Mathematical analysis of complex SIR model with coinfection and density dependence

Ghersheen, Samia; Kozlov, Vladimir; Tkachev, Vladimir G.; Wennergren, Uno

doi:10.1002/cmm4.1042

Cited by 8 publications

(13 citation statements)

References 21 publications

(53 reference statements)

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“…Sincez T w ≥ 0 and z Tw ≥ 0, we conclude that actually, the latter two inequalities are equalities; therefore,z T w = z Tw = 0. (22) holds true for , and the lemma is proved.…”

Section: Proposition 1 Y Solves the Lcp(−a Q) If And Only If Y Is Amentioning

confidence: 79%

“…Then, (20) and (21) obviously hold for . In order to verify (22), we note that z T w =z Tw = 0, where w = q + Mz and…”

Section: Proposition 1 Y Solves the Lcp(−a Q) If And Only If Y Is Amentioning

confidence: 99%

“…We also carried out global stability analysis using a generalized Volterra function for each stable point to study the complete dynamics of disease. The model was formulated, and some of our results were recently announced in Ghersheen et al We analyse the model with the possibility of transmission of two strains simultaneously. However, contrary to Gao et al, to diminish the complexity of model and to study the global behaviour of the system, the reduction of the system is needed to some sense.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

Ghersheen

Kozlov

Tkachev

et al. 2019

Math Methods in App Sciences

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Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection are important in this case. We formulated an susceptible infected recovered (SIR) model that describes the coinfection of the two viral strains in a single host population with an addition of limited growth of susceptible in terms of carrying capacity. The model describes five classes of a population: susceptible, infected by first virus, infected by second virus, infected by both viruses, and completely immune class. We proved that for any set of parameter values, there exists a globally stable equilibrium point. This guarantees that the disease always persists in the population with a deeper connection between the intensity of infection and carrying capacity of population. Increase in resources in terms of carrying capacity promotes the risk of infection, which may lead to destabilization of the population.

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“…Sincez T w ≥ 0 and z Tw ≥ 0, we conclude that actually, the latter two inequalities are equalities; therefore,z T w = z Tw = 0. (22) holds true for , and the lemma is proved.…”

Section: Proposition 1 Y Solves the Lcp(−a Q) If And Only If Y Is Amentioning

confidence: 79%

“…Then, (20) and (21) obviously hold for . In order to verify (22), we note that z T w =z Tw = 0, where w = q + Mz and…”

Section: Proposition 1 Y Solves the Lcp(−a Q) If And Only If Y Is Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

Ghersheen

Kozlov

Tkachev

et al. 2019

Math Methods in App Sciences

Self Cite

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show abstract

“…The conventional compartmental models in epidemiology like SIR, SEIR initiate with the size and density of the population [60,61,62,63,64]. But after the outbreak of COVID-19, questions are being raised by the epidemiologists and the public health experts whether the population size as well as its density along with urbanization matter or not.…”

Section: Methodsmentioning

confidence: 99%

4P Model for Dynamic Prediction of Covid-19 with statistical and machine learning approach: Social Dynamics, Government Roles and Pathogen Behavior on Bangladesh Perspective

Hasan

Ahmmed

Chowdhury

et al. 2020

Preprint

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Introduction: Around the world, scientists are racing hard to understand how Covid-19 epidemic is spreading and growing, thus trying to find ways to prevent it before medications come to pass. Many different models have been proposed so far correlating different factors. Some of them are too localized to indicate a general trend of the pandemic while some others have established transient correlations only.Methods: Hence, in this study, a 4P model has been proposed based on four probabilities (4P) which has been found to be true for all affected countries taking Bangladesh as a case. Efficiency scores have been estimated from survey analysis not only for governing authorities on managing the situation (P(G)) but also for the compliance of the citizens ((P(P)). Since the immune responses of all the people are not uniform to a specific pathogen, the probability of a person getting infected ((P(I)) after being exposed has also been estimated. And the vital one is the probability of Test Positivity ((P(T)) which is a strong indicator of how effectively the infected people are diagnosed and isolated from the rest of the group that affects the rate of growth.Results and Conclusion: All the four parameters have been fitted in a non-linear exponential model that partly updates itself periodically with everyday facts. Along with the model, all the four probabilistic parameters are engaged to train a recurrent neural network using Long-Short Term Memory neural network and the followed trial confirmed a ruling functionality of the 4Ps.

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“…Similarly, Tang et al [32] proposed a mathematical model of dual-infection of dengue and Zika virus. Again, Ghersheen et al [33,34] proposed SIR models to describe dual infection in the same area. Also, Khan et al [35] proposed a co-infection model that includes the Atangana-Baleanu fractional derivative, which is a combination of the human immunodeficiency virus (HIV) and tuberculosis (TB).…”

Section: Introductionmentioning

confidence: 99%

A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

2021

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In this work, we propose a new dynamic mathematical model framework governed by a system of differential equations that integrates both COVID-19 and cholera outbreaks. The estimations of the model parameters are based on the outbreaks of COVID-19 and cholera in Yemen from January 1, 2020 to May 30, 2020. Moreover, we present an optimal control model for minimizing both the number of infected people and the cost associated with each control. Four preventive measures are to be taken to control the outbreaks: social distancing, lockdown, the number of tests, and the number of chlorine water tablets (CWTs). Under the current conditions and resources available in Yemen, various policies are simulated to evaluate the optimal policy. The results obtained confirm that the policy of providing resources for the distribution of CWTs, providing sufficient resources for testing with an average social distancing, and quarantining of infected individuals has significant effects on flattening the epidemic curves.

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Mathematical analysis of complex SIR model with coinfection and density dependence

Cited by 8 publications

References 21 publications

Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

4P Model for Dynamic Prediction of Covid-19 with statistical and machine learning approach: Social Dynamics, Government Roles and Pathogen Behavior on Bangladesh Perspective

A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

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