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In this paper, Gompertz type models are proposed to understand the temporal tumor volume behavior of prostate cancer when a periodical treatment is provided. Existence, uniqueness, and stability of periodic solutions are established. The models are used to fit the data and to forecast the tumor growth behavior based on prostate cancer treatments using capsaicin and docetaxel anticancer drugs. Numerical simulations show that the combination of capsaicin and docetaxel is the most efficient treatment of prostate cancer.

Abstract Background The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. Methods By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. Results We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. Conclusions We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

Studies have shown that sexual transmission, both heterosexually and homosexually, is one of the main ways of HBV infection. Based on this fact, we propose a mathematical model to study the sexual transmission of HBV among adults by classifying adults into men and women and considering both same-sex and opposite-sex transmissions of HBV in adults. Firstly, we calculate the basic reproduction number $ R_{0} $ and the disease-free equilibrium point $ E_{0} $ . Secondly, by analysing the sensitivity of $ R_{0} $ in terms of model parameters, we find that the infection rate among people who have same-sex partners, the frequency of homosexual contact and the immunity rate of adults play important roles in the transmission of HBV. Moreover, we use our model to fit the reported data in China and forecast the trend of hepatitis B. Our results demonstrate that popularizing the basic knowledge of HBV among residents, advocating healthy and reasonable sexual life style, reducing the number of adult carriers, and increasing the immunization rate of adults are effective measures to prevent and control hepatitis B.

Arid ecosystems are known to be sensitive to climate change. The Jornada Basin in the USA, as one representative of arid land, has suffered from land degradation in recent decades. In order to disentangle the climate–vegetation feedback, we analyzed the vegetation dynamics under the effects of climate change via a mathematical model based on the reaction–diffusion mechanism. Using this model, we conducted a sensitive analysis of climate factors and concluded that the ecosystem might experience a catastrophic shift with the climatic deterioration. We considered the non-local interaction term to explain the competition among plants. Additionally, the PLR (power law range) metric was used to quantify the extent of the degradation and to compare the results of the vegetation patterns from the remote sensing data and the simulations. From the results, this model could simulate the trends of land degradation in this area. We found that the land degradation could be mainly attributed to climate changes in recent years. This approach suggests that vegetation patterns can provide hints as to whether the ecosystem is approaching desertification. These results can help with mapping vulnerable arid areas around the world through model simulation and satellite images.

In this paper both deterministic and stochastic models are developed to explore the roles that antibiotic exposure and environmental contamination play in the spread of antibiotic-resistant bacteria, such as methicillin-resistant Staphylococcus aureus (MRSA), in hospitals. Uncolonized patients without or with antibiotic exposure, colonized patients without or with antibiotic exposure, uncontaminated or contaminated healthcare workers, and free-living bacteria are included in the models. Under the assumption that there is no admission of the colonized patients, the basic reproduction number $R_0$ is calculated. It is shown that when $R_0 < 1$, the infection-free equilibrium is globally asymptotically stable; when $R_0>1$, the infection is uniformly persistent. Numerical simulations and sensitivity analysis show that environmental cleaning is a critical intervention, and hospitals should use antibiotics properly and as little as possible. The rapid and efficient treatment of colonized patients, especially those with antibiotic exposure, is key in controlling MRSA infections. Screening and isolating colonized patients at admission, and improving compliance with hand hygiene are also important control strategies.

A deterministic mathematical model with periodic antibiotic prescribing rate is constructed to study the seasonality of Methicillin-resistant Staphylococcus aureus (MRSA) infections taking antibiotic exposure and environmental contamination into consideration. The basic reproduction number $ R_0 $ for the periodic model is calculated under the assumption that there are only uncolonized patients with antibiotic exposure at admission. Sensitivity analysis of $ R_0 $ with respect to some essential parameters is performed. It is shown that the infection would go to extinction if the basic reproduction number is less than unity and would persist if it is greater than unity. Numerical simulations indicate that environmental cleaning is the most important intervention to control the infection, which emphasizes the effect of environmental contamination in MRSA infections. It is also important to highlight the importance of effective antimicrobial stewardship programmes, increase active screening at admission and subsequent isolation of positive cases, and treat patients quickly and efficiently.

Rabies is a serious concern to public health and wildlife management worldwide. Over the last three decades, various mathematical models have been proposed to study the transmission dynamics of rabies. In this paper we provide a mini-review on some reaction-diffusion models describing the spatial spread of rabies among animals. More specifically, we introduce the susceptible-exposed-infectious models for the spatial transmission of rabies among foxes (Murray et al., 1986), the spatiotemporal epidemic model for rabies among raccoons (Neilan and Lenhart, 2011), the diffusive rabies model for skunk and bat interactions (Bonchering et al., 2012), and the reaction-diffusion model for rabies among dogs (Zhang et al., 2012). Numerical simulations on the spatiotemporal dynamics of these models from these papers are presented.

Abstract In this work, we investigate the role of environmental contamination on the clinical epidemiology of antibiotic-resistant bacteria in hospitals. Methicillin-resistant Staphylococcus aureus (MRSA) is a bacterium that causes infections in different parts of the body. It is tougher to treat than most strains of Staphylococcus aureus or staph, because it is resistant to some commonly used antibiotics. Both deterministic and stochastic models are constructed to describe the transmission characteristics of MRSA in hospital setting. The deterministic epidemic model includes five compartments: colonized and uncolonized patients, contaminated and uncontaminated health care workers (HCWs), and bacterial load in environment. The basic reproduction number R 0 is calculated, and its numerical and sensitivity analysis has been performed to study the asymptotic behavior of the model, and to help identify factors responsible for observed patterns of infections. A stochastic epidemic model with stochastic simulations is also presented to supply a comprehensive analysis of its behavior. Data collected from Beijing Tongren Hospital will be used in the numerical simulations of our model. The results can be used to provide theoretical guidance for designing efficient control measures, such as increasing the hand hygiene compliance of HCWs and disinfection rate of environment, and decreasing the transmission rate between environment and patients and HCWs.

Zika virus (ZIKV) disease outbreaks occurred in French Polynesia in 2013–2014 and in Brazil and Colombia in 2015–2016, respectively. Using our recently developed ZIKV disease model, we simulated the reported ZIKV infection cases from French Polynesia, Colombia and the State of Bahia of Brazil. Moreover, we estimated that the infection attack rates were 78.0% (95% confidence interval (CI): 63.5–86.3%) in French Polynesia which closely matches a previous serological study; 20.8% (95% CI: 1.1–50.0%) in Colombia which suggests that the attack rate was most likely less than 50%; and 32.4% (95% CI: 2.5–94.2%) in the State of Bahia in Brazil which suggests that the attack rate is unidentifiable with monthly data in Bahia. Furthermore, we found that the association of precipitation and ZIKV outbreak was more evident in Colombia than the other two places. These results are helpful for us to understand the possible evolution, to control the on-going outbreaks, to prevent the potential geographic spread, and to study the ecological and epidemiological characteristics of ZIKV.

This paper deals with a plant–pollinator model with diffusion and time delay effects. By considering the distribution of eigenvalues of the corresponding linearized equation, we first study stability of the positive constant steady-state and existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated. We then derive an explicit formula for determining the direction and stability of the Hopf bifurcation by applying the normal form theory and the centre manifold reduction for partial functional differential equations. Finally, we present an example and numerical simulations to illustrate the obtained theoretical results.

In order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans, in which each province is regarded as a patch. In each patch the submodel consists of susceptible, exposed, infectious, and vaccinated subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The existence of the disease-free equilibrium is discussed, the basic reproduction number is calculated, and the effect of moving rates of dogs between patches on the basic reproduction number is studied. To investigate the rabies virus clades lineages, the two-patch submodel is used to simulate the human rabies data from Guizhou and Guangxi, Hebei and Fujian, and Sichuan and Shaanxi, respectively. It is found that the basic reproduction number of the two-patch model could be larger than one even if the isolated basic reproduction number of each patch is less than one. This indicates that the immigration of dogs may make the disease endemic even if the disease dies out in each isolated patch when there is no immigration. In order to reduce and prevent geographical spread of rabies in China, our results suggest that the management of dog markets and trades needs to be regulated, and transportation of dogs has to be better monitored and under constant surveillance.

Rift Valley fever (RVF) is an important mosquito-borne viral zoonosis in Africa and the Middle East that causes human deaths and significant economic losses due to huge incidences of death and abortion among infected livestock. Outbreaks of RVF are sporadic and associated with both seasonal and socioeconomic effects. Here we propose an almost periodic three-patch model to investigate the transmission dynamics of RVF virus (RVFV) among ruminants with spatial movements. Our findings indicate that, in Northeastern Africa, human activities, including those associated with the Eid al Adha feast, along with a combination of climatic factors such as rainfall level and hydrological variations, contribute to the transmission and dispersal of the disease pathogen. Moreover, sporadic outbreaks may occur when the two events occur together: 1) abundant livestock are recruited into areas at risk from RVF due to the demand for the religious festival and 2) abundant numbers of mosquitoes emerge. These two factors have been shown to have impacts on the severity of RVF outbreaks. Our numerical results present the transmission dynamics of the disease pathogen over both short and long periods of time, particularly during the festival time. Further, we investigate the impact on patterns of disease outbreaks in each patch brought by festival- and seasonal-driven factors, such as the number of livestock imported daily, the animal transportation speed from patch to patch, and the death rate induced by ceremonial sacrifices. In addition, our simulations show that when the time for festival preparation starts earlier than usual, the risk of massive disease outbreaks rises, particularly in patch 3 (the place where the religious ceremony will be held).

Methicillin-resistant Staphylococcus aureus (MRSA) is endemic in many hospital settings, including nursing homes. It is an important nosocomial pathogen that causes mortality and an economic burden to patients, hospitals, and the community. The epidemiology of the bacteria in nursing homes is both hospital- and community-like. Transmission occurs via hands of health care workers (HCWs) and direct contacts among residents during social activities. In this work, mathematical modeling in both deterministic and stochastic frameworks is used to study dissemination of MRSA among residents and HCWs, persistence and prevalence of MRSA in a population, and possible means of controlling the spread of this pathogen in nursing homes. The model predicts that: (i) without strict screening and decolonization of colonized individuals at admission, MRSA may persist; (ii) decolonization of colonized residents, improving hand hygiene in both residents and HCWs, reducing the duration of contamination of HCWs, and decreasing the resident∶staff ratio are possible control strategies; (iii) the mean time that a resident remains susceptible since admission may be prolonged by screening and decolonization treatment in colonized individuals; (iv) in the stochastic framework, the total number of colonized residents varies and may increase when the admission of colonized residents, the duration of colonization, the average number of contacts among residents, or the average number of contacts that each resident requires from HCWs increases; (v) an introduction of a colonized individual into an MRSA-free nursing home has a much higher probability of leading to a major outbreak taking off than an introduction of a contaminated HCW.

Multidrug-resistant organisms (MDRO) continue to spread in hospitals globally, but the population-level impact of recommended preventive strategies and the relative benefit of individual strategies targeting all MDRO in the hospital setting are unclear. To explore the dynamics of MDRO transmission in the hospital, we develop a model extending data from clinical individual-level studies to quantify the impact of hand hygiene, contact precautions, reducing antimicrobial exposure and screening surveillance cultures in decreasing the prevalence of MDRO colonization and infection. The effect of an ongoing increase in the influx of patients colonized with MDRO into the hospital setting is also quantified. We find that most recommended strategies have substantial effect in decreasing the prevalence of MDRO over time. However, screening for asymptomatic MDRO colonization among patients who are not receiving antimicrobials is of minimal value in reducing the spread of MDRO.

Human rabies is one of the major public-health problems in China. The number of human rabies cases has increased dramatically in the last 15 years, partially due to the poor understanding of the transmission dynamics of rabies and the lack of effective control measures of the disease. In this article, in order to explore effective control and prevention measures we propose a deterministic model to study the transmission dynamics of rabies in China. The model consists of susceptible, exposed, infectious, and recovered subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The model simulations agree with the human rabies data reported by the Chinese Ministry of Health. We estimate that the basic reproduction number R₀ = 2 for the rabies transmission in China and predict that the number of the human rabies is decreasing but may reach another peak around 2030. We also perform some sensitivity analysis of R₀ in terms of the model parameters and compare the effects of culling and immunization of dogs. Our study demonstrates that (i) reducing dog birth rate and increasing dog immunization coverage rate are the most effective methods for controlling rabies in China; and (ii) large scale culling of susceptible dogs can be replaced by immunization of them.

The emergence and ongoing spread of antimicrobial-resistant bacteria is a major public health threat. Infections caused by antimicrobial-resistant bacteria are associated with substantially higher rates of morbidity and mortality compared to infections caused by antimicrobial-susceptible bacteria. The emergence and spread of these bacteria is complex and requires incorporating numerous interrelated factors which clinical studies cannot adequately address.A model is created which incorporates several key factors contributing to the emergence and spread of resistant bacteria including the effects of the immune system, acquisition of resistance genes and antimicrobial exposure. The model identifies key strategies which would limit the emergence of antimicrobial-resistant bacterial strains. Specifically, the simulations show that early initiation of antimicrobial therapy and combination therapy with two antibiotics prevents the emergence of resistant bacteria, whereas shorter courses of therapy and sequential administration of antibiotics promote the emergence of resistant strains.The principal findings suggest that (i) shorter lengths of antibiotic therapy and early interruption of antibiotic therapy provide an advantage for the resistant strains, (ii) combination therapy with two antibiotics prevents the emergence of resistance strains in contrast to sequential antibiotic therapy, and (iii) early initiation of antibiotics is among the most important factors preventing the emergence of resistant strains. These findings provide new insights into strategies aimed at optimizing the administration of antimicrobials for the treatment of infections and the prevention of the emergence of antimicrobial resistance.

In this paper, we study a predator--prey mite model of Leslie type with generalized Holling IV functional response. The model is shown to have very rich bifurcation dynamics, including subcritical and supercritical Hopf bifurcations, degenerate Hopf bifurcation, focustype and cusp-type degenerate Bogdanov--Takens bifurcations of codimension 3, originating from a nilpotent focus or cusp of codimension 3 that acts as the organizing center for the bifurcation set. Coexistence of multiple steady states, multiple limit cycles, and homoclinic cycles is also found. Interestingly, the coexistence of two limit cycles is guaranteed by investigating generalized Hopf bifurcation and degenerate homoclinic bifurcation, and we also find that two generalized Hopf bifurcation points are connected by a saddle-node bifurcation curve of limit cycles, which indicates the existence of global regime for two limit cycles. Our work extends some results in the literature. [ABSTRACT FROM AUTHOR]