Prevalence-based modeling approach of schistosomiasis : global stability analysis and integrated control assessment

A system of nonlinear differential equations is proposed to assess the effects of prevalence-dependent disease contact rate, pathogen’s shedding rates, and treatment rate on the dynamics of schistosomiasis in a general setting. The decomposition techniques by Vidyasagar and the theory of monotone systems are the main ingredients to deal completely with the global asymptotic analysis of the system. Precisely, a threshold quantity for the analysis is derived and the existence of a unique endemic equilibrium is shown. Irrespective of the initial conditions, we prove that the solutions converge either to the disease-free equilibrium or to the endemic equilibrium, depending on whether the derived threshold quantity is less or greater than one. We assess the role of an integrated control strategy driven by human behavior changes through the incorporation of prevalence-dependent increasing the prophylactic treatment and decreasing the contact rate functions, as well as the mechanical water sanitation and the biological elimination of snails. Because schistosomiasis is endemic, the aim is to mitigate the endemic level of the disease. In this regard, we show both theoretically and numerically that: the reduction of contact rate through avoidance of contaminated water, the enhancement of prophylactic treatment, the water sanitation, and the removal of snails can reduce the endemic level and, to an ideal extent, drive schistosomiasis to elimination.The University of Pretoria Senior Postdoctoral Program Grant.https://www.springer.com/journal/403142022-01-20hj2021Mathematics and Applied Mathematic

Advanced Nonlinear Dynamics of Population Biology and Epidemiology

abstract: Modern biology and epidemiology have become more and more driven by the need of mathematical models and theory to elucidate general phenomena arising from the complexity of interactions on the numerous spatial, temporal, and hierarchical scales at which biological systems operate and diseases spread. Epidemic modeling and study of disease spread such as gonorrhea, HIV/AIDS, BSE, foot and mouth disease, measles, and rubella have had an impact on public health policy around the world which includes the United Kingdom, The Netherlands, Canada, and the United States. A wide variety of modeling approaches are involved in building up suitable models. Ordinary differential equation models, partial differential equation models, delay differential equation models, stochastic differential equation models, difference equation models, and nonautonomous models are examples of modeling approaches that are useful and capable of providing applicable strategies for the coexistence and conservation of endangered species, to prevent the overexploitation of natural resources, to control disease’s outbreak, and to make optimal dosing polices for the drug administration, and so forth.View the article as published at https://www.hindawi.com/journals/aaa/2014/214514

Observer design for a schistosomiasis model

This paper deals with the state estimation for a schistosomiasis infection dynamical model described by a continuous non linear system when only the infected human population is measured. The central idea will be studied following two major angles. On the one hand, when all the parameters of the model are supposed to be well known, we will construct a simple observer and a high-gain Luenberger observer based on a canonical controller form and conceived for the nonlinear dynamics where it is implemented. On the other hand, when the nonlinear uncertain continuous-time system is in a bounded-error context, we will introduce a method for designing a guaranteed interval observer. Numerical simulations are included in order to test the behavior and the performance of the given observers.Un observateur 'grand gain' non-linéaire est mis en œuvre pour évaluer l'évolution de dynamique d'une infection de la Bilharziose décrite par un modèle continu non linéaire [1]. On propose un modèle réduit du modèle [1] de la Bilharziose pour construire l'observateur. Des simulations numériques ont été faites pour tester le comportement et la performance de l'observateur proposé

Biomathematics of Chlamydia

Chlamydia trachomatis (C. trachomatis) related sexually transmitted infections are a major global public health concern. C. trachomatis afflict millions of men, women, and children worldwide and frequently result in serious medical diseases. In this thesis, mathematical modeling is applied in order to comprehend the dynamics of Chlamydia pathogens within host, their interactions with the immune systems, behavior in the presence of other pathogens, transmission dynamics in a human population, and the efficacy of control measures. The thesis begins with a brief introduction of the bacteria Chlamydia in Chapter 1. In Chapter 2, we give a brief detail of the mathematical modeling of infectious diseases, and its specific application to study the pathogen. In Chapter 3, a linear delay differential compartmental model is developed, and its special application is shown for a laboratory experiment conducted to study the intracellular development cycle of Chlamydia. The delay accounts for the time spent by bacteria in their various forms and for the time taken to go through the replication cycle. The mathematical model tracks the number of Chlamydia infected cells at each stage of the cell division cycle. Moreover, the formula for the final size of each compartment is derived. With initial conditions taken from the experiment, the model is fitted to results from the laboratory data. This simple linear model is capable of reflecting the outcomes of the laboratory experiment. In Chapter 4, at a population level, a novel mathematical model is introduced to study the dynamics of the co-infection between C. trachomatis, and herpes simplex virus (HSV). The concept of the model is based on the observation that in an individual simultaneously infected with both pathogens, the presence of HSV will make the Chlamydia persistent. In its persistent phase, Chlamydia is not replicating and is non-infectious. Important threshold parameters are obtained for the persistence of both infections. We prove global stability results for the disease-free and the boundary equilibria by applying the theory of asymptotically autonomous systems. Further, the model is calibrated to disease parameters to determine the population prevalence of both diseases and compare it with epidemiological findings. In Chapter 5, a compartmental maturity structured model is developed to investigate an optimal control problem for the treatment of chronic Chlamydia infection. The model takes into account the interaction of the pathogens with the immune system and its effects on the formation of persistent Chlamydia particles. As the system takes the form of a mixed ODE-PDE system, the results of the conventional form of Pontryagin’s maximal principle for ordinary differential equations are not suitable. For our purpose, we construct an optimal control problem for a general maturity compartmental model, and hence it consists of ordinary and partial differential equations, moreover, the boundary conditions are also nonlinear. For a fixed control, we verify the existence, uniqueness, and boundedness of the solutions. The system is numerically simulated for a variety of cost functions in order to calculate the optimal treatment for curing Chlamyida infection. We believe that since our findings were validated for a general model with maturity structure, they may be applied to any specific compartmental model that is compatible with the established system

Parameter Estimation and Mathematical Modeling of Visceral Leishmaniasis Transmission

abstract: The Visceral Leishmaniasis (VL) is primarily endemic in five countries, with India and Sudan having the highest burden. The risk factors associated with VL are either unknown in some regions or vary drastically among empirical studies. Here, a dynamical model, motivated and informed by field data from the literature, is analyzed and employed to identify and quantify the impact of region dependent risks on the VL transmission dynamics. Parameter estimation procedures were developed using model-derived quantities and empirical data from multiple resources. The dynamics of VL depend on the estimates of the control reproductive number, RC, interpreted as the average number of secondary infections generated by a single infectious individual during the infectious period. The distribution of RC was estimated for both India (with mean 2.1 ± 1.1) and Sudan (with mean 1.45 ± 0.57). This suggests that VL can be established in naive regions of India more easily than in naive regions of Sudan. The parameter sensitivity analysis on RC suggests that the average biting rate and transmission probabilities between host and vector are among the most sensitive parameters for both countries. The comparative assessment of VL transmission dynamics in both India and Sudan was carried out by parameter sensitivity analysis on VL-related prevalences (such as prevalences of asymptomatic hosts, symptomatic hosts, and infected vectors). The results identify that the treatment and symptoms’ developmental rates are parameters that are highly sensitive to VL symptomatic and asymptomatic host prevalence, respectively, for both countries. It is found that the estimates of transmission probability are significantly different between India (from human to sandflies with mean of 0.39 ± 0.12; from sandflies to human with mean 0.0005 ± 0.0002) and Sudan (from human to sandflies with mean 0.26 ± 0.07; from sandflies to human with mean 0.0002 ± 0.0001). The results have significant implications for elimination. An increasing focus on elimination requires a review of priorities within the VL control agenda. The development of systematic implementation of con­trol programs based on identified risk factors (such as monitoring of asymptomatically infected individuals) has a high transmission-blocking potential.Dissertation/ThesisDoctoral Dissertation Applied Mathematics for the Life and Social Sciences 201

Housing, Health and Happiness

Despite the importance of housing for people’s well-being, there is little evidence on the causal impact of housing and housing improvement programs on health and welfare. In this paper, we help to fill this gap by investigating the impact of a large-scale effort by the Mexican Government to replace dirt floors with cement floors on child health and adult happiness. We find that replacing dirt floors with cement floors significantly improves the health of young children. Specifically, we find significant decreases in the incidence of parasitic infestations, diarrhea, and the prevalence of anemia, and an improvement in children’s cognitive development. Additionally, we find that replacing dirt floors by cement floors significantly improves adult welfare, as measured by increased satisfaction with their housing and quality of life, as well as by lower scores on depression and perceived stress scales.

Population Density and Spatial Distribution of Neglected Tropical Diseases in Sierra Leone

Neglected tropical diseases (NTDs) are the most common health conditions affecting the poorest residents of sub-Saharan Africa (SSA). These infections affect an estimated 2 billion people worldwide, including 500 million people living in SSA. About 85% of NTD infections are a result of helminth infections; hookworm is also a common occurrence among SSA’s poorest people, especially children. Schistosomiasis is the 2nd most prevalent NTD after hookworm. This quantitative correlational study investigated population distribution and the spread of NTDs in Sierra Leone. The focus was on 5 major NTDs: ascariasis, hookworm, schistosomiasis, soil-transmitted helminthiasis, and trichuris. Data were obtained from the Sierra Leone Ministry of Health and Sanitation and the World Health Organization (N=1,537). Due to data availability, correlation analysis was limited to climate pattern (temperature and precipitation change), population density, and prevalence of NTDs. Logistic regression analysis was also used to test the research hypotheses. Population density was taken as the dependent variable, and temperature and precipitation were taken as the independent variables. The results of this study did not show a relationship between climate patterns, as measured by temperature and precipitation trend, and population density in Sierra Leone. Furthermore, this study did not indicate any association between population density and the prevalence of NTDs in Sierra Leone. In future studies on similar topics, it is recommended that researchers collect pretreatment and posttreatment data on the same populations. Thorough and complete data sets should be collected for population movement and density as well as disease prevalence. More should be done to improve public health infrastructure and funding to prevent the transmission of neglected tropical diseases

Social and environmental epidemiology of schistosomiasis in Ghana

Chemotherapy has provided a realistic approach for controlling schistosomiasis in resource-poor settings such as sub-Saharan Africa and control programmes have mainly adopted an age-targeted strategy of implementation. However, it is being increasingly argued that the setting-specific context in which the transmission of schistosome infections occurs may render this global approach of chemotherapy implementation inefficient. Evidence from different endemic settings points to the fact that the transmission dynamics of schistosome infections is not merely an interplay between humans and the parasites, but also a series complex interactions between environmental and social processes. Hence the degree of the spatial heterogeneity, that often characterises the transmission of infections, may differ for different endemic settings depending on the extent of the interaction between these processes. This thesis employs geostatistical methodology in assessing the collective effects of the social and environmental determinants of schistosome transmission within different endemic settings in Ghana. It also explores how these processes may influence the patterns of transmission at the local level and how these patterns could be utilised in improving the effectiveness of mass chemotherapy intervention programmes

Epidemiological Analysis of Host Populations with Widespread Sub-Patent Infections: African Trypanosomiasis

The epidemiological study of pathogens largely depends on three technologies, serology, microscopy and the polymerase chain reaction (PCR). Serological methods are unable to differentiate between current and past infections. Microscopy has historically been the mainstay of epidemiological study. In recent times the use of microscopy has been in decline, as it has been shown to have an inherent lack of sensitivity and specificity and produces many false negative results. PCR is now the method of choice for screening samples for the presence or absence of pathogens. Although PCR is widely regarded as an extremely sensitive technique, the fact that it assays a very small volume of sample is often overlooked. If the target pathogen is not present in the tiny aliquot of sample from an infected host, then a false negative results will occur. In endemic situations were the pathogen is present at low infection intensities, then the potential for false negatives results of this type is high. This intensity related false negative effect can lead to serious underestimation of diagnosed prevalence and incidence with consequent misinterpretation of the resulting data. This phenomenon has been reported in the literature for a range of pathogens and especially for epidemiological study of schistosomiasis. The extensive occurrence of false negatives during study of schistosomiasis samples was such an obstacle to epidemiological study it prompted the world health organisation to repeatedly call for quantitative methods to be employed to combat the problem. The main objectives of this thesis are to rationalise and simplify the methods of diagnosing African trypanosomes in epidemiological studies and to investigate the consequences of, and methods of dealing with infection intensity related false negative results that occur as a result of widespread sub-patent infections in the study population A new PCR assay was developed that was capable of analysing whole blood placed onto treated filter paper. The PCR assay was capable of differentiating between all the important African trypanosome species, producing a unique size of amplicon for each species of trypanosome. Initial results from repeated screening of human and cattle samples known to be parasitologically positive indicated that many false negative results occur. A more extensive analysis of thirty five bovine blood samples randomly chosen from a collection of field samples revealed that false negative results occurred regularly. The prevalence of infection after a single screening was 14.3% whereas the cumulative prevalence after over 100 repeated screenings rose to 85.7%. This showed that a severe underestimation of prevalence occurs from a single screening of the samples. In order to investigate the consequences of, and develop methods of dealing with this problem, computer based simulations were used to model the dynamics of screening samples with sub-patent infections. In order to construct the model the data obtained from repeat screening of the thirty-five bovine blood samples was fitted to a number of mathematical distributions. A negative binomial distribution best described the distribution of trypanosomes across the hosts. Exploration of the phenomenon with the resulting model showed the extensive underestimation of true prevalence that is possible. The simulations also showed that it is possible for populations with very different patterns of infection and true prevalence to all have the same diagnosed prevalence from a single screening per sample. Statistical comparison of these very different populations by diagnosed prevalence alone would conclude there was no significant difference between the populations. It was therefore concluded that the diagnosed prevalence from a single (or even multiple) screenings is an inadequate and potentially misleading measure of both infected hosts and parasite numbers. In order to deal with these problems new methods were evaluated for use in epidemiological studies. A simple method of producing quantitative measures of infection was advocated. The insensitivity of existing screening methods in detecting significant difference between populations was highlighted and a greatly improved methodology was shown. Finally, a method for inferring the true population prevalence from the data obtained from repeat screening of samples was suggested. Although some of these new methodologies have limitations, they represent a great improvement on the use of a single diagnostic test for each host. The work presented in this thesis highlights a serious potential limitation to our understanding of the epidemiology of pathogens that exist at sub-patent levels, and develops some possible methods of overcoming these limitations