Cacao sustainability: The case of cacao swollen-shoot virus co-infection.

The cacao swollen shoot virus disease (CSSVD) is among the most economically damaging diseases of cacao trees and accounts for almost 15-50% of harvest losses in Ghana. This virus is transmitted by several species of mealybugs (Pseudococcidae, Homoptera) when they feed on cacao plants. One of the mitigation strategies for CSSVD investigated at the Cocoa Research Institute of Ghana (CRIG) is the use of mild-strain cross-protection of cacao trees against the effects of severe strains. In this study, simple deterministic, delay, and stochastic ordinary differential equation-based models to describe the dynamic of the disease and spread of the virus are suggested. Model parameters are estimated using detailed empirical data from CRIG. The modeling outcomes demonstrate a remarkable resemblance between real and simulated dynamics. We have found that models with delay approximate the data better and this agrees with the knowledge that CSSVD epidemics develop slowly. Also, since there are large variations in the data, stochastic models lead to better results. We show that these models can be used to gain useful informative insights about the nature of disease spread.

Mathematical model of Ehrlichia chaffeensis transmission dynamics in dogs.

Ehrlichia chaffeensis is a tick-borne disease transmitted by ticks to dogs. Few studies have mathematical modelled such tick-borne disease in dogs, and none have developed models that incorporate different ticks' developmental stages (discrete variable) as well as the duration of infection (continuous variable). In this study, we develop and analyze a model that considers these two structural variables using integrated semigroups theory. We address the well-posedness of the model and investigate the existence of steady states. The model exhibits a disease-free equilibrium and an endemic equilibrium. We calculate the reproduction number (T0). We establish a necessary and sufficient condition for the bifurcation of an endemic equilibrium. Specifically, we demonstrate that a bifurcation, either backward or forward, can occur at T0=1, leading to the existence, or not, of an endemic equilibrium even when T0<1. Finally, numerical simulations are employed to illustrate these theoretical findings.

Understanding mental health trends during COVID-19 pandemic in the United States using network analysis.

The emergence of COVID-19 in the United States resulted in a series of federal and state-level lock-downs and COVID-19 related health mandates to manage the spread of the virus. These policies may negatively impact the mental health state of the population. This study focused on the trends in mental health indicators following the COVID-19 pandemic amongst four United States geographical regions, and political party preferences. Indicators of interest included feeling anxious, feeling depressed, and worried about finances. Survey data from the Delphi Group at Carnegie Mellon University were analyzed using clustering algorithms and dynamic connectome obtained from sliding window analysis. Connectome refers to the description of connectivity on a network. United States maps were generated to observe spatial trends and identify communities with similar mental health and COVID-19 trends. Between March 3rd, 2021, and January 10th, 2022, states in the southern geographic region showed similar trends for reported values of feeling anxious and worried about finances. There were no identifiable communities resembling geographical regions or political party preference for the feeling depressed indicator. We observed a high degree of correlation among southern states as well as within Republican states, where the highest correlation values from the dynamic connectome for feeling anxious and feeling depressed variables seemingly overlapped with an increase in COVID-19 related cases, deaths, hospitalizations, and rapid spread of the COVID-19 Delta variant.

Impact of public sentiments on the transmission of COVID-19 across a geographical gradient.

COVID-19 is a respiratory disease caused by a recently discovered, novel coronavirus, SARS-COV-2. The disease has led to over 81 million confirmed cases of COVID-19, with close to two million deaths. In the current social climate, the risk of COVID-19 infection is driven by individual and public perception of risk and sentiments. A number of factors influences public perception, including an individual's belief system, prior knowledge about a disease and information about a disease. In this article, we develop a model for COVID-19 using a system of ordinary differential equations following the natural history of the infection. The model uniquely incorporates social behavioral aspects such as quarantine and quarantine violation. The model is further driven by people's sentiments (positive and negative) which accounts for the influence of disinformation. People's sentiments were obtained by parsing through and analyzing COVID-19 related tweets from Twitter, a social media platform across six countries. Our results show that our model incorporating public sentiments is able to capture the trend in the trajectory of the epidemic curve of the reported cases. Furthermore, our results show that positive public sentiments reduce disease burden in the community. Our results also show that quarantine violation and early discharge of the infected population amplifies the disease burden on the community. Hence, it is important to account for public sentiment and individual social behavior in epidemic models developed to study diseases like COVID-19.

Exploring the role of superspreading events in SARS-CoV-2 outbreaks.

The novel coronavirus SARS-CoV-2 emerged in 2019 and subsequently spread throughout the world, causing over 600 million cases and 6 million deaths as of September 7th, 2022. Superspreading events (SSEs), defined here as public or social events that result in multiple infections over a short time span, have contributed to SARS-CoV-2 spread. In this work, we compare the dynamics of SSE-dominated SARS-CoV-2 outbreaks, defined here as outbreaks with relatively higher SSE rates, to the dynamics of non-SSE-dominated SARS-CoV-2 outbreaks. To accomplish this, we derive a continuous-time Markov chain (CTMC) SARS-CoV-2 model from an ordinary differential equation (ODE) SARS-CoV-2 model and incorporate SSEs using an events-based framework. We simulate our model under multiple scenarios using Gillespie's direct algorithm. The first scenario excludes hospitalization and quarantine; the second scenario includes hospitalization, quarantine, premature hospital discharge, and quarantine violation; and the third scenario includes hospitalization and quarantine but excludes premature hospital discharge and quarantine violation. We also vary quarantine violation rates. Results indicate that, with either no control or imperfect control, SSE-dominated outbreaks are more variable but less severe than non-SSE-dominated outbreaks, though the most severe SSE-dominated outbreaks are more severe than the most severe non-SSE-dominated outbreaks. We measure severity by the time it takes for 50 active infections to be achieved; more severe outbreaks do so more quickly. SSE-dominated outbreaks are also more sensitive to control measures, with premature hospital discharge and quarantine violation substantially reducing control measure effectiveness.

Baptism of Fire: Modeling the Effects of Prescribed Fire on Lyme Disease.

Recently, tick-borne illnesses have been trending upward and are an increasing source of risk to people's health in the United States. This is due to range expansion in tick habitats as a result of climate change. Thus, it is imperative to find a practical and cost-efficient way of managing tick populations. Prescribed burns are a common form of land management that can be cost-efficient if properly managed and can be applied across large amounts of land. In this study, we present a compartmental model for ticks carrying Lyme disease and uniquely incorporate the effects of prescribed fire using an impulsive system to investigate the effects of prescribed fire intensity (high and low) and the duration between burns. Our study found that fire intensity has a larger impact in reducing tick population than the frequency between burns. Furthermore, burning at high intensity is preferable to burning at low intensity whenever possible, although high-intensity burns may be unrealistic due to environmental factors. Annual burns resulted in the most significant reduction in infectious nymphs, which are the primary carriers of Lyme disease.

Using Google Health Trends to investigate COVID-19 incidence in Africa.

The COVID-19 pandemic has caused over 500 million cases and over six million deaths globally. From these numbers, over 12 million cases and over 250 thousand deaths have occurred on the African continent as of May 2022. Prevention and surveillance remains the cornerstone of interventions to halt the further spread of COVID-19. Google Health Trends (GHT), a free Internet tool, may be valuable to help anticipate outbreaks, identify disease hotspots, or understand the patterns of disease surveillance. We collected COVID-19 case and death incidence for 54 African countries and obtained averages for four, five-month study periods in 2020-2021. Average case and death incidences were calculated during these four time periods to measure disease severity. We used GHT to characterize COVID-19 incidence across Africa, collecting numbers of searches from GHT related to COVID-19 using four terms: 'coronavirus', 'coronavirus symptoms', 'COVID19', and 'pandemic'. The terms were related to weekly COVID-19 case incidences for the entire study period via multiple linear and weighted linear regression analyses. We also assembled 72 variables assessing Internet accessibility, demographics, economics, health, and others, for each country, to summarize potential mechanisms linking GHT searches and COVID-19 incidence. COVID-19 burden in Africa increased steadily during the study period. Important increases for COVID-19 death incidence were observed for Seychelles and Tunisia. Our study demonstrated a weak correlation between GHT and COVID-19 incidence for most African countries. Several variables seemed useful in explaining the pattern of GHT statistics and their relationship to COVID-19 including: log of average weekly cases, log of cumulative total deaths, and log of fixed total number of broadband subscriptions in a country. Apparently, GHT may best be used for surveillance of diseases that are diagnosed more consistently. Overall, GHT-based surveillance showed little applicability in the studied countries. GHT for an ongoing epidemic might be useful in specific situations, such as when countries have significant levels of infection with low variability. Future studies might assess the algorithm in different epidemic contexts.

A vaccination model for COVID-19 in Gauteng, South Africa.

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection, and we investigate these strategies in early-stage outbreak dynamics. The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies. Using a system of ordinary differential equations, we model the outbreak in the province of Gauteng, assuming that several parameters vary over time. Analyzing data from the time period before vaccination gives the approximate dates of parameter changes, and those dates are linked to government policies. Unknown parameters are then estimated from available case data and used to assess the impact of each policy. Looking forward in time, possible scenarios give projections involving the implementation of two different vaccines at varying times. Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

Viability of Pentadesma in reduced habitat ecosystems within two climatic regions with fruit harvesting.

Habitat loss and harvesting of non-timber forest products (NTFPs) significantly affect the population dynamics. In this paper, we propose a general mathematical modelling approach incorporating the impact of habitat size reduction and non-lethal harvesting of NTFP on population dynamics. The model framework integrates experimental data of Pentadesma butyracea in Benin. This framework allows us to determine the rational non-lethal harvesting level and habitat size to ensure the stability of the plant ecosystem, and to study the impacts of distinct levels of humidity. We suggest non-lethal harvesting policies that maximize the economic benefit for local populations.

To isolate or not to isolate: the impact of changing behavior on COVID-19 transmission.

BACKGROUND: The COVID-19 pandemic has caused more than 25 million cases and 800 thousand deaths worldwide to date. In early days of the pandemic, neither vaccines nor therapeutic drugs were available for this novel coronavirus. All measures to prevent the spread of COVID-19 are thus based on reducing contact between infected and susceptible individuals. Most of these measures such as quarantine and self-isolation require voluntary compliance by the population. However, humans may act in their (perceived) self-interest only. METHODS: We construct a mathematical model of COVID-19 transmission with quarantine and hospitalization coupled with a dynamic game model of adaptive human behavior. Susceptible and infected individuals adopt various behavioral strategies based on perceived prevalence and burden of the disease and sensitivity to isolation measures, and they evolve their strategies using a social learning algorithm (imitation dynamics). RESULTS: This results in complex interplay between the epidemiological model, which affects success of different strategies, and the game-theoretic behavioral model, which in turn affects the spread of the disease. We found that the second wave of the pandemic, which has been observed in the US, can be attributed to rational behavior of susceptible individuals, and that multiple waves of the pandemic are possible if the rate of social learning of infected individuals is sufficiently high. CONCLUSIONS: To reduce the burden of the disease on the society, it is necessary to incentivize such altruistic behavior by infected individuals as voluntary self-isolation.

Impact of Public Health Education Program on the Novel Coronavirus Outbreak in the United States.

The coronavirus outbreak in the United States continues to pose a serious threat to human lives. Public health measures to slow down the spread of the virus involve using a face mask, social-distancing, and frequent hand washing. Since the beginning of the pandemic, there has been a global campaign on the use of non-pharmaceutical interventions (NPIs) to curtail the spread of the virus. However, the number of cases, mortality, and hospitalization continue to rise globally, including in the United States. We developed a mathematical model to assess the impact of a public health education program on the coronavirus outbreak in the United States. Our simulation showed the prospect of an effective public health education program in reducing both the cumulative and daily mortality of the novel coronavirus. Finally, our result suggests the need to obey public health measures as loss of willingness would increase the cumulative and daily mortality in the United States.

Impact of Mobility on Methicillin-Resistant Staphylococcus aureus among Injection Drug Users.

In this study, we develop and present a deterministic model for the transmission dynamics of methicillin-resistant staphylococcus aureus (MRSA) among injection drug users. The model consists of non-injection drug users as well as low-and high-risk injection drug users (IDUs). The model further incorporates the movement of these individuals between large metro, suburban and rural areas. The model parameters were estimated by fitting the model to the 2008-2013 disease prevalence data for non-IDUs obtained from the Agency for Healthcare and Research and Quality (AHRQ), as well as the 2009-2013 Census Bureau data for the number of individuals migrating between three different counties in Kansas. Sensitivity analysis was implemented to determine the parameters with the most significant impact on the total number of infected individuals; the transmission probability, recovery rates, and positive behavioral change parameter for the subgroup have the most significant effect on the number of infected individuals. Furthermore, the sensitivity of the parameters in the different areas was the same when the areas are disconnected. When the areas are connected, the parameters in large-metro areas were the most sensitive, and the rural areas were least sensitive. The result shows that to effectively control the disease across the large metro, suburban and rural areas, it is best to focus on controlling both behavior and disease in the large metro area as this has a trickle-down effect to the other places. However, controlling behavior and disease at the same time in all the areas will lead to the elimination of the disease.

Maximizing tree harvesting benefit from forests under insect infestation disturbances.

Mathematical modeling has been recognized as an important tool to advance the understanding of the synergetic effect of coupled disturbances (stressors) on the forest population dynamics. Nonetheless, most of the modeling done on disturbances focus on individual disturbance agents and the modeling research on disturbances interactions uses predominantly descriptive statistical processes. This state of art points to the need for continuing modeling efforts not only for addressing the link among multiple disturbances but also for incorporating disturbance processes. In this paper, we present an age-structured forest-beetle mechanistic model with tree harvesting. We investigate three scenarios involving the beetles equilibrium states (no beetles, beetles in endemic and epidemic states). Optimal control theory was applied to study three different benefit functions involving healthy and dead trees. The numerical simulations show that maintaining the beetle infestation at endemic level instead of eliminating all the beetles is sufficient to ensure the forest has trees with all ages. Furthermore, the numerical simulations shows that the harvesting benefit decreases as the number of beetles increases in all cases except when the benefit functional includes a cost (ecological and harvest implementation) and the value of wood is equal across all trees (healthy harvested trees, trees killed by beetles, and trees that die naturally).

Transmission Dynamics of Bovine Anaplasmosis in a Cattle Herd.

Bovine anaplasmosis is an infectious disease of cattle caused by the obligate intercellular bacterium, Anaplasma marginale, and it primarily occurs in tropical and subtropical regions of the world. In this study, an age-structured deterministic model for the transmission dynamics of bovine anaplasmosis was developed; the model incorporates symptomatic and asymptomatic cattle classes. Sensitivity analysis was carried out to determine the parameters with the highest impact on the reproduction number. The dominant parameters were the bovine natural and disease-induced death rates, disease progression rate in adult cattle, the mechanical devices transmission probability and contact rates, the pathogen contamination, and decay rates on the mechanical devices. The result of the sensitivity analysis suggests that control strategies to effectively prevent/control the spread of bovine anaplasmosis should focus on these parameters according to their positive or negative effect as seen from the sensitivity index. Following the results of the sensitivity analysis, three control strategies were investigated, namely, bovine-culling, safety-control, and universal. In addition to these strategies, three effectiveness levels (low, medium, and high) were considered for each control strategy using the cumulative number of newly infected cases in both juvenile and adult cattle as measure function. The universal strategy (comprising both cattle-culling and safety-control strategies) is only marginally better at reducing the number of infected cattle compare to the safety-control strategy. This result suggests that efforts should be aimed at improving and maintaining good hygiene practices; furthermore, the added benefit of culling infected cows is only minimal and not cost-efficient.

Transmission dynamics for Methicilin-resistant Staphalococous areus with injection drug user.

BACKGROUND: Methicillin-resistant Staphylococcus aureus (MRSA) is a bacterial pathogen resistance to antibiotics including methicillin. The resistance first emerged in 1960 in a healthcare setting only after two years of using methicillin as a viable treatment for methicillin-susceptible Staphylococcus aureus. MRSA leads to infections in different parts of the body including the skin, bloodstream, lungs, or the urinary tract. METHODS: A deterministic model for methicillin-resistant Staphylococcus aureus (MRSA) with injection drug users is designed. The model incorporates transmission of MRSA among non-injection drug users and injection drug users (IDUs) who are both low-and high-risk users. A reduced MRSA transmission model with only non-IDUs is fitted to a 2008-2013 MRSA data from the Agency for Healthcare and Research and Quality (AHRQ). The parameter estimates obtained are projected onto the parameters for the low-and high-risk IDUs subgroups using risk factors obtained by constructing a risk assessment ethogram. Sensitivity analysis is carried out to determine parameters with the greatest impact on the reproduction number using the reduced non-IDUs model. Change in risk associated behaviors was studied using the full MRSA transmission model via the increase in risky behaviors and enrollment into rehabilitation programs or clean needle exchange programs. Three control effectiveness levels determined from the sensitivity analysis were used to study control of disease translation within the subgroups. RESULTS: The sensitivity analysis indicates that the transmission probability and recovery rates within the subgroup have the highest impact on the reproduction number of the reduced non-IDU model. Change in risk associated behaviors from non-IDUs to low-and high-risk IDUs lead to more MRSA cases among the subgroups. However, when more IDUs enroll into rehabilitation programs or clean needle exchange programs, there was a reduction in the number of MRSA cases in the community. Furthermore, MRSA burden within the subgroups can effectively be curtailed in the community by implementing moderate- and high-effectiveness control strategies. CONCLUSIONS: MRSA burden can be curtailed among and within non-injection drug users and both low-and high-risk injection drug users by encouraging positive change in behaviors and by moderate- and high-effectiveness control strategies that effectively targets the transmission probability and recovery rates within the subgroups in the community.

Optimal control and cost-effective analysis of malaria/visceral leishmaniasis co-infection.

In this paper, a deterministic model involving the transmission dynamics of malaria/visceral leishmaniasis co-infection is presented and studied. Optimal control theory is then applied to investigate the optimal strategies for curtailing the spread of the diseases using the use of personal protection, indoor residual spraying and culling of infected reservoirs as the system control variables. Various combination strategies were examined so as to investigate the impact of the controls on the spread of the disease. And we investigated the most cost-effective strategy of all the control strategies using three approaches, the infection averted ratio (IAR), the average cost-effectiveness ratio (ACER) and incremental cost-effectiveness ratio (ICER). Our results show that the implementation of the strategy combining all the time dependent control variables is the most cost-effective control strategy. This result is further emphasized by using the results obtained from the cost objective functional, the ACER, and the ICER.

Defining the Risk of Zika and Chikungunya Virus Transmission in Human Population Centers of the Eastern United States.

The recent spread of mosquito-transmitted viruses and associated disease to the Americas motivates a new, data-driven evaluation of risk in temperate population centers. Temperate regions are generally expected to pose low risk for significant mosquito-borne disease; however, the spread of the Asian tiger mosquito (Aedes albopictus) across densely populated urban areas has established a new landscape of risk. We use a model informed by field data to assess the conditions likely to facilitate local transmission of chikungunya and Zika viruses from an infected traveler to Ae. albopictus and then to other humans in USA cities with variable human densities and seasonality. Mosquito-borne disease occurs when specific combinations of conditions maximize virus-to-mosquito and mosquito-to-human contact rates. We develop a mathematical model that captures the epidemiology and is informed by current data on vector ecology from urban sites. The model demonstrates that under specific but realistic conditions, fifty-percent of introductions by infectious travelers to a high human, high mosquito density city could initiate local transmission and 10% of the introductions could result in 100 or more people infected. Despite the propensity for Ae. albopictus to bite non-human vertebrates, we also demonstrate that local virus transmission and human outbreaks may occur when vectors feed from humans even just 40% of the time. Inclusion of human behavioral changes and mitigations were not incorporated into the models and would likely reduce predicted infections. This work demonstrates how a conditional series of non-average events can result in local arbovirus transmission and outbreaks of human disease, even in temperate cities.

Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus.

We developed a new age-structured deterministic model for the transmission dynamics of chikungunya virus. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the stable disease-free equilibrium is globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model undergoes, in the presence of disease induced mortality, the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the qualitative dynamics of the model are not altered by the inclusion of age structure. This is further emphasized by the sensitivity analysis results, which shows that the dominant parameters of the model are not altered by the inclusion of age structure. However, the numerical simulations show the flaw of the exclusion of age in the transmission dynamics of chikungunya with regard to control implementations. The exclusion of age structure fails to show the age distribution needed for an effective age based control strategy, leading to a one size fits all blanket control for the entire population.

Transit times and mean ages for nonautonomous and autonomous compartmental systems.

We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von Förster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory generalises the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford approach model, and we demonstrate that the nonautonomous versions of transit time and mean age differ significantly from the autonomous quantities when calculated for that model.