scholarly journals A Mathematical Model to Control the Prevalence of a Directly and Indirectly Transmitted Disease

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2562
Author(s):  
Begoña Cantó ◽  
Carmen Coll ◽  
Maria Jesús Pagán ◽  
Joan Poveda ◽  
Elena Sánchez

In this paper, a mathematical model to describe the spread of an infectious disease on a farm is developed. To analyze the evolution of the infection, the direct transmission from infected individuals and the indirect transmission from the bacteria accumulated in the enclosure are considered. A threshold value of population is obtained to assure the extinction of the disease. When this size of population is exceeded, two control procedures to apply at each time are proposed. For each of them, a maximum number of steps without control and reducing the prevalence of disease is obtained. In addition, a criterion to choose between both procedures is established. Finally, the results are numerically simulated for a hypothetical outbreak on a farm.

2018 ◽  
Vol 115 (12) ◽  
pp. E2782-E2790 ◽  
Author(s):  
Alicia N. M. Kraay ◽  
Andrew F. Brouwer ◽  
Nan Lin ◽  
Philip A. Collender ◽  
Justin V. Remais ◽  
...  

Rotavirus is considered a directly transmitted disease due to its high infectivity. Environmental pathways have, therefore, largely been ignored. Rotavirus, however, persists in water sources, and both its surface water concentrations and infection incidence vary with temperature. Here, we examine the potential for waterborne rotavirus transmission. We use a mechanistic model that incorporates both direct and waterborne transmission pathways, coupled with a hydrological model, and we simulate rotavirus transmission between two communities with interconnected water sources. To parameterize temperature dependency, we estimated temperature-dependent decay rates in water through a meta-analysis. Our meta-analysis suggests that rotavirus decay rates are positively associated with temperature (n= 39,P< 0.001). This association is stronger at higher temperatures (over 20 °C), consistent with tropical climate conditions. Our model analysis demonstrates that water could disseminate rotavirus between the two communities for all modeled temperatures. While direct transmission was important for disease amplification within communities, waterborne transmission could also amplify transmission. In standing-water systems, the modeled increase in decay led to decreased disease, with every 1 °C increase in temperature leading to up to a 2.4% decrease in incidence. These effect sizes are consistent with prior meta-analyses, suggesting that environmental transmission through water sources may partially explain the observed associations between temperature and rotavirus incidence. Waterborne rotavirus transmission is likely most important in cooler seasons and in communities that use slow-moving or stagnant water sources. Even when indirect transmission through water cannot sustain outbreaks, it can seed outbreaks that are maintained by high direct transmission rates.


CALCOLO ◽  
1979 ◽  
Vol 16 (4) ◽  
pp. 399-414 ◽  
Author(s):  
G. I. Marchuk ◽  
L. N. Belykh

2000 ◽  
Vol 3 (1) ◽  
pp. 63-77 ◽  
Author(s):  
A. V. Kolobov ◽  
A. A. Polezhaev ◽  
G. I. Solyanik

Metastasis is the outcome of several selective sequential steps where one of the first and necessary steps is the progressive overgrowth or dominance of a small number of metastatic cells in a tumour. In spite of numerous experimental investigations concerning the growth advantage of metastatic cells, the mechanisms resulting in their dominance are still unknown. Metastatic cell overgrowth occurs even if doubling time of the metastatic subpopulation is shorter than that of all others subpopulations in a heterogeneous tumour. In order to examine the hypothesis that under conditions of competition of cell subpopulations for common substrata cell motility of the slow-growing subpopulation can result in its dominance in a heterogeneous tumour, a mathematical model of heterogeneous tumour growth is suggested. The model describes two cell subpopulations which can grow with different rates and transform into the resting state depending on the concentration of the substrate consumed by both subpopulations. The slow-growing subpopulation is assumed to be motile. In numerical simulations it is shown that this subpopulation is able to overgrow the other one. The dominance phenomenon (resulting from random cell motion) depends on the motility coefficient in a threshold manner: in a heterogeneous tumour the slow-dividing motile subpopulation is able to overgrow its non-motile counterparts if its motility coefficient exceeds a certain threshold value. Computations demonstrate independence of the motile cells overgrowth from the initial tumour composition.


2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.


1996 ◽  
Vol 16 (1_suppl) ◽  
pp. 176-178 ◽  
Author(s):  
Gianpaolo Amici ◽  
Giusto Viglino ◽  
Giovambattista Virga ◽  
Carmen Gandolfo ◽  
Giorgio Da Rin ◽  
...  

Poor compliance in peritoneal dialysis (PD) is a significant cause of dropout and morbidity. PD Adequest software, which, through a mathematical model, predicts the effect of the dialysis prescription on the basis of the peritoneal transport, may be used to identify the noncompliant patient. Fifty patients from two dialysis centers, aged 65.9±1.5 years and on PD for 28.6±4.7 months, were studied. A peritoneal equilibration test (PET) was carried out and 24hour urine and dialysate were collected. Total weekly creatinine clearance (CrCI, L/week/1.73 m2) was calculated, as well as the glomerular filtration rate [(GFR), mL/min, mean CrCI and urea nitrogen clearance (UNCI)]. The dialytic schedules used were then introduced into the program and the parameters were recalculated using the software model. Nine patients considered noncompliant from their case histories were used to assess the differences of reference between expected and measured values. The control group was significantly different from the noncompliant group in the percentage of the CrCI and the serum creatinine (sCR) differences. The noncompliance threshold value was calculated from the mean of the lower 95% confidence interval of the compliant group and the higher one of the noncompliant group (-5.3%) for CrCI and vice versa for sCR (+10%), which behaved to the contrary. Reassessing the patients, 11 (22%) were identified as probably noncompliant.


2018 ◽  
Vol 10 (2) ◽  
pp. 151
Author(s):  
Ibrahim Isa Adamu ◽  
Sulaiman Usman

Neisseria gonorrhea infection; a sexually transmitted disease, is caused primarily by a type of germ; a bacteria called neisseria gonorrhea. The infection is a major public health challenge today due to the high incidence of infections accompanied by a dwindling number of treatment options especially in developing and underdeveloped countries. In this paper, we developed a mathematical model for the transmission dynamics of neisseria gonorrhea infection and studied the effect of natural immunity and treatment as the only available control interventions on the spread of the disease in a population. We computed the model disease-free equilibrium and analyzed its local and global stability in a well-defined positively invariant and attracting set Ω using the next-generation matrix plus linearization method and the comparison theorem respectively. The disease-free equilibrium was proved to be both locally and globally asymptotically stable if $R_0<1$ and unstable if $R_0>1$. We conducted sensitivity analysis of parameters in the basic reproduction number $R_0$ using the normalized forward sensitivity index method. Results of the analysis revealed that $R_0$ decreases with increase in treatment and natural immunity rates. The results of the numerical simulations carried out using MATLAB R2012B showed that there is increase in new infections due to increased contact with infected individuals in the susceptible population and that, with increased treatment rate and controlled death due to the disease in the population, neisseria gonorrhea infection would be wiped out within 300 days of the treatment intervention.


2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Chikodili Helen Ugwuishiwu ◽  
D. S. Sarki ◽  
G. C. E. Mbah

In this paper, a system of deterministic model is presented for the dynamical analysis of the interactional consequence of criminals and criminality on victimisation under two distinguishable forms of rehabilitation—the behavioural reformation of criminals and the emotional psychotherapy of victims. A threshold value, R0=maxRK,RV, responsible for the persistence of crime/criminality and victimisation, is obtained and, using it, stability analyses on the model performed. The impact of an effective implementation of the two forms of rehabilitation was found to be substantial on crime and criminality, while an ineffective implementation of same was observed to have a detrimental consequence. The prevention of repeat victimisation was seen to present a more viable option for containing crime than the noncriminalisation of victims. Further, the removal of criminals, either through quitting or death, among others, was also found to have a huge positive impact. Numerical simulations were performed for a variety of mixing criminal scenarios to verify the analytical results obtained.


2020 ◽  
Vol 19 ◽  
pp. 103510
Author(s):  
Anwarud Din ◽  
Kamal Shah ◽  
Aly Seadawy ◽  
Hussam Alrabaiah ◽  
Dumitru Baleanu

1995 ◽  
Vol 03 (03) ◽  
pp. 889-902 ◽  
Author(s):  
URSULA FORYS

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.


2015 ◽  
Vol 76 (13) ◽  
Author(s):  
Nurul Aida Nordin ◽  
Rohanin Ahmad ◽  
Rashidah Ahmad

This paper introduces the usage of three controls as a way to reduce the occurrence of vector-borne disease. The governing equation of the dynamical system used in this paper describes both direct and indirect transmission mode of vector-borne disease. This means that the disease can be transmitted in two different ways. First, it can be transmitted through mosquito bites and the other is through human blood transfusion. The three controls that are incorporated in the dynamical system include a measurement of basic practice for blood donation procedure, self-prevention effort and vector control strategy by health authority. The optimality system of the three controls is characterized using optimal control theory and the existence and uniqueness of the optimal control are established. Then, the effect of the incorporation of the three controls is investigated by performing numerical simulation. 


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