Modeling of Control Efforts against Rhipicephalus sanguineus, the Vector of Rocky Mountain Spotted Fever in Sonora Mexico.

Rocky Mountain spotted fever (RMSF) is a significant health problem in Sonora, Mexico. The tick vector, Rhipicephalus sanguineus, feeds almost exclusively on domestic dogs that, in this region, also serve as the reservoir for the tick-borne pathogen, Rickettsia rickettsii. A process-based mathematical model of the life cycle of R. sanguineus was developed to predict combinations of insecticidal dog collars and long-lasting insecticidal wall treatments resulting in suppression of indoor tick populations. Because of a high burden of RMSF in a rural community near the Sonora state capital of Hermosillo, a test area was treated with a combination of insecticidal dog collars and long-lasting insecticidal wall treatments from March 2018 to April 2019, with subsequent reduction in RMSF cases and deaths. An estimated 80% of the dogs in the area had collars applied and 15% of the houses were treated. Data on tick abundance on walls and dogs, collected during this intervention, were used to parameterize the model. Model results show a variety of treatment combinations likely to be as successful as the one carried out in the test community.

Larval flushing alters malaria endemicity patterns in regions with similar habitat abundance.

A model of Anopheles gambiae populations dynamics coupled with Plasmodium falciparum transmission dynamics is extended to include mechanisms of larval flushing which are known to occur. Flushing dynamics are modeled using a simulation that incorporates seasonal, autocorrelated, and random components based on 30 years of rainfall data for the Kakamega District of the western Kenya highlands. The model demonstrates that flushing phenomena can account for differences between regions with the same annual larval habitat pattern, changing the World Health Organization endemicity classification from either hyperendemic or holoendemic to hypoendemic disease patterns. Mesoendemic patterns of infection occur at the boundary of the holoendemic to hypoendemic transition. For some levels of flushing the entomological inoculation rate drops to an insignificant amount and disease disappears, while the annual indoor resting density remains well above zero. In these scenarios, the disease is hypoendemic, yet the model shows that outbreaks can occur when disease is introduced at particular time points.

Review on mathematical modeling of honeybee population dynamics.

Honeybees have an irreplaceable position in agricultural production and the stabilization of natural ecosystems. Unfortunately, honeybee populations have been declining globally. Parasites, diseases, poor nutrition, pesticides, and climate changes contribute greatly to the global crisis of honeybee colony losses. Mathematical models have been used to provide useful insights on potential factors and important processes for improving the survival rate of colonies. In this review, we present various mathematical tractable models from different aspects: 1) simple bee-only models with features such as age segmentation, food collection, and nutrient absorption; 2) models of bees with other species such as parasites and/or pathogens; and 3) models of bees affected by pesticide exposure. We aim to review those mathematical models to emphasize the power of mathematical modeling in helping us understand honeybee population dynamics and its related ecological communities. We also provide a review of computational models such as VARROAPOP and BEEHAVE that describe the bee population dynamics in environments that include factors such as temperature, rainfall, light, distance and quality of food, and their effects on colony growth and survival. In addition, we propose a future outlook on important directions regarding mathematical modeling of honeybees. We particularly encourage collaborations between mathematicians and biologists so that mathematical models could be more useful through validation with experimental data.

Dilution and amplification effects in Lyme disease: Modeling the effects of reservoir-incompetent hosts on Borrelia burgdorferi sensu stricto transmission.

The literature on Lyme disease includes a lively debate about the paradoxical role of changing deer populations. A decrease in the number of deer will both (1) reduce the incidence of Lyme disease by decreasing the host populations for ticks and therefore tick populations, and (2) enhance the incidence of Lyme disease by offering fewer reservoir-incompetent hosts for ticks, forcing the vector to choose reservoir-competent, and therefore possibly diseased, hosts to feed on. A review of field studies exploring the net impact of changing deer populations shows mixed results. In this manuscript, we investigate the hypothesis that the balance of these two responses to changing deer populations depends on the relative population sizes of reservoir-competent vs. reservoir-incompetent hosts and the presence of host preference in larval and adult stages. A temperature driven seasonal model of Borrelia burgdorferi sensu stricto (cause of Lyme disease) transmission among three host types (reservoir-competent infected and uninfected hosts, and reservoir-incompetent hosts) is constructed as a system of nonlinear ordinary differential equations. The model, which produces biologically reasonable results for both the tick vector Ixodes scapularis Say 1921 and the hosts, is used to investigate the effects of reservoir-incompetent host removal on both tick populations and disease prevalence for various relative population sizes of reservoir-competent hosts vs. reservoir-incompetent hosts. In summary, the simulation results show that the model with host preference appears to be more accurate than the one with no host preference. Given these results, we found that removal of adult I. scapularis(Say) hosts is likely to reduce questing nymph populations. At very low levels questing adult abundance may rise with lack of adult hosts. There is a dilution effect at low reservoir-competent host populations and there is an amplification effect at high reservoir-competent host populations.

A mathematical model of HIV dynamics treated with a population of gene-edited haematopoietic progenitor cells exhibiting threshold phenomenon.

The use of gene-editing technology has the potential to excise the CCR5 gene from haematopoietic progenitor cells, rendering their differentiated CD4-positive (CD4+) T cell descendants HIV resistant. In this manuscript, we describe the development of a mathematical model to mimic the therapeutic potential of gene editing of haematopoietic progenitor cells to produce a class of HIV-resistant CD4+ T cells. We define the requirements for the permanent suppression of viral infection using gene editing as a novel therapeutic approach. We develop non-linear ordinary differential equation models to replicate HIV production in an infected host, incorporating the most appropriate aspects found in the many existing clinical models of HIV infection, and extend this model to include compartments representing HIV-resistant immune cells. Through an analysis of model equilibria and stability and computation of $R_0$ for both treated and untreated infections, we show that the proposed therapy has the potential to suppress HIV infection indefinitely and return CD4+ T cell counts to normal levels. A computational study for this treatment shows the potential for a successful 'functional cure' of HIV. A sensitivity analysis illustrates the consistency of numerical results with theoretical results and highlights the parameters requiring better biological justification. Simulations of varying level production of HIV-resistant CD4+ T cells and varying immune enhancements as the result of these indicate a clear threshold response of the model and a range of treatment parameters resulting in a return to normal CD4+ T cell counts.

A Malaria Transmission Model Predicts Holoendemic, Hyperendemic, and Hypoendemic Transmission Patterns Under Varied Seasonal Vector Dynamics.

A model is developed of malaria (Plasmodium falciparum) transmission in vector (Anopheles gambiae) and human populations that include the capacity for both clinical and parasite suppressing immunity. This model is coupled with a population model for Anopheles gambiae that varies seasonal with temperature and larval habitat availability. At steady state, the model clearly distinguishes uns hypoendemic transmission patterns from stable hyperendemic and holoendemic patterns of transmission. The model further distinguishes hyperendemic from holoendemic disease based on seasonality of infection. For hyperendemic and holoendemic transmission, the model produces the relationship between entomological inoculation rate and disease prevalence observed in the field. It further produces expected rates of immunity and prevalence across all three endemic patterns. The model does not produce mesoendemic transmission patterns at steady state for any parameter choices, leading to the conclusion that mesoendemic patterns occur during transient states or as a result of factors not included in this study. The model shows that coupling the effect of varying larval habitat availability with the effects of clinical and parasite-suppressing immunity is enough to produce known patterns of malaria transmission.

Effect of Rising Temperature on Lyme Disease: Ixodes scapularis Population Dynamics and Borrelia burgdorferi Transmission and Prevalence.

Warmer temperatures are expected to increase the incidence of Lyme disease through enhanced tick maturation rates and a longer season of transmission. In addition, there could be an increased risk of disease export because of infected mobile hosts, usually birds. A temperature-driven seasonal model of Borrelia burgdorferi (Lyme disease) transmission among four host types is constructed as a system of nonlinear ordinary differential equations. The model is developed and parametrized based on a collection of lab and field studies. The model is shown to produce biologically reasonable results for both the tick vector (Ixodes scapularis) and the hosts when compared to a different set of studies. The model is used to predict the response of Lyme disease risk to a mean annual temperature increase, based on current temperature cycles in Hanover, NH. Many of the risk measures suggested by the literature are shown to change with increased mean annual temperature. The most straightforward measure of disease risk is the abundance of infected questing ticks, averaged over a year. Compared to this measure, which is difficult and resource-intensive to track in the field, all other risk measures considered underestimate the rise of risk with rise in mean annual temperature. The measure coming closest was "degree days above zero." Disease prevalence in ticks and hosts showed less increase with rising temperature. Single field measurements at the height of transmission season did not show much change at all with rising temperature.

Reduction of Mosquito Abundance Via Indoor Wall Treatments: A Mathematical Model.

Insecticidal indoor residual wall treatment is a major tool for the control of malaria, with the goals of reducing indoor vector density and vector life span, in addition to reducing transmission rates of disease. Dynamics of the malaria vector, Anopheles gambiae, in the Emutete region in the Western Kenya highlands are based on an already existing model in the literature. In this paper, the framework is used to predict vector reduction due to four types of indoor wall treatments: two cases of indoor residual spraying of DDT and two types of pyrethrin-based INESFLY insecticidal paint. These treatments differ primarily in the duration of their persistence on walls. The model shows the extent of suppression of vector abundance over time due to each of the four treatments. It predicts that indoor residual spraying may have no noticeable effect at all if the percent coverage is not high enough or the persistence of the mortality effect is low, but will have a substantial effect at higher coverage rates and/or higher persistence. For treatments with longer persistence of mortality, the model predicts a coverage threshold above which extra treatment has little to no effect. For treatments of short persistence of mortality, the seasonal timing of treatment has a noticeable effect on the duration of vector suppression. Overall, the model supports claims in the literature that wall treatments have the capacity to reduce the vector burden.

A Mathematical Model of Forager Loss in Honeybee Colonies Infested with Varroa destructor and the Acute Bee Paralysis Virus.

We incorporate a mathematical model of Varroa destructor and the Acute Bee Paralysis Virus with an existing model for a honeybee colony, in which the bee population is divided into hive bees and forager bees based on tasks performed in the colony. The model is a system of five ordinary differential equations with dependent variables: uninfected hive bees, uninfected forager bees, infected hive bees, virus-free mites and virus-carrying mites. The interplay between forager loss and disease infestation is studied. We study the stability of the disease-free equilibrium of the bee-mite-virus model and observe that the disease cannot be fought off in the absence of varroacide treatment. However, the disease-free equilibrium can be stable if the treatment is strong enough and also if the virus-carrying mites become virus-free at a rate faster than the mite birth rate. The critical forager loss due to homing failure, above which the colony fails, is calculated using simulation experiments for disease-free, treated and untreated mite-infested, and treated virus-infested colonies. A virus-infested colony without varroacide treatment fails regardless of the forager mortality rate.

A Mathematical Model of the Honeybee-Varroa destructor-Acute Bee Paralysis Virus System with Seasonal Effects.

A mathematical model for the honeybee-varroa mite-ABPV system is proposed in terms of four differential equations for the: infected and uninfected bees in the colony, number of mites overall, and of mites carrying the virus. To account for seasonal variability, all parameters are time periodic. We obtain linearized stability conditions for the disease-free periodic solutions. Numerically, we illustrate that, for appropriate parameters, mites can establish themselves in colonies that are not treated with varroacides, leading to colonies with slightly reduced number of bees. If some of these mites carry the virus, however, the colony might fail suddenly after several years without a noticeable sign of stress leading up to the failure. The immediate cause of failure is that at the end of fall, colonies are not strong enough to survive the winter in viable numbers. We investigate the effect of the initial disease infestation on collapse time, and how varroacide treatment affects long-term behavior. We find that to control the virus epidemic, the mites as disease vector should be controlled.