Modeling the Impact of Exogenous Boosting and Universal Varicella Vaccination on the Clinical and Economic Burden of Varicella and Herpes Zoster in a Dynamic Population for England and Wales.

Universal varicella vaccination (UVV) in England and Wales has been hindered by its potential impact on exogenous boosting and increase in herpes zoster (HZ) incidence. We projected the impact of ten UVV strategies in England and Wales on the incidence of varicella and HZ and evaluated their cost-effectiveness over 50 years. The Maternal-Susceptible-Exposed-Infected-Recovered-Vaccinated transmission model was extended in a dynamically changing, age-structured population. Our model estimated that one- or two-dose UVV strategies significantly reduced varicella incidence (70-92%), hospitalizations (70-90%), and mortality (16-41%) over 50 years. A small rise in HZ cases was projected with UVV, peaking 22 years after introduction at 5.3-7.1% above pre-UVV rates. Subsequently, HZ incidence steadily decreased, falling 12.2-14.1% below pre-UVV rates after 50 years. At a willingness-to-pay threshold of 20,000 GBP/QALY, each UVV strategy was cost-effective versus no UVV. Frontier analysis showed that one-dose UVV with MMRV-MSD administered at 18 months is the only cost-effective strategy compared to other strategies. HZ incidence varied under alternative exogenous boosting assumptions, but most UVV strategies remained cost-effective. HZ vaccination decreased HZ incidence with minimal impact on the cost-effectiveness. Introducing a UVV program would significantly reduce the clinical burden of varicella and be cost-effective versus no UVV after accounting for the impact on HZ incidence.

Mathematical modeling and analysis of COVID-19 pandemic in Nigeria.

A mathematical model is designed and used to study the transmission dynamics and control of COVID-19 in Nigeria. The model, which was rigorously analysed and parametrized using COVID-19 data published by the Nigeria Centre for Disease Control (NCDC), was used to assess the community-wide impact of various control and mitigation strategies in some jurisdictions within Nigeria (notably the states of Kano and Lagos, and the Federal Capital Territory, Abuja). Numerical simulations of the model showed that COVID-19 can be effectively controlled in Nigeria using moderate levels of social-distancing strategy in the jurisdictions and in the entire nation. Although the use of face masks in public can significantly reduce COVID-19 in Nigeria, its use, as a sole intervention strategy, may fail to lead to a substantial reduction in disease burden. Such substantial reduction is feasible in the jurisdictions (and the entire Nigerian nation) if the public face mask use strategy is complemented with a social-distancing strategy. The community lockdown measures implemented in Nigeria on March 30, 2020 need to be maintained for at least three to four months to lead to the effective containment of COVID-19 outbreaks in the country. Relaxing, or fully lifting, the lockdown measures sooner, in an effort to re-open the economy or the country, may trigger a deadly second wave of the pandemic.

Dynamics of a two-sex model for the population ecology of dengue mosquitoes in the presence of Wolbachia.

The release of Wolbachia-infected mosquitoes into the population of wild mosquitoes is one of the promising biological control method for combating the population abundance of mosquitoes that cause deadly diseases, such as dengue. In this study, a new two-sex mathematical model for the population ecology of dengue mosquitoes and disease is designed and used to assess the population-level impact of the periodic release of Wolbachia-infected mosquitoes. Rigorous analysis of the model, which incorporates many of the lifecycle features of dengue disease and the cytoplasmic incompatibility property of Wolbachia bacterium in mosquitoes, reveal that the disease-free equilibrium of the model is locally-asymptotically stable whenever a certain epidemiological threshold, known as the reproduction number of the model (denoted by R0W), is less than unity. The model is shown, using centre manifold theory, to undergo the phenomenon of backward bifurcation at R0W=1. The consequence of this bifurcation is that Wolbachia may not persist, or dengue disease may not be effectively-controlled, when R0W is less than unity. Such persistence and elimination will depend on the initial sizes of the sub-populations of the model. Two mechanisms were identified for which the backward bifurcation phenomenon can be removed. When backward bifurcation does not occur, the associated non-trivial disease-free equilibrium is shown to be globally-asymptotically stable when the reproduction number of the model is less than unity. Numerical simulations, using data relevant to dengue transmission dynamics in northern Queensland, Australia, shows that releasing Wolbachia-infected mosquitoes every three weeks, for a one-year duration, can lead to the effective control of the population abundance of the local wild mosquitoes, and that such effective control increases with increasing number of Wolbachia-infected mosquitoes released (resulting in the reduction of over 90% of the wild mosquito population from their baseline values). Furthermore, simulations show that releasing only adult male Wolbachia-infected mosquitoes provide more beneficial population-level impact (in terms of reducing the population abundance of the wild mosquitoes), in comparison to releasing adult female Wolbachia-infected mosquitoes. Increasing the frequency of Wolbachia release (e.g., from the default release frequency of every three weeks to weekly) does not significantly affect the effectiveness of the Wolbachia-based control program in curtailing the local abundance of the wild mosquitoes. Finally, it was shown that the cytoplasmic incompatibility property of Wolbachia bacterium does not significantly affect the effectiveness of the Wolbachia-based mosquito control strategy implemented in the community.

Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment.

This paper addresses the synergistic interaction between HIV and mycobacterium tuberculosis using a deterministic model, which incorporates many of the essential biological and epidemiological features of the two dis- eases. In the absence of TB infection, the model (HIV-only model) is shown to have a globally asymptotically stable, disease-free equilibrium whenever the associated reproduction number is less than unity and has a unique endemic equilibrium whenever this number exceeds unity. On the other hand, the model with TB alone (TB-only model) undergoes the phenomenon of back- ward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. The analysis of the respective reproduction thresholds shows that the use of a targeted HIV treatment (using anti-retroviral drugs) strategy can lead to effective control of HIV provided it reduces the relative infectiousness of individuals treated (in comparison to untreated HIV-infected individuals) below a certain threshold. The full model, with both HIV and TB, is simulated to evaluate the impact of the various treatment strategies. It is shown that the HIV-only treatment strategy saves more cases of the mixed infection than the TB-only strategy. Further, for low treatment rates, the mixed-only strategy saves the least number of cases (of HIV, TB, and the mixed infection) in comparison to the other strategies. Thus, this study shows that if resources are limited, then targeting such resources to treating one of the diseases is more beneficial in reducing new cases of the mixed infection than targeting the mixed infection only diseases. Finally, the universal strategy saves more cases of the mixed infection than any of the other strategies.