Mathematical Biosciences and Engineering

A discrete dynamic model for human epidemics was developed in present study. The model included major parameters as transmission strength and its decline parameters, mean incubation period, hospitalization time, non-hospitalization daily mortality, non-hospitalization daily recovery rate, and hospitalization proportion, etc. Sensitivity analysis of the model indicated the total cumulative cases significantly increased with initial transmission strength, hospitalization time. The total cumulative cases significantly decreased with transmission strengths decline and hospitalization proportion, and linearly decreased with non-hospitalization daily mortality and non-hospitalization daily recovery rate. In a certain range, the total cumulative cases significantly increased with mean incubation period. Sensitivity analysis demonstrated that dynamic change of transmission strength is one of the most important and controllable factors. In addition, reducing the delay for hospitalization is much effective in weakening disease epidemic. Non-hospitalization recovery rate is of importance for enhancing immunity to recover from the disease.

Homeostasis is kind of force that makes living organism to live. In this study, we suggest an integral equation that models homeostasis in living organism. We also showed that various situations can be modeled by homeostasis, and give mathematical interpretation of mechanism of living organism. With our proposed integral equation, one can handle homeostasis quantitatively, and this approach is expected to unveil various hidden properties of living organism.

Moving infected animals and sharing contaminated vehicles are considered as the most potent ways for between-farm disease transmission. The objective of this study is to develop a network-based simulation model to investigate the effects of direct contact, indirect contact, and their combination on a hypothetical foot-and-mouth disease spreading between beef-cattle farms in southwest Kansas, US, and explore the effect of different types of information-sharing networks on preventing the disease spreading. Based on synthetic cattle and truck movement data in southwest Kansas, we build a farm-level contact network with three layers, a cattle movement layer (direct contact), a truck movement layer (indirect contact), and an information-sharing layer. Through scenario analyses, we compare the disease transmission dynamics, the distribution of outbreak epidemic size, and the disease breakout percentage of different contact structures - only direct contact, only indirect contact, and their combination. In addition, we evaluate different types of information sharing methods by comparing the epidemic size and the estimated economic loss. Simulation results show that neither direct contact nor indirect contact individually can result in a massive outbreak of the disease, but their combination plays a significant role. Additionally, we detect different probabilities of disease outbreaks by starting the simulations at different farms; starting at some farms with high capacity increases the probability of disease outbreaks. Three different information sharing-networks are developed and found effective in preventing the disease from spreading and reducing the economic loss. The information-sharing layer based on trading records has the best performance when compared with a random network and a geographic network.

Estimating the changing risk of low crop yield in a changing climate is an important task in various fields of agricultural research. According to the extreme value theory, the probability of extreme events can be approximated using generalized Pareto distributions. In this study, non-stationary generalized Pareto distributions were used to estimate the changing risk of low crop yield. The proposed methods were applied to global yield data for maize, wheat, rice, and soybean collected from 1961 to 2022, as well as local yield data for wheat, rice, and soybean in Japan, from a start date of either 1948 or 1958 and running to 2020. The results illustrated exacerbated trends of low-yield risk in maize crops in Africa; maize, wheat, and rice in Americas; maize and wheat in Western, Central, and Southern Asia; maize and wheat in Europe; and soybean in Japan. Only wheat in Japan showed trends of mitigating the risk of low yields. The proposed models were also validated through simulations. The results showed that the models can generally estimate the changing risks accurately, and the precision depends on the size of the data set. Although there is still room for improvement in the models, the present study demonstrates that it is possible to estimate changes in the risk of low yield using a data-driven approach based on extreme value theory without assumptions about climate and crop physiology.

Bladder cancer is composed of proliferative and immunogenic phenotypes, which ultimately play a significant role in the growth of the tumor. By using ordinary differential equation models, this paper models the impact of high and low immunogenic cell populations on non-muscle invasive bladder cancer when treated with and without the Bacillus Calmette-Guerin vaccine. Furthermore, this paper models the impact that the Bacillus Calmette-Guerin vaccine has on inflammatory cytokines, which inhibit the growth of tumors by stimulating an immune response. We focus primarily on how the immunogenicity phenotype impacts population dynamics in non-muscle invasive bladder cancer.

Absorbing Markov Chains are an important mathematical tool used for different applications in science. On the other hand, cancer and its metastases in children have a significant impact on health due to their degree of lethality. Therefore, the aim of this work is to model the metastatic pathways of the main childhood cancers worldwide. The probabilities of generating metastases, from a primary site to secondary and tertiary sites, were characterized by constructing a directed graph and the associated transition matrix. In addition, the time of absorption and the probabilities of absorption by each absorbing state were calculated.

A novel coronavirus pneumonia initially identified in Wuhan, China and provisionally named 2019-nCoV has surged in the public. In anticipation of substantial burdens on healthcare system following this human-to-human spread, we aim to scrutinise the currently available information and evaluate the burden of healthcare systems during this outbreak in Wuhan. We applied a modified SIR model to project the actual number of infected cases and the specific burdens on isolation wards and intensive care units, given the scenarios of different diagnosis rates as well as different public health intervention efficacy. Our estimates suggest the actual number of infected cases could be much higher than the reported, with estimated 26,701 cases (as of 28th January 2020) assuming 50% diagnosis rate if no public health interventions were implemented. The estimated burdens on healthcare system could be largely reduced if at least 70% efficacy of public health intervention is achieved.

The article presents a novel stochastic mathematical model of mitosis in heterogeneous (multiple-phenotype), age-dependent cell populations. The developed computational techniques involve flexible use of differentiation tree diagrams. The applicability of the model is discussed in the context of the Haeckelian (biogenetic) paradigm. In particular, the article puts forward the conjecture of generality of Haeckels recapitulation law. The conjecture is briefly collated against relevant scientific evidence and elaborated for the specific case of evolving/mutable cell phenotypes as considered by the model. The feasibility, basic regimes and the convenience of the model are tested on examples and experimental data, and the corresponding open source simulation software is described and demonstrated.

Brucellosis imposes substantial impacts on livestock production and public health worldwide. A stochastic, age-structured model incorporating herd demographics was developed describing within- and between-herd transmission of Brucella abortus in dairy cattle herds. The model was fitted to data from a cross-sectional study conducted in Punjab State of India and used to evaluate the effectiveness of control strategies under consideration. Based on model results, stakeholder acceptance and constraints regarding vaccine supply, vaccination of replacement calves in large farms should be prioritised. Test and removal applied at early stages of the control programme where seroprevalence is high would not constitute an effective use of resources. Critically, under current model assumptions, significant numbers of animals removed (culled or not used for breeding) in this strategy would be removed based on false positive results. To achieve sustained reductions in brucellosis, policymakers must commit to maintaining vaccination in the long term, which may eventually reduce frequency of infection in the livestock reservoir to a low enough level for elimination to be a realistic objective. This exercise provided important insights into the control of brucellosis in India, which has the largest cattle population globally, and a general framework for evaluating control strategies in endemic settings.

Livestock morbidity and death from Q-fever have been high, endangering local farmers livelihoods and affecting food security in Ghana. It is essential to understand the transmission dynamics of Q-fever to protect both the health of the animals and the main source of income for the community. A non-linear ordinary differential equation incorporating a vaccinated compartment was formulated and analyzed to gain insights into the spread of Q-fever. Routh Hurwitz criterion and Lyapunov function were used respectively to analyze the local and global stability of the disease-free equilibrium (Q0). We analyzed the behavior of the model compartments and discovered that many key factors significantly influence the persistence or eradication of Q-fever. Increased vaccination rates decrease the susceptible livestock while increasing the vaccinated livestock, potentially reducing the risk of outbreaks and limiting the spread of infections. A higher recovery rate leads to a quicker recovery, which aids in epidemic control by boosting population immunity and reducing the infectious time. The infection level rises when R0 > 1, indicating a typical transcritical bifurcation behavior, but this growth stays steady and does not result in unbounded advancement. Author summaryQ-fever presents considerable health hazards to livestock in Ghanas Tropical Savannah Grassland, adversely affecting local farmers income and food security in regions such as North Tongu municipality. To elucidate the transmission dynamics of the disease and safeguard both animal health and the communitys principal economic resource, we proposed a mathematical model employing non-linear differential equations that incorporate a vaccine compartment. This model enables the evaluation of how parameters such as vaccination and recovery rates influence the transmission of Q-fever in livestock. Our findings indicate that increased vaccination rates may diminish the population of susceptible livestock, hence reducing the possibility of outbreaks. In addition, a rapid recovery rate not only diminishes the duration of infectiousness in livestock but also enhances herd immunity, assisting in the containment of possible epidemics. The proposed model indicates that as R0 exceeds 1, the infection level rises, displaying transcritical bifurcation behavior. However, this rise stabilizes and prevents uncontrolled spread. These findings emphasize the value of vaccination and recovery techniques in controlling and possibly eliminating Q-fever in cattle, which would ultimately help Ghanaian farming communities remain sustainable.

Foot-and-mouth disease (FMD) is a highly contagious disease that spreads among cloven-hoofed animals. Although not deadly, FMD can cause major delays in meat and dairy production. One major concern is that the foot-and-mouth disease virus (FMDV) can persist in African buffalo hosts as natural reservoirs for long periods of time, causing the pathogens to reemerge in susceptible populations. In this paper, we present a novel immuno-epidemiological model of FMD in the African buffalo host populations. Upon infection, the hosts can undergo two phases, namely the acute and the carrier stages. In our model, we divide the infectious population based upon these two stages so that we can dynamically capture the immunological characteristics of both phases of the disease to better understand the carriers role in disease transmission. We first define the within-host viral-immune kinetics dependent epidemiological basic reproduction number[R] 0 and show that it is a threshold condition for the local stability of the disease-free equilibrium and existence of the endemic equilibrium. We also analytically show that the system always displays forward bifurcation with respect to between-host epidemic parameters. Later, by using a sensitivity analysis (SA) approach developed for multi-scale models, we assess the impact of the acute infection and carrier phase immunological parameters on[R] 0. Interestingly, our numerical results show that the within-carrier infected host immune kinetics parameters and the susceptible individual recruitment rates play significant roles in disease persistence, which are consistent with experimental and field studies.

The ongoing pandemic disease COVID-19 has caused worldwide social and financial disruption. As many countries are engaged in designing vaccines, the harmful second and third waves of COVID-19 have already appeared in many countries. To investigate changes in transmission rates and the effect of social distancing in the USA, we formulate a system of ordinary differential equations using data of confirmed cases and deaths in these states: California, Texas, Florida, Georgia, Illinois, Louisiana, Michigan, and Missouri in the USA to be able to investigate changes in transmission rates of the outbreak and effect of social distancing. Our models and the corresponding parameter estimations show social distancing reduces the transmission by 60% to 90%, and thus obeying the movement restriction rules plays a crucial rule to reduce the magnitudes of the outbreak waves. Our analysis shows the current management restrictions do not sufficiently slow the disease propagation.

Different sources of noises endogenous and exogenous to the cancer are involved in its stochastic growth. The aim of this study is to propose the stochastic version of Montijano-Bergues-Bory-Gompertz equation for the unperturbed tumor growth kinetics. The maximum likelihood estimators for the intrinsic tumor growth rate and the growth decelerating factor, and their respective discrete time approximations were analytically calculated. Different simulations of the deterministic and stochastic of this equation were made for different values of their respective parameters. Limit conditions for the average diffusion coefficient and the growth decelerating factor were established. The tumor volume at the infinite was calculated for several values of parameters of the stochastic Montijano-Bergues-Bory-Gompertz equation. Furthermore, descriptive statistic for the maximum likelihood estimators of the intrinsic tumor growth rate was computed for several parameters of this equation. The results evidenced that solid tumors there are for values of the average diffusion coefficient and the growth decelerating factor less than their respective limit values. The transition between avascular and vascular phases of the unperturbed tumor growth kinetics was revealed in the plot of the discrete time approximation for the maximum likelihood estimator of the growth decelerating factor versus the discrete time approximation for the maximum likelihood estimator of the intrinsic tumor growth rate. These results were connected with different findings in the literature. In conclusion, the stochastic Montijano-Bergues-Bory-Gompertz equation may be applied in the experiment to describe the unperturbed tumor growth kinetics, as previously demonstrated for its deterministic version, in order to estimate the parameters of this equation and their connection with processes involved in the growth, progression and metastasis of unperturbed solid tumors. Author summaryIn order to comprehend the unperturbed tumor growth, we investigate a new mathematical model called the stochastic Montijano-Bergues-Bory-Gompertz equation. This study is made based on the ideas of Ferrante et al. and the deterministic version of the Montijano-Bergues-Bory-Gompertz equation. By applying this stochastic equation, we aim to provide valuable insights into how tumors grow and spread throughout the body. We focus on estimating key parameters that are essential for understanding the dynamic processes involved in the unperturbed tumor behavior. Our findings may help researchers to understand the stochastic nature of the unperturbed tumor growth; know the existence of transitions in the unperturbed tumor growth kinetics, probably between avascular and vascular phases; and reveal the values of the model parameters for which the solid tumor is functional, non-functional or does not exist. These aspects may be relevant to propose an individualized anticancer therapy aimed at minimizing the different noise sources that occur during the unperturbed tumor growth. Overall, this study contributes to our ongoing efforts to improve cancer treatment strategies and enhance patient outcomes by fostering a better understanding of tumor biology.

BackgroundThe 2019 new coronavirus, "2019-nCoV", was discovered from Wuhan Viral Pneumonia cases in December 2019, and was named by the World Health Organization on January 12, 2020. In the early stage, people knows little about the 2019-nCoV virus was not clear, and the spread period was encountering Chinas annual spring migration, which made the epidemic spread rapidly from Wuhan to almost all provinces in China. MethodsThis study builds a SEIRD model that considers the movement of people across regions, revealing the effects of three measures on controlling the spread of the epidemic.Based on MATLAB R2017a, computational experiments were performed to simulate the epidemic prevention and control measures. FindingsThe research results show that current prevention and control measures in China are very necessary. This study further validates the concerns of international and domestic experts regarding asymptomatic transmission (E-status). InterpretationThe results of this study are applicable to explore the impact of the implementation of relevant measures on the prevention and control of epidemic spread, and to identify key individuals that may exist during the spread of the epidemic.

Accurate prediction of the temporal and spatial characteristics of COVID-19 infection can provide favorable guidance for epidemic prevention and control. We first introduce individual antibody dynamics into an agent-based model. Antibody dynamics model can well explain the antibody fading effects through time. Based on this model, we further developed an agent-based approach which considers the dynamic behaviors of each individual antibodies. The method can effectively reflect the dynamic interaction between the antibody and the virus in each host body in the overall population. Using this method, we can accurately predict the temporal and spatial characteristics of the epidemic. It can quantitatively calculate the number and spatial distribution of infected persons with different symptoms at different times. At the same time, our model can predict the prevention and control effect of different prevention and control measures. At present, Chinas dynamic zero strategies mainly include large-scale nucleic acid test, isolation of positive infected persons and their close contacts. Our model demonstrates that for a less infectious and more virulent variant, this approach can achieve good preventive effect. The effect of reducing social contacts and quarantining only positive infected persons is relatively weaker on epidemic control. This can explain why Chinas targeted epidemic-control measures had an excellent performance in 2020 and 2021. However, our model also warns that for the highly infectious and less virulent variant, targeted epidemic-control measures can no longer achieve effective control of the epidemic. Therefore, we must choose to quarantine potential infected groups in a wider range (such as the quarantine of secondary close contact and tertiary close contact) or coexist with the virus. Furthermore, our model has a strong traceability ability, which can effectively conduct epidemiological investigation to unearth patient number zero based on the early epidemic distribution. In the end, our model expands the traditional approaches of epidemiological simulation and provides an alternative in epidemic modeling. Major findingsFirst, a method was developed to integrate the characteristics of individual antibody dynamics into epidemic prediction; Second, this model can effectively predict the spatiotemporal characteristics of patients with different symptoms (including asymptomatic patients, mild and severe patients, etc.); Thirdly, this model proves that Chinas dynamic zero strategy which include the quarantine of close contact people is more efficient than just isolating positive cases; Fourth: This model also reflects the limitations of targeted epidemic-control strategies and warns that for the highly infectious and less virulent variant, targeted epidemic-control measures can no longer achieve effective control of the epidemic; Fifth, this model can help epidemiological research and find out patient zero according to the early incidence of the epidemic.

Following the suggestion of L. F. Jaffe [1] we propose a mathematical model of fast calcium induced calcium influx waves (CICI Waves). They can propagate at relatively high speeds (up to 1300 micrometers/s). According to [1], they propagate due to a mechanochemical interaction of actomyosin network with the cell membrane. The local stretching of the membrane caused by actin filaments opens mechanically operated ion channels resulting in the influx of calcium to the cell. Moreover, stretching a cells membrane at one point opens nearby stretch activated calcium channels because the mechanical force is relayed by the actin filaments interconnected by myosin bridges. The number of bridges as well as filament density increases with calcium concentration, causing the contraction of the actomyosin network. Thus, the force acting on the membrane from tangled actin filaments is transmitted ahead of the moving front of the calcium concentration. As a result, the ion channels are opened even before the signal of calcium reaches them. This leads to much larger propagation speed of CICI waves in comparison with calcium induced calcium released (CICR) waves, where the wave is sustained by the diffusion of calcium and autocatalytic release of calcium from the internal stores (e.g. endoplasmic reticula).

Here we analyze Darwinian dynamics of cancer introduced in [1], extended by including a competition matrix, and evaluate (i) when the eco-evolutionary equilibrium is positive and (ii) when the eco-evolutionary equilibrium is asymptotically stable.

The approximation of the age distributions of cancers was carried out using a complex mutational model presented in our work [1]. Datasets from the American National Cancer Institute (SEER program) were used. We approximated the datasets for the age distributions of lung, stomach, colon and breast cancer in women; cancer of the lung, stomach, colon and prostate in men. The average number of mutations (required for cancer formation) averaged over the four types of cancer is 5 mutations per cell in women and in men. The average (over the four types of cancer) mutation rate is estimated as 1.0 {middle dot} 10 -1 mutations per year per cell for women and 3.8 {middle dot} 10 -1 mutations per year per cell for men. This article is a continuation of work [1].

In this paper, we estimate the reproductive number R0 of COVID-19 based on Wallinga and Lipsitch framework [11] and a novel statistical time delay dynamic system. We use the observed data reported in CCDCs paper to estimate distribution of the generation interval of the infection and apply the simulation results from the time delay dynamic system as well as released data from CCDC to fit the growth rate. The conclusion is: Based our Fudan-CCDC model, the growth rate r of COVID-19 is almost in [0.30, 0.32] which is larger than the growth rate 0.1 estimated by CCDC [9], and the reproductive number R0 of COVID-19 is estimated by 3.25 [≤] R0 [≤] 3.4 if we simply use R = 1 + r * Tc with Tc = 7.5, which is bigger than that of SARS. Some evolutions and predictions are listed.

In this paper, mathematical mutational models of the age distribution of cancers are obtained. These are two models - a simple model and a complex model, which takes into account the growth of the cell population and the transmission of mutations to daughter cells. Using the resulting formulas, we approximated real age-specific cancer incidence datasets in women (colon, lung, mammary, stomach) and men (colon, lung, prostate, stomach). We estimated parameters such as the average number of mutations (per cell per unit of time) and number of mutations required for cancer to occur. The number of mutations averaged (over four types of cancer) required for cancer to occur is 5.5 (mutations per cell for women) and 6.25 (mutations per cell for men) for the complex mutational model. As an alternative to mutational models, we also consider the model of delayed carcinogenic event.