Replicating superspreader dynamics with compartmental models.

Infectious disease outbreaks often exhibit superspreader dynamics, where most infected people generate no, or few secondary cases, and only a small fraction of individuals are responsible for a large proportion of transmission. Although capturing this heterogeneity is critical for estimating outbreak risk and the effectiveness of group-specific interventions, it is typically neglected in compartmental models of infectious disease transmission-which constitute the most common transmission dynamic modeling framework. In this study we propose different classes of compartmental epidemic models that incorporate transmission heterogeneity, fit them to a number of real outbreak datasets, and benchmark their performance against the canonical superspreader model (i.e., the negative binomial branching process model). We find that properly constructed compartmental models can capably reproduce observed superspreader dynamics and we provide the pathogen-specific parameter settings required to do so. As a consequence, we also show that compartmental models parameterized according to a binary clinical classification have limited support.

Quantifying the impact of Wolbachia releases on dengue infection in Townsville, Australia.

From October 2014 to February 2019, local authorities in Townsville, North Queensland, Australia continually introduced Wolbachia-infected mosquitoes to control seasonal outbreaks of dengue infection. In this study, we develop a mathematical modelling framework to estimate the effectiveness of this intervention as well as the relative dengue transmission rates of Wolbachia-infected and wild-type mosquitoes. We find that the transmission rate of Wolbachia-infected mosquitoes is reduced approximately by a factor of 20 relative to the uninfected wild-type population. In addition, the Townsville Wolbachia release program led to a 65% reduction in predicted dengue incidence during the release period and over 95% reduction in the 24 months that followed. Finally, to investigate the potential impact of other Wolbachia release programs, we use our estimates of relative transmissibility to calculate the relationship between the reproductive number of dengue and the proportion of Wolbachia-infected mosquitoes in the vector population.

A Systematic Review of Mathematical Models of Dengue Transmission and Vector Control: 2010-2020.

Vector control methods are considered effective in averting dengue transmission. However, several factors may modify their impact. Of these controls, chemical methods, in the long run, may increase mosquitoes' resistance to chemicides, thereby decreasing control efficacy. The biological methods, which may be self-sustaining and very effective, could be hampered by seasonality or heatwaves (resulting in, e.g., loss of Wolbachia infection). The environmental methods that could be more effective than the chemical methods are under-investigated. In this study, a systematic review is conducted to explore the present understanding of the effectiveness of vector control approaches via dengue transmission models.

Modelling the ecological dynamics of mosquito populations with multiple co-circulating Wolbachia strains.

Wolbachia intracellular bacteria successfully reduce the transmissibility of arthropod-borne viruses (arboviruses) when introduced into virus-carrying vectors such as mosquitoes. Despite the progress made by introducing Wolbachia bacteria into the Aedes aegypti wild-type population to control arboviral infections, reports suggest that heat-induced loss-of-Wolbachia-infection as a result of climate change may reverse these gains. Novel, supplemental Wolbachia strains that are more resilient to increased temperatures may circumvent these concerns, and could potentially act synergistically with existing variants. In this article, we model the ecological dynamics among three distinct mosquito (sub)populations: a wild-type population free of any Wolbachia infection; an invading population infected with a particular Wolbachia strain; and a second invading population infected with a distinct Wolbachia strain from that of the first invader. We explore how the range of possible characteristics of each Wolbachia strain impacts mosquito prevalence. Further, we analyse the differential system governing the mosquito populations and the Wolbachia infection dynamics by computing the full set of basic and invasive reproduction numbers and use these to establish stability of identified equilibria. Our results show that releasing mosquitoes with two different strains of Wolbachia did not increase their prevalence, compared with a single-strain Wolbachia-infected mosquito introduction and only delayed Wolbachia dominance.

Population heterogeneity in Plasmodium vivax relapse risk.

A key characteristic of Plasmodium vivax parasites is their ability to adopt a latent liver-stage form called hypnozoites, able to cause relapse of infection months or years after a primary infection. Relapses of infection through hypnozoite activation are a major contributor to blood-stage infections in P vivax endemic regions and are thought to be influenced by factors such as febrile infections which may cause temporary changes in hypnozoite activation leading to 'temporal heterogeneity' in reactivation risk. In addition, immunity and variation in exposure to infection may be longer-term characteristics of individuals that lead to 'population heterogeneity' in hypnozoite activation. We analyze data on risk of P vivax in two previously published data sets from Papua New Guinea and the Thailand-Myanmar border region. Modeling different mechanisms of reactivation risk, we find strong evidence for population heterogeneity, with 30% of patients having almost 70% of all P vivax infections. Model fitting and data analysis indicates that individual variation in relapse risk is a primary source of heterogeneity of P vivax risk of recurrences. Trial Registration: ClinicalTrials.gov NCT01640574, NCT01074905, NCT02143934.

Mathematical analysis of a two-strain tuberculosis model in Bangladesh.

Tuberculosis (TB) is an airborne infectious disease that causes millions of deaths worldwide each year (1.2 million people died in 2019). Alarmingly, several strains of the causative agent, Mycobacterium tuberculosis (MTB)-including drug-susceptible (DS) and drug-resistant (DR) variants-already circulate throughout most developing and developed countries, particularly in Bangladesh, with totally drug-resistant strains starting to emerge. In this study we develop a two-strain DS and DR TB transmission model and perform an analysis of the system properties and solutions. Both analytical and numerical results show that the prevalence of drug-resistant infection increases with an increasing drug use through amplification. Both analytic results and numerical simulations suggest that if the basic reproduction numbers of both DS ([Formula: see text]) and DR ([Formula: see text]) TB are less than one, i.e. [Formula: see text] the disease-free equilibrium is asymptotically stable, meaning that the disease naturally dies out. Furthermore, if [Formula: see text], then DS TB dies out but DR TB persists in the population, and if [Formula: see text] both DS TB and DR TB persist in the population. Further, sensitivity analysis of the model parameters found that the transmission rate of both strains had the greatest influence on DS and DR TB prevalence. We also investigated the effect of treatment rates and amplification on both DS and DR TB prevalence; results indicate that inadequate or inappropriate treatment makes co-existence more likely and increases the relative abundance of DR TB infections.

Modelling direct and herd protection effects of vaccination against the SARS-CoV-2 Delta variant in Australia.

OBJECTIVES: To analyse the outcomes of COVID-19 vaccination by vaccine type, age group eligibility, vaccination strategy, and population coverage. DESIGN: Epidemiologic modelling to assess the final size of a COVID-19 epidemic in Australia, with vaccination program (Pfizer, AstraZeneca, mixed), vaccination strategy (vulnerable first, transmitters first, untargeted), age group eligibility threshold (5 or 15 years), population coverage, and pre-vaccination effective reproduction number ( Reffv¯ ) for the SARS-CoV-2 Delta variant as factors. MAIN OUTCOME MEASURES: Numbers of SARS-CoV-2 infections; cumulative hospitalisations, deaths, and years of life lost. RESULTS: Assuming Reffv¯ = 5, the current mixed vaccination program (vaccinating people aged 60 or more with the AstraZeneca vaccine and people under 60 with the Pfizer vaccine) will not achieve herd protection unless population vaccination coverage reaches 85% by lowering the vaccination eligibility age to 5 years. At Reffv¯ = 3, the mixed program could achieve herd protection at 60-70% population coverage and without vaccinating 5-15-year-old children. At Reffv¯ = 7, herd protection is unlikely to be achieved with currently available vaccines, but they would still reduce the number of COVID-19-related deaths by 85%. CONCLUSION: Vaccinating vulnerable people first is the optimal policy when population vaccination coverage is low, but vaccinating more socially active people becomes more important as the Reffv¯ declines and vaccination coverage increases. Assuming the most plausible Reffv¯ of 5, vaccinating more than 85% of the population, including children, would be needed to achieve herd protection. Even without herd protection, vaccines are highly effective in reducing the number of deaths.

Change in outbreak epicentre and its impact on the importation risks of COVID-19 progression: A modelling study.

BACKGROUND: The outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) that was first detected in the city of Wuhan, China has now spread to every inhabitable continent, but now the attention has shifted from China to other epicentres. This study explored early assessment of the influence of spatial proximities and travel patterns from Italy on the further spread of SARS-CoV-2 worldwide. METHODS: Using data on the number of confirmed cases of COVID-19 and air travel data between countries, we applied a stochastic meta-population model to estimate the global spread of COVID-19. Pearson's correlation, semi-variogram, and Moran's Index were used to examine the association and spatial autocorrelation between the number of COVID-19 cases and travel influx (and arrival time) from the source country. RESULTS: We found significant negative association between disease arrival time and number of cases imported from Italy (r = -0.43, p = 0.004) and significant positive association between the number of COVID-19 cases and daily travel influx from Italy (r = 0.39, p = 0.011). Using bivariate Moran's Index analysis, we found evidence of spatial interaction between COVID-19 cases and travel influx (Moran's I = 0.340). Asia-Pacific region is at higher/extreme risk of disease importation from the Chinese epicentre, whereas the rest of Europe, South-America and Africa are more at risk from the Italian epicentre. CONCLUSION: We showed that as the epicentre changes, the dynamics of SARS-CoV-2 spread change to reflect spatial proximities.

A Review: Aedes-Borne Arboviral Infections, Controls and Wolbachia-Based Strategies.

Arthropod-borne viruses (Arboviruses) continue to generate significant health and economic burdens for people living in endemic regions. Of these viruses, some of the most important (e.g., dengue, Zika, chikungunya, and yellow fever virus), are transmitted mainly by Aedes mosquitoes. Over the years, viral infection control has targeted vector population reduction and inhibition of arboviral replication and transmission. This control includes the vector control methods which are classified into chemical, environmental, and biological methods. Some of these control methods may be largely experimental (both field and laboratory investigations) or widely practised. Perceptively, one of the biological methods of vector control, in particular, Wolbachia-based control, shows a promising control strategy for eradicating Aedes-borne arboviruses. This can either be through the artificial introduction of Wolbachia, a naturally present bacterium that impedes viral growth in mosquitoes into heterologous Aedes aegypti mosquito vectors (vectors that are not natural hosts of Wolbachia) thereby limiting arboviral transmission or via Aedes albopictus mosquitoes, which naturally harbour Wolbachia infection. These strategies are potentially undermined by the tendency of mosquitoes to lose Wolbachia infection in unfavourable weather conditions (e.g., high temperature) and the inhibitory competitive dynamics among co-circulating Wolbachia strains. The main objective of this review was to critically appraise published articles on vector control strategies and specifically highlight the use of Wolbachia-based control to suppress vector population growth or disrupt viral transmission. We retrieved studies on the control strategies for arboviral transmissions via arthropod vectors and discussed the use of Wolbachia control strategies for eradicating arboviral diseases to identify literature gaps that will be instrumental in developing models to estimate the impact of these control strategies and, in essence, the use of different Wolbachia strains and features.

Modeling the potential of wAu-Wolbachia strain invasion in mosquitoes to control Aedes-borne arboviral infections.

Arboviral infections such as dengue, Zika and chikungunya are fast spreading diseases that pose significant health problems globally. In order to control these infections, an intracellular bacterium called Wolbachia has been introduced into wild-type mosquito populations in the hopes of replacing the vector transmitting agent, Aedes aegypti with one that is incapable of transmission. In this study, we developed a Wolbachia transmission model for the novel wAu strain which possesses several favourable traits (e.g., enhanced viral blockage and maintenance at higher temperature) but not cyctoplasmic incompatibility (CI)-when a Wolbachia-infected male mosquito mates with an uninfected female mosquito, producing no viable offspring. This model describes the competitive dynamics between wAu-Wolbachia-infected and uninfected mosquitoes and the role of imperfect maternal transmission. By analysing the system via computing the basic reproduction number(s) and stability properties, the potential of the wAu strain as a viable strategy to control arboviral infections is established. The results of this work show that enhanced maintenance of Wolbachia infection at higher temperatures can overcome the lack of CI induction to support wAu-Wolbachia infected mosquito invasion. This study will support future arboviral control programs, that rely on the introduction of new Wolbachia variants.

Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh.

Tuberculosis (TB) is the seventh leading cause of morbidity and mortality in Bangladesh. Although the National TB control program (NTP) of Bangladesh is implementing its nationwide TB control strategies, more specific and effective single or combination interventions are needed to control drug-susceptible (DS) and multi-drug resistant (MDR) TB. In this study, we developed a two strain TB mathematical model with amplification and fit it to the Bangladesh TB data to understand the transmission dynamics of DS and MDR TB. Sensitivity analysis was used to identify important parameters. We evaluated the cost-effectiveness of varying combinations of four basic control strategies including distancing, latent case finding, case holding and active case finding, all within the optimal control framework. From our fitting, the model with different transmission rates between DS and MDR TB best captured the Bangladesh TB reported case counts. The estimated basic reproduction number for DS TB was 1.14 and for MDR TB was 0.54, with an amplification rate of 0.011 per year. The sensitivity analysis also indicated that the transmission rates for both DS and MDR TB had the largest influence on prevalence. To reduce the burden of TB (both DS and MDR), our finding suggested that a quadruple control strategy that combines distancing control, latent case finding, case holding and active case finding is the most cost-effective. Alternative strategies can be adopted to curb TB depending on availability of resources and policy makers' decisions.

Role of modelling in COVID-19 policy development.

Models have played an important role in policy development to address the COVID-19 outbreak from its emergence in China to the current global pandemic. Early projections of international spread influenced travel restrictions and border closures. Model projections based on the virus's infectiousness demonstrated its pandemic potential, which guided the global response to and prepared countries for increases in hospitalisations and deaths. Tracking the impact of distancing and movement policies and behaviour changes has been critical in evaluating these decisions. Models have provided insights into the epidemiological differences between higher and lower income countries, as well as vulnerable population groups within countries to help design fit-for-purpose policies. Economic evaluation and policies have combined epidemic models and traditional economic models to address the economic consequences of COVID-19, which have informed policy calls for easing restrictions. Social contact and mobility models have allowed evaluation of the pathways to safely relax mobility restrictions and distancing measures. Finally, models can consider future end-game scenarios, including how suppression can be achieved and the impact of different vaccination strategies.

Modelling insights into the COVID-19 pandemic.

Coronavirus disease 2019 (COVID-19) is a newly emerged infectious disease caused by the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) that was declared a pandemic by the World Health Organization on 11th March, 2020. Response to this ongoing pandemic requires extensive collaboration across the scientific community in an attempt to contain its impact and limit further transmission. Mathematical modelling has been at the forefront of these response efforts by: (1) providing initial estimates of the SARS-CoV-2 reproduction rate, R0 (of approximately 2-3); (2) updating these estimates following the implementation of various interventions (with significantly reduced, often sub-critical, transmission rates); (3) assessing the potential for global spread before significant case numbers had been reported internationally; and (4) quantifying the expected disease severity and burden of COVID-19, indicating that the likely true infection rate is often orders of magnitude greater than estimates based on confirmed case counts alone. In this review, we highlight the critical role played by mathematical modelling to understand COVID-19 thus far, the challenges posed by data availability and uncertainty, and the continuing utility of modelling-based approaches to guide decision making and inform the public health response. †Unless otherwise stated, all bracketed error margins correspond to the 95% credible interval (CrI) for reported estimates.

Economic Consequences of the COVID-19 Outbreak: the Need for Epidemic Preparedness.

COVID-19 is not only a global pandemic and public health crisis; it has also severely affected the global economy and financial markets. Significant reductions in income, a rise in unemployment, and disruptions in the transportation, service, and manufacturing industries are among the consequences of the disease mitigation measures that have been implemented in many countries. It has become clear that most governments in the world underestimated the risks of rapid COVID-19 spread and were mostly reactive in their crisis response. As disease outbreaks are not likely to disappear in the near future, proactive international actions are required to not only save lives but also protect economic prosperity.

Early Transmission Dynamics of Novel Coronavirus (COVID-19) in Nigeria.

On 31 December 2019, the World Health Organization (WHO) was notified of a novel coronavirus disease in China that was later named COVID-19. On 11 March 2020, the outbreak of COVID-19 was declared a pandemic. The first instance of the virus in Nigeria was documented on 27 February 2020. This study provides a preliminary epidemiological analysis of the first 45 days of COVID-19 outbreak in Nigeria. We estimated the early transmissibility via time-varying reproduction number based on the Bayesian method that incorporates uncertainty in the distribution of serial interval (time interval between symptoms onset in an infected individual and the infector), and adjusted for disease importation. By 11 April 2020, 318 confirmed cases and 10 deaths from COVID-19 have occurred in Nigeria. At day 45, the exponential growth rate was 0.07 (95% confidence interval (CI): 0.05-0.10) with a doubling time of 9.84 days (95% CI: 7.28-15.18). Separately for imported cases (travel-related) and local cases, the doubling time was 12.88 days and 2.86 days, respectively. Furthermore, we estimated the reproduction number for each day of the outbreak using a three-weekly window while adjusting for imported cases. The estimated reproduction number was 4.98 (95% CrI: 2.65-8.41) at day 22 (19 March 2020), peaking at 5.61 (95% credible interval (CrI): 3.83-7.88) at day 25 (22 March 2020). The median reproduction number over the study period was 2.71 and the latest value on 11 April 2020, was 1.42 (95% CrI: 1.26-1.58). These 45-day estimates suggested that cases of COVID-19 in Nigeria have been remarkably lower than expected and the preparedness to detect needs to be shifted to stop local transmission.

Heterogeneous infectiousness in mathematical models of tuberculosis: A systematic review.

TB mathematical models employ various assumptions and approaches in dealing with the heterogeneous infectiousness of persons with active TB. We reviewed existing approaches and considered the relationship between them and existing epidemiological evidence. We searched the following electronic bibliographic databases from inception to 9 October 2018: MEDLINE, EMBASE, Biosis, Global Health and Scopus. Two investigators extracted data using a standardised data extraction tool. We included in the review any transmission dynamic model of M. tuberculosis transmission explicitly simulating heterogeneous infectiousness of person with active TB. We extracted information including: study objective, model structure, number of active TB compartments, factors used to stratify the active TB compartment, relative infectiousness of each active TB compartment and any intervention evaluated in the model. Our search returned 1899 unique references, of which the full text of 454 records were assessed for eligibility, and 99 studies met the inclusion criteria. Of these, 89 used compartmental models implemented with ordinary differential equations, while the most common approach to stratification of the active TB compartment was to incorporate two levels of infectiousness. However, various clinical characteristics were used to stratify the active TB compartments, and models differed as to whether they permitted transition between these states. Thirty-four models stratified the infectious compartment according to sputum smear status or pulmonary involvement, while 18 models stratified based on health care-related factors. Variation in infectiousness associated with drug-resistant M. tuberculosis was the rationale for stratifying active TB in 33 models, with these models consistently assuming that drug-resistant active TB cases were less infectious. Given the evidence of extensive heterogeneity in infectiousness of individuals with active TB, an argument exists for incorporating heterogeneous infectiousness, although this should be considered in light of the objectives of the study and the research question. PROSPERO Registration: CRD42019111936.

Mathematical analysis of a Wolbachia invasive model with imperfect maternal transmission and loss of Wolbachia infection.

Arboviral infections, especially dengue, continue to cause significant health burden in their endemic regions. One of the strategies to tackle these infections is to replace the main vector agent, Ae. aegypti, with the ones incapable of transmitting the virus. Wolbachia, an intracellular bacterium, has shown promise in achieving this goal. However, key factors such as imperfect maternal transmission, loss of Wolbachia infection, reduced reproductive capacity and shortened life-span affect the dynamics of Wolbachia in different forms in the Ae. aegypti population. In this study, we developed a Wolbachia transmission dynamic model adjusting for imperfect maternal transmission and loss of Wolbachia infection. The invasive reproductive number that determines the likelihood of replacement of the Wolbachia-uninfected (WU) population is derived and with it, we established the local and global stability of the equilibrium points. This analysis clearly shows that cytoplasmic incompatibility (CI) does not guarantee establishment of the Wolbachia-infected (WI) mosquitoes as imperfect maternal transmission and loss of Wolbachia infection could outweigh the gains from CI. Optimal release programs depending on the level of imperfect maternal transmission and loss of Wolbachia infection are shown. Hence, it is left to decision makers to either aim for replacement or co-existence of both populations.

Flooding in Townsville, North Queensland, Australia, in February 2019 and Its Effects on Mosquito-Borne Diseases.

In February 2019, a major flooding event occurred in Townsville, North Queensland, Australia. Here we present a prediction of the occurrence of mosquito-borne diseases (MBDs) after the flooding. We used a mathematical modelling approach based on mosquito population abundance, survival, and size as well as current infectiousness to predict the changes in the occurrences of MBDs due to flooding in the study area. Based on 2019 year-to-date number of notifiable MBDs, we predicted an increase in number of cases, with a peak at 104 by one-half month after the flood receded. The findings in this study indicate that Townsville may see an upsurge in the cases of MBDs in the coming days. However, the burden of diseases will go down again if the mosquito control program being implemented by the City Council continues. As our predictions focus on the near future, longer term effects of flooding on the occurrence of mosquito-borne diseases need to be studied further.

Modeling the dynamics of Plasmodium vivax infection and hypnozoite reactivation in vivo.

The dynamics of Plasmodium vivax infection is characterized by reactivation of hypnozoites at varying time intervals. The relative contribution of new P. vivax infection and reactivation of dormant liver stage hypnozoites to initiation of blood stage infection is unclear. In this study, we investigate the contribution of new inoculations of P. vivax sporozoites to primary infection versus reactivation of hypnozoites by modeling the dynamics of P. vivax infection in Thailand in patients receiving treatment for either blood stage infection alone (chloroquine), or the blood and liver stages of infection (chloroquine + primaquine). In addition, we also analysed rates of infection in a study in Papua New Guinea (PNG) where patients were treated with either artesunate, or artesunate + primaquine. Our results show that up to 96% of the P. vivax infection is due to hypnozoite reactivation in individuals living in endemic areas in Thailand. Similar analysis revealed the around 70% of infections in the PNG cohort were due to hypnozoite reactivation. We show how the age of the cohort, primaquine drug failure, and seasonality may affect estimates of the ratio of primary P. vivax infection to hypnozoite reactivation. Modeling of P. vivax primary infection and hypnozoite reactivation provides important insights into infection dynamics, and suggests that 90-96% of blood stage infections arise from hypnozoite reactivation. Major differences in infection kinetics between Thailand and PNG suggest the likelihood of drug failure in PNG.