Optimal control and cost-effectiveness analysis of Fasciola hepatica model

A deterministic model with an optimal control framework is formulated to analyse the cost-effectiveness of intervention measures used to control Fasciola hepatica in cattle populations. Using the Volterra-Lyapunov stability method, it is noted that the model is globally stable at the endemic equilibrium point. The Pontryagin maximum principle has been applied to determine optimal disease control conditions, including strategies such as pasture management, treatment of infected cattle, and molluscicide use. Numerical simulations for the optimum problem show that double and triple controls have significant effects on reducing disease transmission. The results indicate that for optimal impact, the molluscicide control parameter should always be at its highest possible value. The incremental cost-effectiveness ratio (ICER) analysis of strategies to reduce the disease shows that pasture management combined with molluscicide use will be the most effective and least expensive option. The molluscicide intervention rate should always be at its maximum value for better control of the disease. Educational programs for proper pasture management conditions and sufficient use of molluscicides can significantly reduce the spread of Fasciola hepatica among cattle and humans.

Control of schistosomiasis by the selective competitive and predatory intervention of intermediate hosts: A mathematical modeling approach

Schistosomiasis, a freshwater-borne neglected tropical disease, disproportionately affects impoverished communities mainly in the tropical regions. Transmission involves humans and intermediate host (IH) snails. This manuscript introduces a mathematical model to probe schistosomiasis dynamics and the role of non-host snail competitors and predators as biological control agents for IH snails. The numerical analyses include investigations into steady-state conditions and reproduction numbers associated with uncontrolled scenarios, as well as scenarios involving non-host snail competitors and/or predators. Sensitivity analysis reveals that increasing snail mortality rates is a key to reducing the IH snail population and control of the transmission. Results show that specific snail competitors and/or predators with strong competition/predation abilities reduce IH snails and the subsequent infectious cercaria populations, reduce the transmission, and possibly eradicate the disease, while those with weaker abilities allow disease persistence. Hence our findings advocate for the effectiveness of snail competitors with suitable competitive pressures and/or predators with appropriate predatory abilities as nature-based solutions for combating schistosomiasis, all while preserving IH snail biodiversity. However, if these strategies are implemented at insignificant levels, IH snails can dominate, and disease persistence may pose challenges. Thus, experimental screening of potential (native) snail competitors and/or predators is crucial to assess the likely behavior of biological agents and determine the optimal biological control measures for IH snails.

A compartmental model for Schistosoma japonicum transmission dynamics in the Philippines

Schistosomiasis is a chronic and debilitating neglected tropical disease (NTD), second only to malaria as one of the most devastating parasitic diseases. Caused by a parasitic flatworm of the genus Schistosoma, infection occurs when skin comes in contact with contaminated freshwater that contains schistosome-hosting snails. The disease continues to be endemic in many regions of the Philippines, where it poses a significant public health challenge due to a lack of healthcare resources. In the Philippines, additional mammalian reservoirs for the S. japonicum parasite, especially bovines such as carabaos, also facilitate the spread of schistosomiasis. We extend existing compartment models to include human, snail, bovine, and free-living Schistosoma for a comprehensive look at the transmission dynamics of the disease. Sensitivity analysis of model parameters shows that the carabaos themselves can sustain the endemicity of schistosomiasis. Thus, we consider the control method of farming mechanization to avoid contaminated freshwater sources. We find that a reduction of contaminated water contacts by at least 77% will break the transmission cycle and eliminate the disease. However, reducing the contact by about 70% will still result in decrease of human schistosomiasis prevalence to under 1% in 15 years or less. Achieving such high reduction of contact rates could be a daunting task, especially in rural areas. Still, the potential to eliminate or at least reduce the schistosomiasis prevalence should be considered an additional benefit of mechanization efforts in the Philippines.

The transmission mechanism theory of disease dynamics: Its aims, assumptions and limitations

Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which now span over a century is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process. Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history, dating back to over a century now, that knowledge has not yet been formalized into a scientific theory. In this article, we formalize this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system, disease dynamics is determined by transmission as the main dynamic disease process. Therefore, the transmission mechanism theory of disease dynamics can be seen as formalizing knowledge that has been inherent in the study of infectious disease dynamics using single scale mathematical and computational models for over a century now. The objective of this article is to summarize this existing knowledge about single scale modelling of infectious dynamics by means of a scientific theory called the transmission mechanism theory of disease dynamics and highlight its aims, assumptions and limitations.

Schistosomiasis model with treatment, habitat modification and biological control

Schistosomiasis is a parasitic disease caused by Schistosoma worm infection. Some species of snails can serve as the intermediate hosts for the parasite. Numerous interventions have been performed to repress the snail population. One of them is the use of molluscicide. Nevertheless, it is debated that molluscicide intervention has negative impacts on the ecosystem. To investigate the impact of more environmentally friendly interventions, we develop a schistosomiasis model with treatment, habitat modification and biological control. The biological control agent examined in our model is a snail predator. Moreover, to investigate the impact of snail habitat modification, we assume that the snail population grows logistically. We show that all solutions of our model are non-negative and bounded. We also study the existence and stability conditions of equilibrium points. The basic reproduction numbers are determined using the next-generation operator. Linearization combined with the Routh-Hurwitz criterion is used to prove the local stability condition of disease-free equilibrium points. Bifurcation theory is applied to investigate the local stability condition of the endemic equilibrium points. To examine the global behavior of our model, we use asymptotically autonomous system theory and construct a Lyapunov function. We perform several numerical simulations to validate and support our deductive results. Our results show that early treatment can reduce the basic reproduction number and schistosomiasis cases. In addition, modifying snail habitat and releasing the snail predator at the snail habitat can reduce schistosomiasis prevalence. We suggest using snail predators which can hunt and kill snails effectively as a biological control agent.

A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding

To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number [Formula: see text], while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter values from published literature are used for numerical simulations and where applicable, uncertainty analysis on the non-dimensional system parameters is performed using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques. Sensitivity analysis to determine the relative importance of model parameters to disease transmission shows that the environment-related parameters namely, [Formula: see text] (snails shedding rate of cercariae), [Formula: see text] (probability that cercariae shed by snails survive), c (fraction of the contaminated environment sprayed by molluscicides) and [Formula: see text] (mortality rate of cercariae) are the most significant to mitigate the spread of schistosomiasis. Mollusciciding, which directly impacts the contaminated environment as a single control strategy is more effective compared to treatment. However, concurrently applying mollusciciding and treatment will yield a better outcome.

Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

Schistosomiasis is a parasitic disease caused by the schistosoma worm. A snail can act as the intermediate host for the parasite. Snail-population control is considered to be an effective way to control schistosomiasis spread. In this paper, we discuss the schistosomiasis model incorporating a snail predator as a biological control agent. We prove that the solutions of the model are non-negative and bounded. The existence condition of equilibrium points is investigated. We determine the basic reproduction number when the predator goes to extinction and when the predator survives. The local stability condition of disease-free equilibrium point is proved using linearization, and the Lienard–Chipart and Routh–Hurwitz criteria. We use center-manifold theory to prove the local stability condition of the endemic equilibrium points. Furthermore, we constructed a Lyapunov function to investigate the global stability condition of the disease-free equilibrium points. To support the analytical results, we presented some numerical simulation results. Our findings suggest that a snail predator as a biological control agent can reduce schistosomiasis prevalence. Moreover, the snail-predator birth rate plays an essential role in controlling schistosomiasis spread.

Interventions can shift the thermal optimum for parasitic disease transmission

Temperature constrains the transmission of many pathogens. Interventions that target temperature-sensitive life stages, such as vector control measures that kill intermediate hosts, could shift the thermal optimum of transmission, thereby altering seasonal disease dynamics and rendering interventions less effective at certain times of the year and with global climate change. To test these hypotheses, we integrated an epidemiological model of schistosomiasis with empirically determined temperature-dependent traits of the human parasite Schistosoma mansoni and its intermediate snail host (Biomphalaria spp.). We show that transmission risk peaks at 21.7 °C (T _opt ), and simulated interventions targeting snails and free-living parasite larvae increased T _opt by up to 1.3 °C because intervention-related mortality overrode thermal constraints on transmission. This T _opt shift suggests that snail control is more effective at lower temperatures, and global climate change will increase schistosomiasis risk in regions that move closer to T _opt Considering regional transmission phenologies and timing of interventions when local conditions approach T _opt will maximize human health outcomes.

Modeling schistosomiasis transmission: the importance of snail population structure

Background

Schistosomiasis is a neglected tropical disease endemic in 54 countries. A major Schistosoma species, Schistosoma mansoni, is sustained via a life cycle that includes both human and snail hosts. Mathematical models of S. mansoni transmission, used to elucidate the complexities of the transmission cycle and estimate the impact of intervention efforts, often focus primarily on the human host. However, S. mansoni incurs physiological costs in snails that vary with the age of the snail when first infected. Snail demography and the age of snail infection could thus affect the force of infection experienced by humans, which is frequently used to predict the impact of various control strategies.

Methods

To address how these snail host and parasite interactions influence model predictions, we developed deterministic models of schistosomiasis transmission that include varying complexity in the snail population age structure. Specifically, we examined how model outputs, such as schistosome prevalence in human and snail populations, respond to the inclusion of snail age structure.

Results

Our models suggest that snail population age structure modifies the force of infection experienced by humans and the relationship between snail infection prevalence and corresponding human infection prevalence. There are significant differences in estimated snail infection, cercarial density and mean worm burden between models without snail population dynamics and those with snail populations, and between models with a homogeneous snail population and those with age stratification. The variation between finely age-stratified snail populations and those grouped into only juvenile and adult life stages is, however, minimal.

Conclusions

These results indicate that including snails and snail age structure in a schistosomiasis transmission model alters the relationship between snail and human infection prevalence. This highlights the importance of accounting for a heterogeneous intermediate host population in models of schistosomiasis transmission where the impact of proposed control measures is being considered.

OPTIMAL CONTROL ANALYSIS OF A HUMAN–BOVINE SCHISTOSOMIASIS MODEL

We formulate and analyze a deterministic mathematical model for the transmission dynamics of schistosomiasis with treatment of both humans and bovines and mollu-sciciding of the contaminated environment. The model effective reproduction number is derived and analytical results show that the disease-free and endemic equilibria are both locally and globally asymptotically stable. Pontryagin’s Maximum Principle which uses both Lagrangian and Hamiltonian principles with respect to a time-dependent constant is used to establish the existence of the optimal control problem and to derive the necessary conditions for optimal control of the disease. Mollusciciding of the contaminated environment has a major impact on disease control. However, combining it with treatment could help mitigate the spread of the disease compared to applying each control measure individually. Numerical simulations are performed to support theoretical results.

GLOBAL DYNAMICS OF A SEASONAL MATHEMATICAL MODEL OF SCHISTOSOMIASIS TRANSMISSION WITH GENERAL INCIDENCE FUNCTION

In this paper, we investigate a nonautonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the nonautonomous model by taking into account the effect of climate change on the transmission. Through rigorous analysis via theories and methods of dynamical systems, we show that the nonautonomous model has a globally asymptotically stable disease-free periodic equilibrium when the associated basic reproduction ratio [Formula: see text] is less than unity. Otherwise, the system admits at least one positive periodic solutions if [Formula: see text] is greater than unity. Secondly, using the average of periodic functions, we further derive the autonomous model associated with the nonautonomous model. Therefore, we show that the disease-free equilibrium of the autonomous model is locally and globally asymptotically stable when the associated reproduction ratio [Formula: see text] is less than unity. When [Formula: see text] is greater than unity, the existence and global asymptotic stability of the endemic equilibrium is established under certain conditions. Finally, using linear and nonlinear specific incidence function, we perform some numerical simulations to illustrate our theoretical results.

Modeling the Transmission Dynamics of Clonorchiasis in Foshan, China

Clonorchiasis, known as the Chinese liver fluke disease, is caused by Clonorchis sinensis infection with food-borne liver fluke, which is transmitted via snails to freshwater fish and then to human beings or other piscivorous mammals. Clonorchis sinensis infection is mainly related to liver and biliary disorders, especially cholangiocarcinoma, and has an increased human-health impact due to the greater consumption of raw freshwater fish. In this article, we propose a deterministic model to describe the spread of clonorchiasis among human-snail-fish populations and use the model to simulate the data on the numbers of inspected and infected individuals of Foshan City, located in Guangdong Province in the southeast of P.R China, from 1980-2010. Mathematical and numerical analyses of the model are carried out to understand the transmission dynamics of clonorchiasis and explore effective control measures for the local outbreaks of the disease. We find that (i) the transmission of clonorchiasis from cercariae to fish plays a more important role than that from eggs to snails and from fish to humans; (ii) As the cycle of infection-treatment-reinfection continues, it is unlikely that treatment with drugs alone can control and eventually eradicate clonorchiasis. These strongly suggest that a more comprehensive approach needs to include environmental modification in order to break the cercariae-fish transmission cycle, to enhance awareness about the disease, and to improve prevention measures.

A mathematical model for the seasonal transmission of schistosomiasis in the lake and marshland regions of China

Schistosomiasis, a parasitic disease caused by \textit{ Schistosoma Japonicum}, is still one of the most serious parasitic diseases in China and remains endemic in seven provinces, including Hubei, Anhui, Hunan, Jiangsu, Jiangxi, Sichuan, and Yunnan. The monthly data of human schistosomiasis cases in Hubei, Hunan, and Anhui provinces (lake and marshland regions) released by the Chinese Center for Disease Control and Prevention (China CDC) display a periodic pattern with more cases in late summer and early autumn. Based on this observation, we construct a deterministic model with periodic transmission rates to study the seasonal transmission dynamics of schistosomiasis in these lake and marshland regions in China. We calculate the basic reproduction number R0, discuss the dynamical behavior of solutions to the model, and use the model to fit the monthly data of human schistosomiasis cases in Hubei. We also perform some sensitivity analysis of the basic reproduction number R0 in terms of model parameters. Our results indicate that treatment of at-risk population groups, improving sanitation, hygiene education, and snail control are effective measures in controlling human schistosomiasis in these lakes and marshland regions.

PREVENTING THE SPREAD OF SCHISTOSOMIASIS IN GHANA: POSSIBLE OUTCOMES OF INTEGRATED OPTIMAL CONTROL STRATEGIES

The goal of a future free from schistosomiasis in Ghana can be achieved through integrated strategies, targeting simultaneously several stages of the life cycle of the schistosome parasite. In this paper, the transmission of schistosomiasis is modeled as a multi-scale 12-dimensional system of ODEs that includes vector-host and within-host dynamics of infection. An explicit expression for the basic reproduction number [Formula: see text] is obtained via the next generation method, this expression being interpreted in biological terms, as well as in terms of reproductive numbers for each type of interaction involved. After discussing the stability of the disease-free equilibrium and the existence and uniqueness of the endemic equilibrium, the Center Manifold Theory is used to show that for values of [Formula: see text] larger than 1, but close to 1, the unique endemic equilibrium is locally asymptotically stable. A sensitivity analysis indicates that [Formula: see text] is most sensitive to the natural death rate of the vector population, while numerical simulations of optimal control strategies reveal that the most effective strategy for the control and possible elimination of schistosomiasis should combine sanitary measures (access to safe water, improved sanitation and hygiene education), large-scale treatment of infected population and vector control measures (via the use of molluscicides), for a significant amount of time.

Towards interruption of schistosomiasis transmission in sub-Saharan Africa: developing an appropriate environmental surveillance framework to guide and to support 'end game' interventions

Schistosomiasis is a waterborne parasitic disease in sub-Saharan Africa, particularly common in rural populations living in impoverished conditions. With the scale-up of preventive chemotherapy, national campaigns will transition from morbidity- to transmission-focused interventions thus formal investigation of actual or expected declines in environmental transmission is needed as 'end game' scenarios arise. Surprisingly, there are no international or national guidelines to do so in sub-Saharan Africa. Our article therefore provides an introduction to key practicalities and pitfalls in the development of an appropriate environmental surveillance framework. In this context, we discuss how strategies need to be adapted and tailored to the local level to better guide and support future interventions through this transition. As detection of egg-patent infection in people becomes rare, careful sampling of schistosome larvae in freshwater and in aquatic snails with robust species-specific DNA assays will be required. Appropriate metrics, derived from observed prevalence(s) as compared with predetermined thresholds, could each provide a clearer insight into contamination- and exposure-related dynamics. Application could be twofold, first to certify areas currently free from schistosomiasis transmission or second to red-flag recalcitrant locations where extra effort or alternative interventions are needed.

Hydrology and density feedbacks control the ecology of intermediate hosts of schistosomiasis across habitats in seasonal climates

We report about field and theoretical studies on the ecology of the aquatic snails (Bulinus spp. and Biomphalaria pfeifferi) that serve as obligate intermediate hosts in the complex life cycle of the parasites causing human schistosomiasis. Snail abundance fosters disease transmission, and thus the dynamics of snail populations are critically important for schistosomiasis modeling and control. Here, we single out hydrological drivers and density dependence (or lack of it) of ecological growth rates of local snail populations by contrasting novel ecological and environmental data with various models of host demography. Specifically, we study various natural and man-made habitats across Burkina Faso's highly seasonal climatic zones. Demographic models are ranked through formal model comparison and structural risk minimization. The latter allows us to evaluate the suitability of population models while clarifying the relevant covariates that explain empirical observations of snail abundance under the actual climatic forcings experienced by the various field sites. Our results link quantitatively hydrological drivers to distinct population dynamics through specific density feedbacks, and show that statistical methods based on model averaging provide reliable snail abundance projections. The consistency of our ranking results suggests the use of ad hoc models of snail demography depending on habitat type (e.g., natural vs. man-made) and hydrological characteristics (e.g., ephemeral vs. permanent). Implications for risk mapping and space-time allocation of control measures in schistosomiasis-endemic contexts are discussed.

A mathematical modelling framework for linked within-host and between-host dynamics for infections with free-living pathogens in the environment

In this study we develop a mathematical modelling framework for linking the within-host and between-host dynamics of infections with free-living pathogens in the environment. The resulting linked models are sometimes called immuno-epidemiological models. However, there is still no generalised framework for linking the within-host and between-host dynamics of infectious diseases. Furthermore, for infections with free-living pathogens in the environment, there is an additional stumbling block in that there is a gap in knowledge on how environmental factors (through water, air, soil, food, fomites, etc.) alter many aspects of such infections including susceptibility to infective dose, persistence of infection, pathogen shedding and severity of the disease. In this work, we link the two subsystems (within-host and between-host models) by identifying the within-host and between-host variables and parameters associated with the environmental dynamics of the pathogen and then design a feedback of the variables and parameters across the within-host and between-host models using human schistosomiasis as a case study. We study the mathematical properties of the linked model and show that the model is epidemiologically well-posed. Using results from the analysis of the endemic equilibrium expression, the disease reproductive number R0, and numerical simulations of the full model, we adequately account for the reciprocal influence of the linked within-host and between-host models. In particular, we illustrate that for human schistosomiasis, the outcome of infection at the individual level determines if, when and how much the individual host will further transmit the infectious agent into the environment, eventually affecting the spread of the infection in the host population. We expect the conceptual modelling framework developed here to be applicable to many infectious disease with free-living pathogens in the environment beyond the specific disease system of human schistosomiasis considered here.

Field transmission intensity of Schistosoma japonicum measured by basic reproduction ratio from modified Barbour's model

BACKGROUND

Schistosomiasis japonica, caused by infection with Schistosoma japonicum, is still recognized as a major public health problem in the Peoples' Republic of China. Mathematical modelling of schistosomiasis transmission has been undertaken in order to assess and project the effects of various control strategies for elimination of the disease. Seasonal fluctuations in transmission may have the potential to impact on the population dynamics of schistosomiasis, yet no model of S. japonicum has considered such effects. In this paper, we characterize the transmission dynamics of S. japonicum using a modified version of Barbour's model to account for seasonal variation (SV), and investigate the effectiveness of the control strategy adopted in Liaonan village of Xingzi county, Jiangxi Province.

METHODS

We use mathematical tools for stability analysis of periodic systems and derive expressions for the basic reproduction ratio of S. japonicum in humans; we parameterise such expressions with surveillance data to investigate the conditions for persistence or elimination of the disease in the study village. We perform numerical simulations and parametric sensitivity analysis to understand local transmission conditions and compare values of the basic reproductive ratio with and without seasonal fluctuations.

RESULTS

The explicit formula of the basic reproduction ratio for the SV-modified Barbour's model is derived. Results show that the value of the basic reproduction ratio, R0, of Liaonan village, Xingzi county is located between 1.064 and 1.066 (very close to 1), for schistosomiasis transmission during 2006 to 2010, after intensification of control efforts.

CONCLUSIONS

Our modified version of the Barbour model to account for seasonal fluctuations in transmission has the potential to provide better estimations of infection risk than previous models. Ignoring seasonality tends to underestimate R0 values albeit only marginally. In the absence of simultaneous R0 estimations for villages not under control interventions (such villages do not currently exist in China), it is difficult to assess whether control strategies have had a substantial impact on levels of transmission, as the parasite population would still be able to maintain itself at an endemic level, highlighting the difficulties faced by elimination efforts.