Mathematical Modelling of the Co-Infection Dynamics of Typhoid Fever with Plasmodium Vivax and Plasmodium Falciparum with Treatment
Zeleke Amare Workie,
Purnachandra Rao Koya
Issue:
Volume 7, Issue 1, March 2022
Pages:
1-25
Received:
26 December 2021
Accepted:
15 January 2022
Published:
24 January 2022
DOI:
10.11648/j.mma.20220701.11
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Abstract: Malaria and typhoid fever are infectious and communicable diseases. Malaria remains one of the largest killer diseases in the world caused by one or more species of plasmodium parasites. Typhoid fever, also known as enteric fever, is a systemic bacterial infection disease caused by a highly virulent and invasive Salmonella enterica serovar Typhi (S. Typhi). Malaria and typhoid fever co-infection is the most endemic disease and a major public health problem in many tropical developing countries. Both diseases share similar transmission factor and often have the similar symptom. Because of the high prevalence of malaria and typhoid fever in these developing countries, co-infections are common. In addition to true co-infection of malaria and typhoid fever, the major challenges on managing controlling these diseases are false diagnoses due to similar signs and symptoms and false positive results in testing methods. In this study, we have formulated a mathematical model based on a system of non-linear first order ordinary differential equations to study the dynamics of the co-infection dynamics of plasmodium vivax- typhoid fever and plasmodium falciparum -typhoid fever. We have proved the existence of the disease free and endemic equilibrium points of the model and we used a non-linear stability analysis method to prove the local and global stabilities of these equilibrium points. Further, the positivity and boundedness of the solution of the model developed is verified to discover that the model equation is mathematically and epidemiologically well posed. We obtained the basic reproduction number R0 for the co-infection dynamics of plasmodium vivax, plasmodium falciparum and typhoid fever diseases in terms of the three basic reproduction numbers of the separate diseases using the standard data obtained from different sources. The separate diseases disappear from the community whenever the reproduction number R0 is very small and less than unity. On the other hand, the diseases co-exist whenever their reproduction numbers exceed unity (regardless which of the numbers is larger). The sensitivity analysis is discussed in detail to identify the most influential parameters that enhance the co-infection of malaria and typhoid fever disease in a given population. Numerical simulation is also done to illustrate the influence of different parameters on the basic reproduction number.
Abstract: Malaria and typhoid fever are infectious and communicable diseases. Malaria remains one of the largest killer diseases in the world caused by one or more species of plasmodium parasites. Typhoid fever, also known as enteric fever, is a systemic bacterial infection disease caused by a highly virulent and invasive Salmonella enterica serovar Typhi (S...
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Mathematical Study of the Optimal Control of COVID-19 Transmission Amongst the Vaccinated Individuals
Christopher Chukwuma Asogwa,
Stephen Ekwueme Aniaku,
Emmanuel Chukwudi Mbah
Issue:
Volume 7, Issue 1, March 2022
Pages:
26-32
Received:
25 February 2022
Accepted:
22 March 2022
Published:
31 March 2022
DOI:
10.11648/j.mma.20220701.12
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Abstract: Center for Disease control, informs that it takes two weeks after one is fully vaccinated for the body to build protection (immunity) against the virus that causes COVID-19. Moreover, no vaccine is hundred percent effective and that includes the COVID-19 vaccines. This implies that one can still contact and spread the virus for some days after getting vaccinated. In this paper, we formulated a model for COVID-19 transmission dynamics amongst the vaccinated individuals using differential equations. We analyzed all the parameters that are responsible for the disease spread and showed the effect of other social control measures, like the use of face masks in the public, on the spread of the virus. Numerical values of these parameters were derived from some acknowledged literatures, some calculated with the data from other literatures and others judiciously estimated. The disease reproduction number R0 was obtained and found that the disease will only spread if its value exceeds one. Numerical simulation was carried out on the model, using MATLAB to show the dynamics in the different compartments and the effect of these other social control measures on the disease spread among the vaccinated individuals. The result showed that in the absence of other social control measures, almost all the vaccinated persons will be infected and will be able to infect others especially within few days of receiving the COVID-19 vaccine.
Abstract: Center for Disease control, informs that it takes two weeks after one is fully vaccinated for the body to build protection (immunity) against the virus that causes COVID-19. Moreover, no vaccine is hundred percent effective and that includes the COVID-19 vaccines. This implies that one can still contact and spread the virus for some days after gett...
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