# Robert J Smith's research while affiliated with University of Ottawa and other places

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## Publications (46)

To eradicate plant diseases and maintain the number of infected plants below an economic threshold, two impulsive plant-disease models with periodic and state-dependent nonlinear cultural control are established. We focus on saturated nonlinear roguing (identifying and removing infected plants), with three situations for healthy plants: constant re...

Respiratory Syncytial Virus (RSV) is an acute respiratory infection that infects millions of children and infants worldwide. Recent research has shown promise for the development of a vaccine, with a range of vaccine types now in clinical trials or preclinical development. We extend an existing mathematical model with seasonal transmission to inclu...

Eradication of malaria from the world in the latter part of the twentieth century proved an elusive, albeit desirable, objective. Unfortunately, resurgence of malarial incidence is currently underway. Key to understanding effective control schemes such as indoor residual spraying (spraying insecticide inside houses to kill the malarial vector mosqu...

There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a threat to eradication. We develop a model of impulsive differential equations to account for a resistant strain of mosquitoes tha...

Enfuvirtide (formerly T20) is an injectable fusion inhibitor that has established effective antiretroviral activity and excellent tolerability in extensively pretreated patients. This fusion inhibitor does not affect the metabolism of other co-administrated drugs for metabolic drug interactions involving enfuvirtide. Few mathematical models have co...

The growing number of reported avian influenza cases has prompted awareness of the effectiveness of pharmaceutical or/and non-pharmaceutical interventions that aim to suppress the transmission rate. We propose two Filippov models with threshold policy: the avian-only model with culling of infected birds and the SIIR (Susceptible-Infected-Infected-R...

Human papillomavirus (HPV) infection is the most common sexually transmitted infection, which is linked to several cancers and genital warts. Depending on the Canadian province, the quadrivalent vaccine is given to girls in grades 4 through 10 with either a two- or three-dose schedule. We use a mathematical model to address the following research q...

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mat...

The ability to predict the conditions under which antibodies protect against viral infection would transform our approach to vaccine development. A more complete understanding is needed of antibody protection against lentivirus infection, as well as the role of mutation in resistance to an antibody vaccine. Recently, an example of antibody-mediated...

We introduce the notion of impulse extension equations for linear fixed-time impulsive differential equations (IDEs) with strictly inhomogeneous impulses. These differential equations can be thought of as representing the underlying processes for which such linear fixed-time IDEs are a limiting case. We will establish basic existence and uniqueness...

Cholera, characterized by severe diarrhea and rapid dehydration, is a water-borne infectious disease caused by the bacterium Vibrio cholerae. Haiti offers the most recent example of the tragedy that can befall a country and its people when cholera strikes. While cholera has been a recognized disease for two centuries, there is no strategy for its e...

The emergence of drug resistance is one of the most prevalent reasons for treatment failure in HIV therapy. This has severe implications for the cost of treatment, survival and quality of life.
We use mathematical modelling to describe the interaction between T cells, HIV-1 and protease inhibitors. We use impulsive differential equations to examine...

The widespread impact of avian influenza viruses not only poses risks to birds, but also to humans. The viruses spread from birds to humans and from human to human In addition, mutation in the primary strain will increase the infectiousness of avian influenza. We developed a mathematical model of avian influenza for both bird and human populations....

Substance abuse remains a global problem, with immense health and social consequences. Crystal meth, known as 'tik' in South Africa, is a growing problem, and its supply chains have equally grown due to increased numbers of 'tik' users, especially in the Western Cape province of South Africa. We consider a model for 'tik' use that tracks drug-suppl...

HIV has spread widely in mainland China, but there is significant geographic variation in the severity of the epidemic. We aimed to assess the HIV/AIDS epidemic in mainland China accurately, and address the effect of population mobility on it. Markov-Chain Monte-Carlo simulations and Latin Hypercube Sampling were used to estimate the basic reproduc...

In order to control plant diseases and eventually maintain the number of infected plants below the economic threshold, a specific management strategy called the threshold policy is proposed, resulting in Filippov systems. These are a class of piecewise smooth systems of differential equations with a discontinuous right-hand side. The aim of this wo...

The chronic wasting disease (CWD) is a prion infectious disease that affects members of the deer family in North America. Concerns about the economic consequences of the presence of CWD have led management agencies to seek effective strategies to control the CWD distribution and prevalence. Current mathematical models are either based on complex si...

Prior studies have shown that imprisonment is a major risk factor for hepatitis C infection, with the risk of infection directly proportional to the length of incarceration. Women are at least twice as likely as men to contract HCV as they have limited access to information, health services and safe intravenous drug injecting equipments. We develop...

Resistance to a postinfection HIV vaccine that stimulates cytotoxic T-lymphocytes (CTLs) depends on the relationship between the vaccine strength, the fitness cost of the mutant strain, and the rate of mutant escape. If the vaccine is strong enough, both strains of the virus should be controlled by administering the vaccine sufficiently often. Howe...

There is an urgent need to understand how the provision of information influences individual risk perception and how this in turn shapes the evolution of epidemics. Individuals are influenced by information in complex and unpredictable ways. Emerging infectious diseases, such as the recent swine flu epidemic, may be particular hotspots for a media-...

The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease di...

Recently, the first drug in a new class of antiretroviral HIV drugs was approved, the fusion inhibitor enfuvirtide. We develop a mathematical model that describes the binding of the virus to T cells. We model the effect of enfuvirtide upon this process using impulsive differential equations. We find equilibria and determine stability in the case of...

Transmission of Drug Resistance
Understanding the dynamics of drug-resistant strains of HIV and the key determinants affecting their evolution and spread is crucial for predicting future effects of drug treatment. Current models can only track one resistant strain, so Smith? et al. (p. 697 , published online 14 January) used empirical data from San...

We argue that the HIV epidemic in the United States is considerably more widespread than is officially reported. The occasional reports of outbreaks in cities like Washington DC, comparison with other countries in the developed world and our mathematical models, all point to the conclusion that the number of people living with HIV, but not AIDS, in...

Induction-maintenance therapy is a treatment regime where patients are prescribed an intense course of treatment for a short period of time (the induction phase), followed by a simplified long-term regimen (maintenance). Since induction therapy has a significantly higher chance of pill fatigue than maintenance therapy, patients might take drug holi...

A major deficit of all approaches to epidemic modelling to date has been the need to approximate or guess at human behaviour in disease-transmission-related contexts. Avatars are generally human-like figures in virtual computer worlds controlled by human individuals.
We introduce the concept of a "havatar", which is a (human, avatar) pairing. Evide...

There has been a sudden increase in the amount of money donors are willing to spend on the worldwide HIV/AIDS epidemic. Present plans are to hold most of the money in reserve and spend it slowly. However, rapid spending may be the best strategy for halting this disease.
We develop a mathematical model that predicts eradication or persistence of HIV...

The majority of cells infected with the human immunodeficiency virus are activated CD4(+) T cells, which can be treated with antiretoviral drugs. However, an obstacle to eradication is the presence of viral reservoirs, such as latently infected CD4(+) T cells. Such cells may be less susceptible to antiretroviral drugs and may persist at low levels...

We present a model consisting of six differential equations to show that sufficiently large doses of HAART tend to suppress the HIV blips that may otherwise occur because of change in the infection coefficient of the virus. We also show that large doses of HAART will eradicate the reservoir of latently infected CD4+ T cells in a patient.

Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrat...

To stimulate the immune system's natural defenses, a post-infection HIV vaccination program to regularly boost cytotoxic T-lymphocytes has been proposed. We develop a mathematical model to describe such a vaccination program, where the strength of the vaccine and the vaccination intervals are constant. We apply the theory of impulsive differential...

Mathematical models of HIV therapy have traditionally amalgamated the action of antiretroviral drugs, trading the complexity of the situation in favour of simpler-and hence mathematically tractable-models. However, the effects of ignoring such dynamics remain underexamined. In this paper, the traditional method of dosing (where the dose is modelled...

Recently, provincial health programs in Canada and elsewhere have begun rolling out vaccination against human papillomavirus for girls aged 9-13. While vaccination is voluntary, the cost of vaccination is waived, to encourage parents to have their daughters vaccinated. Adult women who are eligible for the vaccine may still receive it, but at a cost...

Indoor residual spraying—spraying insecticide inside houses to kill mosquitoes—is an important method for controlling malaria vectors in sub-Saharan Africa. We propose a mathematical model for both regular and non-fixed spraying, using impulsive differential equations. First, we determine the stability properties of the nonimpulsive system. Next, w...

We explore effect of disease spread in both urban and rural populations for heterosexual transmission. We develop a two-sex model for the spread of HIV using ordinary differential equations. We then use two methods to calculate the basic reproductive ratio (R0) and demonstrate that one is more biologically reasonable than the other. Furthermore, in...

Indoor residual spraying—spraying insecticide inside houses to kill mosquitoes—is an important method
for controlling malaria vectors in sub-Saharan Africa. We propose a mathematical model for both regular
and non-fixed spraying, using impulsive differential equations. First, we determine the stability properties
of the nonimpulsive system. Next, w...

Recent breakthroughs in malaria vaccines have given new hope that a safe, effective malaria vaccine may be found. The following
epidemiological questions are addressed: 1. What level of vaccination coverage is required to offset the limitations of an
imperfect diseasemodifying vaccine? 2. Could the introduction of a low-efficacy malaria vaccine lea...

The following questions were addressed: would the introduction of vaginal microbicides substantially reduce the risk of female sex workers (FSWs) acquiring HIV? Which factor would it be most important to maximize, microbicide efficacy or microbicide use? What level of microbicide efficacy and use would be necessary to counterbalance a possible redu...

Most current candidate HIV vaccines seem to produce little protection against infection, but reduce viral load and slow the decline in CD4 lymphocyte numbers. Such disease-modifying vaccines could potentially provide important population-level benefits by reducing transmission, but could possibly also increase transmission. We address the following...

We explore effect of disease spread in both urban and rural populations for heterosex- ual transmission. We develop a two-sex model for the spread of HIV using ordinary differential equations. We then use two methods to calculate the basic reproductive ratio (R0) and demonstrate that one is more biologically reasonable than the other. Furthermore,...

Vaginal microbicides hold great hope of reducing the spread of HIV and other sexually transmitted infections, as they provide women with a female-controlled protection option. The design and testing of vaginal microbicides thus far has been targeted primarily towards women. We argue that such thinking is limited and that, by ignoring men's needs an...

## Citations

... This hypothesis led Church and Smith? [5] to pose the following question: "Is it always safe to assume that sufficiently short processes occur instantaneously?" They found that this is not always true, albeit for a limited class of equations. ...

... Gene resistance control cannot be widely used due to its high cost, and vector control through insecticide spraying has a small risk of failure due to selection for more damaging virus strains [14][15][16]. However, the cultural control including roguing or removal of diseased plants has been practised and could be more effective [17][18][19][20]. erefore, a successful plant disease control program depends on a plant production system which is closely aligned with the goals of pest management [21][22][23]. ...

... The most common intervention considered is vaccination or monoclonal immunoprophylaxis that induces full temporary immunity to RSV infection (Acedo et al. 2010a, b;Brand et al. 2020;Goldstein et al. 2018;Hodgson et al. 2020;Jornet-Sanz et al. 2017;Kinyanjui et al. 2015;Nugraha and Nuraini 2017;van Boven et al. 2020); however, vaccination inducing partial temporary immunity to RSV infection Kinyanjui et al. 2020;Pan-Ngum et al. 2017;Smith et al. 2017;Yamin et al. 2016), public awareness campaigns (Nugraha and Nuraini 2017), and treatment (Rosa and Torres 2018a, b), are also considered. Interventions are generally assumed to occur uniformly throughout the year, however, exceptions include models that assume vaccination occurs at arbitrary time points throughout the year (Smith et al. 2017), seasonally according to the pattern observed in influenza vaccination (Yamin et al. 2016), at enrollment of primary school (Poletti et al. 2015), and prior to the RSV season (Goldstein et al. 2018;Hodgson et al. 2020). ...

... Many mathematical models have been developed to describe the effect of the entry inhibitors on HIV progression. Mathematical models in [11,14] suggest that a combination of fusion inhibitors (enfuvirtide) and protease inhibitors gives a better outcome than single-drug activity in suppressing the viral load and inhibiting viral entry into the host cell. Magombedze et al. [48] developed mathematical models of the immuno-pathogenesis of HIV infection by incorporating three different stages of the HIV replication cycle: viral entry, transcription from viral RNA to DNA, and production of HIV viral particles to study the effect of their inhibitors. ...

... Early evaluations indicated that malaria transmission had dropped considerably, resulting in a 60% reduction in child mortality following the first 4 years of interventions [12], and a corresponding 50% drop in parasite prevalence in children aged between 1 and 14 years [13]. However, despite its island status, a study in 2013 demonstrated that travel to the mainland of Equatorial Guinea increased the risk of infection in travellers themselves, and in non-travellers living in neighbourhoods with high proportions of travellers [14], highlighting the impact of population movement on malaria transmission levels [15][16][17][18]. ...

... The theory of impulsive differential equations and inclusions has been systematically developed (see e.g., the monographs [1][2][3][4], and the references therein), among other things, especially because of many practical applications (see e.g., References [1,[4][5][6][7][8][9][10][11]). These applications concern fluctuations of pendulum systems under impulsive effects, remittent oscillators, population dynamics, oxygen-driven self-cycling fermentation process, nutrient-driven self-cycling fermentation process, various impulsive drug effects, optimal impulsive vaccination for an SIR control model, an SEIRS epidemic model, malaria vector model, impulsive insecticide spraying, HIV induction-maintenance therapy, and so forth. ...

... Although mathematical modelling investigations into H5N6 are infrequent, there have been a handful of analyses that estimate various subtypes of avian influenza for poultry and human activities [5,6]. Several studies have chosen to use bilinear recurrence estimates to investigate avian influenza propagation, including bird and human populations, for accessibility [7]. ...

... For instance, when disease occurs, people pay more attention to personal hygiene (frequent hand washing, wearing masks, consuming safe drinking water), choose to prevent it through antibiotics, change their travel routes to stay away from areas with high disease prevalence, and thus achieve a reduced risk of contracting the disease. Recently, mathematical epidemiological models on the influence of human behavior have become increasingly available [1,3,10,12,48,51,52]. ...

... While each jurisdictional program has undergone a series of policy changes, program information is scattered across multiple sources and there is no national database that compiles this information. There have been several descriptions of HPV vaccination programs [5][6][7][8], but no analysis of the evolution of HPV vaccination policies and vaccination coverage in all Canadian jurisdictions. As Canada prepares to implement the prevention strategies designed to meet the World Health Organization's goal of eliminating cervical cancer [8], it is essential that Canadian policymakers take stock of the current status of HPV vaccination. ...

... Ciupe et al. [7] studied a model for EIAV strains and neutralizing antibodies. Schwartz et al. [8] derived a model for EIAV to predict the condition to eradicate the wild-type infection with antibody infusions. ...