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

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

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

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 (R0s) and DR (R0r) TB are less than one, i.e. max[R0s, R0r]max[R0s,1], then DS TB dies out but DR TB persists in the population, and if R0s>max[R0r,1] 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

Can environmental DNA be used to detect first arrivals of the cane toad, Rhinella marina, into novel locations?

Eradicating invasive species is difficult, but success is more likely when populations are small after arrival. The cane toad, Rhinella marina, is an invasive pest species that threatens native fauna worldwide. Increasingly, environmental DNA (eDNA) is used as a technique to monitor the presence of invasive species given its power to detect low numbers of individuals. We aimed to investigate eDNA persistence in freshwater at three different temperatures (25, 30 and 35°C) and eDNA detection thresholds for R. marina using controlled experiments in aquaria. For the latter, two water volumes and two cane toad exposure times were used (800 or 200 L volume with 5 or 30 min exposure). A 15‐ml water sample was collected from each replicated aquaria and preserved with 5 ml Longmire's buffer. Environmental DNA was extracted and four technical quantitative PCR replicates were analyzed targeting the cane toad 16S rDNA mitochondrial gene. Environmental DNA decayed rapidly in water and was reliably detected for up to 3 days after cane toad removal, regardless of the temperature treatment. Also, cane toad eDNA was detected in the water after a 5‐min initial exposure of a single individual in 800 L of water. Under the physical parameters tested here, a positive detection means that a cane toad has been in contact with the water body between 1 and 3 days prior to the sampling event. The results of the present study show the importance of eDNA for determining the presence of a species that occurs at low abundance in a small water body, such as at the onset of a cane toad invasion

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 feature

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

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

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