209] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Revised: 02/15/2020] [Accepted: 02/19/2020] [Indexed: 01/22/2023]
Abstract
Lassa fever, also known as Lassa hemorrhagic fever, is a virus that has generated recurrent outbreaks in West Africa. We use mechanistic modelling to study the Lassa fever epidemics in Nigeria from 2016-19. Our model describes the interaction between human and rodent populations with the consideration of quarantine, isolation and hospitalization processes. Our model supports the phenomenon of forward bifurcation where the stability between disease-free equilibrium and endemic equilibrium exchanges. Moreover, our model captures well the incidence curves from surveillance data. In particular, our model is able to reconstruct the periodic rodent and human forces of infection. Furthermore, we suggest that the three major epidemics from 2016-19 can be modelled by properly characterizing the rodent (or human) force of infection while the estimated human force of infection also present similar patterns across outbreaks. Our results suggest that the initial susceptibility likely increased across the three outbreaks from 2016-19. Our results highlight the similarity of the transmission dynamics driving three major Lassa fever outbreaks in the endemic areas.
Collapse
Affiliation(s)
- Salihu S Musa
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong; Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
| | - Shi Zhao
- School of Nursing, The Hong Kong Polytechnic University, Hong Kong; JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong; Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China
| | - Daozhou Gao
- Mathematics and Science College, Shanghai Normal University, Shanghai, China
| | - Qianying Lin
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong; Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI, USA
| | - Gerardo Chowell
- School of Public Health, Georgia State University, Atlanta, GA, USA; Fogarty International Center, National Institute of Health, Bethesda, MD, USA
| | - Daihai He
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong.
| |
Collapse
|
11
|
Large-scale Lassa fever outbreaks in Nigeria: quantifying the association between disease reproduction number and local rainfall. Epidemiol Infect 2020; 148:e4. [PMID: 31918780 PMCID: PMC7019145 DOI: 10.1017/s0950268819002267] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Lassa fever (LF) is increasingly recognised as an important rodent-borne viral haemorrhagic fever presenting a severe public health threat to sub-Saharan West Africa. In 2017–18, LF caused an unprecedented epidemic in Nigeria and the situation was worsening in 2018–19. This work aims to study the epidemiological features of epidemics in different Nigerian regions and quantify the association between reproduction number (R) and state rainfall. We quantify the infectivity of LF by the reproduction numbers estimated from four different growth models: the Richards, three-parameter logistic, Gompertz and Weibull growth models. LF surveillance data are used to fit the growth models and estimate the Rs and epidemic turning points (τ) in different regions at different time periods. Cochran's Q test is further applied to test the spatial heterogeneity of the LF epidemics. A linear random-effect regression model is adopted to quantify the association between R and state rainfall with various lag terms. Our estimated Rs for 2017–18 (1.33 with 95% CI 1.29–1.37) was significantly higher than those for 2016–17 (1.23 with 95% CI: (1.22, 1.24)) and 2018–19 (ranged from 1.08 to 1.36). We report spatial heterogeneity in the Rs for epidemics in different Nigerian regions. We find that a one-unit (mm) increase in average monthly rainfall over the past 7 months could cause a 0.62% (95% CI 0.20%–1.05%)) rise in R. There is significant spatial heterogeneity in the LF epidemics in different Nigerian regions. We report clear evidence of rainfall impacts on LF epidemics in Nigeria and quantify the impact.
Collapse
|
12
|
Harvim P, Zhang H, Georgescu P, Zhang L. Transmission Dynamics and Control Mechanisms of Vector-Borne Diseases with Active and Passive Movements Between Urban and Satellite Cities. Bull Math Biol 2019; 81:4518-4563. [PMID: 31641984 DOI: 10.1007/s11538-019-00671-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Accepted: 10/10/2019] [Indexed: 11/26/2022]
Abstract
A metapopulation model which explicitly integrates vector-borne and sexual transmission of an epidemic disease with passive and active movements between an urban city and a satellite city is formulated and analysed. The basic reproduction number of the disease is explicitly determined as a combination of sexual and vector-borne transmission parameters. The sensitivity analysis reveals that the disease is primarily transmitted via the vector-borne mode, rather than via sexual transmission, and that sexual transmission by itself may not initiate or sustain an outbreak. Also, increasing the population movements from one city to the other leads to an increase in the basic reproduction number of the later city but a decrease in the basic reproduction number of the former city. The influence of other significant parameters is also investigated via the analysis of suitable partial rank correlation coefficients. After gauging the effects of mobility, we explore the potential effects of optimal control strategies relying upon several distinct restrictions on population movement.
Collapse
Affiliation(s)
- Prince Harvim
- Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, People's Republic of China
| | - Hong Zhang
- School of Economics and Management, Changzhou Institute of Technology, Changzhou, 213032, Jiangsu, People's Republic of China
| | - Paul Georgescu
- Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506, Iasi, Romania
| | - Lai Zhang
- School of Mathematical Science, Yangzhou University, Yangzhou, 225002, Jiangsu, People's Republic of China.
| |
Collapse
|
13
|
Dudley DM, Aliota MT, Mohr EL, Newman CM, Golos TG, Friedrich TC, O'Connor DH. Using Macaques to Address Critical Questions in Zika Virus Research. Annu Rev Virol 2019; 6:481-500. [PMID: 31180813 PMCID: PMC7323203 DOI: 10.1146/annurev-virology-092818-015732] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Zika virus (ZIKV) and nonhuman primates have been inextricably linked since the virus was first discovered in a sentinel rhesus macaque in Uganda in 1947. Soon after ZIKV was epidemiologically associated with birth defects in Brazil late in 2015, researchers capitalized on the fact that rhesus macaques are commonly used to model viral immunity and pathogenesis, quickly establishing macaque models for ZIKV infection. Within months, the susceptibility of pregnant macaques to experimental ZIKV challenge and ZIKV-associated abnormalities in fetuses was confirmed. This review discusses key unanswered questions in ZIKV immunity and in the pathogenesis of thecongenital Zika virus syndrome. We focus on those questions that can be best addressed in pregnant nonhuman primates and lessons learned from developing macaque models for ZIKV amid an active epidemic.
Collapse
Affiliation(s)
- Dawn M Dudley
- Department of Pathology and Laboratory Medicine, University of Wisconsin-Madison, Madison, Wisconsin 53711, USA; , ,
| | - Matthew T Aliota
- Department of Veterinary and Biomedical Sciences, University of Minnesota, Twin Cities, Saint Paul, Minnesota 55108, USA;
| | - Emma L Mohr
- Department of Pediatrics, School of Medicine and Public Health, University of Wisconsin-Madison, Madison, Wisconsin 53792, USA;
| | - Christina M Newman
- Department of Pathology and Laboratory Medicine, University of Wisconsin-Madison, Madison, Wisconsin 53711, USA; , ,
| | - Thaddeus G Golos
- Wisconsin National Primate Research Center, University of Wisconsin-Madison, Madison, Wisconsin 53715, USA; ,
- Departments of Comparative Biosciences and Obstetrics and Gynecology, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Thomas C Friedrich
- Wisconsin National Primate Research Center, University of Wisconsin-Madison, Madison, Wisconsin 53715, USA; ,
- Department of Pathobiological Sciences, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - David H O'Connor
- Department of Pathology and Laboratory Medicine, University of Wisconsin-Madison, Madison, Wisconsin 53711, USA; , ,
- Wisconsin National Primate Research Center, University of Wisconsin-Madison, Madison, Wisconsin 53715, USA; ,
| |
Collapse
|
14
|
Amrun SN, Yee W, Abu Bakar F, Lee B, Kam Y, Lum F, Tan JJL, Lim VWX, Watthanaworawit W, Ling C, Nosten F, Renia L, Leo Y, Ng LFP. Novel differential linear B-cell epitopes to identify Zika and dengue virus infections in patients. Clin Transl Immunology 2019; 8:e1066. [PMID: 31372218 PMCID: PMC6659153 DOI: 10.1002/cti2.1066] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Revised: 06/09/2019] [Accepted: 06/09/2019] [Indexed: 12/11/2022] Open
Abstract
OBJECTIVES Recent Zika virus (ZIKV) outbreaks challenged existing laboratory diagnostic standards, especially for serology-based methods. Because of the genetic and structural similarity of ZIKV with other flaviviruses, this results in cross-reactive antibodies, which confounds serological interpretations. METHODS Plasma from Singapore ZIKV patients was screened longitudinally for antibody responses and neutralising capacities against ZIKV. Samples from healthy controls, ZIKV patients and DENV patients were further assessed using ZIKV and DENV peptides of precursor membrane (prM), envelope (E) or non-structural 1 (NS1) viral proteins in a peptide-based ELISA for epitope identification. Identified epitopes were re-validated and diagnostically evaluated using sera of patients with DENV, bacteria or unknown infections from Thailand. RESULTS Long-lasting ZIKV-neutralising antibodies were elicited during ZIKV infection. Thirteen potential linear B-cell epitopes were identified, and of these, four common flavivirus, three ZIKV-specific and one DENV-specific differential epitopes had more than 50% sensitivity and specificity. Notably, ZIKV-specific peptide 26 on domain I/II of E protein (amino acid residues 271-288) presented 80% sensitivity and 85.7% specificity. Importantly, the differential epitopes also showed significance in differentiating non-flavivirus patient samples. CONCLUSION Linear B-cell epitope candidates to differentiate between ZIKV and DENV infections were identified, providing the first step towards the design of a much-needed serology-based assay.
Collapse
Affiliation(s)
- Siti Naqiah Amrun
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Wearn‐Xin Yee
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Farhana Abu Bakar
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Bernett Lee
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Yiu‐Wing Kam
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Fok‐Moon Lum
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Jeslin JL Tan
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Vanessa WX Lim
- Communicable Diseases CentreInstitute of Infectious Diseases and EpidemiologyTan Tock Seng HospitalSingapore CitySingapore
| | - Wanitda Watthanaworawit
- Shoklo Malaria Research UnitMahidol‐Oxford Tropical Medicine Research UnitFaculty of Tropical MedicineMahidol UniversityMae SotThailand
| | - Clare Ling
- Shoklo Malaria Research UnitMahidol‐Oxford Tropical Medicine Research UnitFaculty of Tropical MedicineMahidol UniversityMae SotThailand
| | - Francois Nosten
- Shoklo Malaria Research UnitMahidol‐Oxford Tropical Medicine Research UnitFaculty of Tropical MedicineMahidol UniversityMae SotThailand
- Centre for Tropical Medicine and Global HealthNuffield Department of MedicineUniversity of OxfordOxfordUK
| | - Laurent Renia
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
| | - Yee‐Sin Leo
- Communicable Diseases CentreInstitute of Infectious Diseases and EpidemiologyTan Tock Seng HospitalSingapore CitySingapore
- Lee Kong Chian School of MedicineNanyang Technological UniversitySingapore CitySingapore
- Saw Swee Hock School of Public HealthNational University of SingaporeSingapore CitySingapore
| | - Lisa FP Ng
- Singapore Immunology NetworkAgency for Science, Technology and Research (A*STAR)Singapore CitySingapore
- National Institute of Health ResearchHealth Protection Research Unit in Emerging and Zoonotic InfectionsLiverpoolUK
- Institute of Infection and Global HealthUniversity of LiverpoolLiverpoolUK
- Department of BiochemistryYong Loo Lin School of MedicineNational University of SingaporeSingapore CitySingapore
| |
Collapse
|
15
|
Zhao S, Musa SS, Fu H, He D, Qin J. Simple framework for real-time forecast in a data-limited situation: the Zika virus (ZIKV) outbreaks in Brazil from 2015 to 2016 as an example. Parasit Vectors 2019; 12:344. [PMID: 31300061 PMCID: PMC6624944 DOI: 10.1186/s13071-019-3602-9] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Accepted: 07/06/2019] [Indexed: 12/11/2022] Open
Abstract
Background In 2015–2016, Zika virus (ZIKV) caused serious epidemics in Brazil. The key epidemiological parameters and spatial heterogeneity of ZIKV epidemics in different states in Brazil remain unclear. Early prediction of the final epidemic (or outbreak) size for ZIKV outbreaks is crucial for public health decision-making and mitigation planning. We investigated the spatial heterogeneity in the epidemiological features of ZIKV across eight different Brazilian states by using simple non-linear growth models. Results We fitted three different models to the weekly reported ZIKV cases in eight different states and obtained an R2 larger than 0.995. The estimated average values of basic reproduction numbers from different states varied from 2.07 to 3.41, with a mean of 2.77. The estimated turning points of the epidemics also varied across different states. The estimation of turning points nevertheless is stable and real-time. The forecast of the final epidemic size (attack rate) is reasonably accurate, shortly after the turning point. The knowledge of the epidemic turning point is crucial for accurate real-time projection of the outbreak. Conclusions Our simple models fitted the epidemic reasonably well and thus revealed the spatial heterogeneity in the epidemiological features across Brazilian states. The knowledge of the epidemic turning point is crucial for real-time projection of the outbreak size. Our real-time estimation framework is able to yield a reliable prediction of the final epidemic size. Electronic supplementary material The online version of this article (10.1186/s13071-019-3602-9) contains supplementary material, which is available to authorized users.
Collapse
Affiliation(s)
- Shi Zhao
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China. .,Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China.
| | - Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Hao Fu
- Department of Crop Science and Technology, College of Agriculture, South China Agricultural University, Guangzhou, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China.
| | - Jing Qin
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
| |
Collapse
|
16
|
Barrera R, Amador M, Acevedo V, Beltran M, Muñoz JL. A comparison of mosquito densities, weather and infection rates of Aedes aegypti during the first epidemics of Chikungunya (2014) and Zika (2016) in areas with and without vector control in Puerto Rico. MEDICAL AND VETERINARY ENTOMOLOGY 2019; 33:68-77. [PMID: 30225842 PMCID: PMC6378603 DOI: 10.1111/mve.12338] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2018] [Revised: 05/25/2018] [Accepted: 07/26/2018] [Indexed: 05/25/2023]
Abstract
In Puerto Rico, the first records of the transmission of Chikungunya (CHIKV) and Zika (ZIKV) viruses were confirmed in May 2014 and December 2015, respectively. Transmission of CHIKV peaked in September 2014, whereas that of ZIKV peaked in August 2016. The emergence of these mosquito-transmitted arboviruses in the context of a lack of human population immunity allowed observations of whether the outbreaks were associated with Aedes aegypti (Diptera: Culicidae) densities and weather. Mosquito density was monitored weekly in four communities using sentinel autocidal gravid ovitraps (AGO traps) during 2016 in order to provide data to be compared with the findings of a previous study carried out during the 2014 CHIKV epidemic. Findings in two communities protected against Ae. aegypti using mass AGO trapping (three traps per house in most houses) were compared with those in two nearby communities without vector control. Mosquito pools were collected to detect viral RNA of ZIKV, CHIKV and dengue virus. In areas without vector control, mosquito densities and rates of ZIKV detection in 2016 were significantly higher, similarly to those observed for CHIKV in 2014. The density of Ae. aegypti in treated sites was less than two females/trap/week, which is similar to the putative adult female threshold for CHIKV transmission. No significant differences in mosquito density or infection rates with ZIKV and CHIKV at the same sites between years were observed. Although 2016 was significantly wetter, mosquito densities were similar.
Collapse
Affiliation(s)
- R. Barrera
- Entomology and Ecology Team, Dengue BranchCenters for Disease Control and PreventionSan JuanPuerto Rico
| | - M. Amador
- Entomology and Ecology Team, Dengue BranchCenters for Disease Control and PreventionSan JuanPuerto Rico
| | - V. Acevedo
- Entomology and Ecology Team, Dengue BranchCenters for Disease Control and PreventionSan JuanPuerto Rico
| | - M. Beltran
- Molecular Diagnostic Laboratory, Dengue BranchCenters for Disease Control and PreventionSan JuanPuerto Rico
| | - J. L. Muñoz
- Molecular Diagnostic Laboratory, Dengue BranchCenters for Disease Control and PreventionSan JuanPuerto Rico
| |
Collapse
|
17
|
Karkhah A, Nouri HR, Javanian M, Koppolu V, Masrour-Roudsari J, Kazemi S, Ebrahimpour S. Zika virus: epidemiology, clinical aspects, diagnosis, and control of infection. Eur J Clin Microbiol Infect Dis 2018; 37:2035-2043. [PMID: 30167886 DOI: 10.1007/s10096-018-3354-z] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2018] [Accepted: 08/09/2018] [Indexed: 11/24/2022]
Abstract
Zika virus (ZIKV) is an emerging pathogen of huge public health significance to human beings. Although majority of infections are benign with self-limiting symptoms, the recent outbreak has established an association with the increased incidence of some congenital anomalies such as microcephaly. In other words, due to the large extent of the virus and mosquito vectors, the infection has become a thoughtful health problem for human societies, though now, there are no antiviral therapies or vaccines against this virus. In spite of extensive research carried out by scientists, not so much information has been gathered about this viral infection. In the current review, we prepared an overview of the remarkable progress made in understanding about the epidemiology, immunology, clinical presentation, and diagnosis methods of ZIKV infection.
Collapse
Affiliation(s)
- Ahmad Karkhah
- Cellular and Molecular Biology Research Center, Health Research Institute, Babol University of Medical Sciences, Babol, Iran.,Student Research Committee, School of Medicine, Babol University of Medical Sciences, Babol, Iran
| | - Hamid Reza Nouri
- Cellular and Molecular Biology Research Center, Health Research Institute, Babol University of Medical Sciences, Babol, Iran
| | - Mostafa Javanian
- Infectious Diseases and Tropical Medicine Research Center, Health Research Institute, Babol University of Medical Sciences, Babol, Iran
| | - Veerendra Koppolu
- Scientist Biopharmaceutical Development Medimmune, Gaithersburg, MD, 20878, USA
| | - Jila Masrour-Roudsari
- Infectious Diseases and Tropical Medicine Research Center, Health Research Institute, Babol University of Medical Sciences, Babol, Iran
| | - Sohrab Kazemi
- Cellular and Molecular Biology Research Center, Health Research Institute, Babol University of Medical Sciences, Babol, Iran
| | - Soheil Ebrahimpour
- Infectious Diseases and Tropical Medicine Research Center, Health Research Institute, Babol University of Medical Sciences, Babol, Iran.
| |
Collapse
|
18
|
Zhao S, Stone L, Gao D, He D. Modelling the large-scale yellow fever outbreak in Luanda, Angola, and the impact of vaccination. PLoS Negl Trop Dis 2018; 12:e0006158. [PMID: 29338001 PMCID: PMC5798855 DOI: 10.1371/journal.pntd.0006158] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Revised: 02/05/2018] [Accepted: 12/11/2017] [Indexed: 11/18/2022] Open
Abstract
BACKGROUND Yellow fever (YF), transmitted via bites of infected mosquitoes, is a life-threatening viral disease endemic to tropical and subtropical regions of Africa and South America. YF has largely been controlled by widespread national vaccination campaigns. Nevertheless, between December 2015 and August 2016, YF resurged in Angola, quickly spread and became the largest YF outbreak for the last 30 years. Recently, YF resurged again in Brazil (December 2016). Thus, there is an urgent need to gain better understanding of the transmission pattern of YF. MODEL The present study provides a refined mathematical model, combined with modern likelihood-based statistical inference techniques, to assess and reconstruct important epidemiological processes underlying Angola's YF outbreak. This includes the outbreak's attack rate, the reproduction number ([Formula: see text]), the role of the mosquito vector, the influence of climatic factors, and the unusual but noticeable appearance of two-waves in the YF outbreak. The model explores actual and hypothetical vaccination strategies, and the impacts of possible human reactive behaviors (e.g., response to media precautions). FINDINGS While there were 73 deaths reported over the study period, the model indicates that the vaccination campaign saved 5.1-fold more people from death and saved from illness 5.6-fold of the observed 941 cases. Delaying the availability of the vaccines further would have greatly worsened the epidemic in terms of increased cases and deaths. The analysis estimated a mean [Formula: see text] and an attack rate of 0.09-0.15% (proportion of population infected) over the whole period from December 2015 to August 2016. Our estimated lower and upper bounds of [Formula: see text] are in line with previous studies. Unusually, [Formula: see text] oscillated in a manner that was "delayed" with the reported deaths. High recent number of deaths were associated (followed) with periods of relatively low disease transmission and low [Formula: see text], and vice-versa. The time-series of Luanda's YF cases suggest the outbreak occurred in two waves, a feature that would have become far more prominent had there been no mass vaccination. The waves could possibly be due to protective reactive behavioral changes of the population affecting the mosquito population. The second wave could well be an outcome of the March-April rainfall patterns in the 2016 El Niño year by creating ideal conditions for the breeding of the mosquito vectors. The modelling framework is a powerful tool for studying future YF epidemic outbreaks, and provides a basis for future vaccination campaign evaluations.
Collapse
Affiliation(s)
- Shi Zhao
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Lewi Stone
- School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia
- Biomathematics Unit, Department of Zoology, Tel Aviv University, Ramat Aviv, Israel
| | - Daozhou Gao
- Department of Mathematics, Shanghai Normal University, Shanghai, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| |
Collapse
|
19
|
Kibona IE, Yang C. SIR Model of Spread of Zika Virus Infections: ZIKV Linked to Microcephaly Simulations. Health (London) 2017. [DOI: 10.4236/health.2017.98086] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|